An Overview on Wavelets in Source Coding, Communications, and Networks
---
paper_title: 3D WAVELET-BASED COMPRESSION OF HYPERSPECTRAL IMAGERY

paper_content:

Since hyperspectral imagery is generated by collecting hundreds of contiguous bands, uncompressed hyperspectral imagery can be very large, with a single image potentially occupying hundreds of megabytes. For instance, the Airborne Visible InfraRed Imaging Spectrometer (AVIRIS) sensor is capable of collecting several gigabytes of data per day. Compression is thus necessary to facilitate both the storage and the transmission of hyperspectral images. Since hyperspectral imagery is typically collected on remote acquisition platforms, such as satellites, the transmission of such data to central, often terrestrial, reception sites can be a critical issue. Thus, compression schemes oriented to the task of remote transmission are becoming increasingly of interest in hyperspectral applications. Although there have been a number of approaches to the compression of hyperspectral imagery proposed in recent years—prominent techniques would include vector quantization (VQ) (e.g., [1, 2]) or principal component analysis (PCA) (e.g., [3, 4]) applied to spectral pixel vectors, as well as 3D extensions of common image-compression methods such as the discrete cosine transform (DCT) (e.g., [5])—most of the approaches as proposed are not particularly well-suited to the image-transmission task. That is, in many applications involving the communication of images, progressive transmission is desired in that successive reconstructions of the image are possible. In such a scenario, the receiver can produce a low-quality representation of the image after having received only a small portion of the transmitted bitstream, and this “preview” representation can be successively refined in
---
paper_title: Shape-Adaptive Embedded Coding of Ocean-Temperature Imagery

paper_content:

An embedded wavelet-based coder for the shape-adaptive coding of ocean-temperature data is described. The proposed coder, 3D binary set splitting with k-A trees (3D-BISK), is based upon the popular bitplane-coding paradigm and is specifically designed for shape-adaptive coding. Other similar coding methods use octree-based set partitioning; however, 3D-BISK employs a simpler set decomposition based on k-A trees which makes it more flexible when considering shape-adaptive coding. The performance of 3D-BISK is compared to prominent shape-adaptive coders and superior performance is demonstrated for a variety of ocean-temperature datasets.
---
paper_title: Progressive 3-D coding of hyperspectral images based on JPEG 2000

paper_content:

In this letter we propose a new technique for progressive coding of hyperspectral data. Specifically, we employ a hybrid three-dimensional wavelet transform for spectral and spatial decorrelation in the framework of Part 2 of the JPEG 2000 standard. Both onboard and on-the-ground compression are addressed. The resulting technique is compliant with the JPEG 2000 family of standards and provides competitive performance with respect to state-of-the-art techniques.
---
paper_title: Wavelet Filter Evaluation for Image Compression

paper_content:

Choice of filter bank in wavelet compression is a critical issue that affects image quality as well as system design. Although regularity is sometimes used in filter evaluation, its success at predicting compression performance is only partial. A more reliable evaluation can be obtained by considering an L-level synthesis/analysis system as a single-input, single-output, linear shift-variant system with a response that varies according to the input location module (2(L),2(L)). By characterizing a filter bank according to its impulse response and step response in addition to regularity, we obtain reliable and relevant (for image coding) filter evaluation metrics. Using this approach, we have evaluated all possible reasonably short (less than 36 taps in the synthesis/analysis pair) minimum-order biorthogonal wavelet filter banks. Of this group of over 4300 candidate filter banks, we have selected and present here the filters best suited to image compression. While some of these filters have been published previously, others are new and have properties that make them attractive in system design.
---
paper_title: Best wavelet packet bases in a rate-distortion sense

paper_content:

A fast rate-distortion (R-D) optimal scheme for coding adaptive trees whose individual nodes spawn descendents forming a disjoint and complete basis cover for the space spanned by their parent nodes is presented. The scheme guarantees operation on the convex hull of the operational R-D curve and uses a fast dynamic programing pruning algorithm to markedly reduce computational complexity. Applications for this coding technique include R. Coefman et al.'s (Yale Univ., 1990) generalized multiresolution wavelet packet decomposition, iterative subband coders, and quadtree structures. Applications to image processing involving wavelet packets as well as discrete cosine transform (DCT) quadtrees are presented. >
---
paper_title: Best Anisotropic 3-D Wavelet Decomposition in a Rate-Distortion Sense

paper_content:

Hyperspectral sensors have been of a growing interest over the past few decades for Earth observation as well as deep space exploration. However, the amount of data provided by such sensors requires an efficient compression system which is yet to be defined. It is hoped that the particular statistical properties of such images can be used to obtain very efficient compression algorithms. This paper proposes a method to find the most suitable wavelet decomposition for hyperspectral images and introduces the possibility of non isotropic decomposition. The decomposition is made by choosing the decomposition that provides an optimal rate-distortion trade-off. The obtained decomposition exhibits better performances in terms of rate-distortion curves compared to isotropic decomposition for high bitrates as well as for low bitrates.
---
paper_title: Sub-band coding of digital images using symmetric short kernel filters and arithmetic coding techniques

paper_content:

A simple and efficient method of subband coding of digital images is reported. First, a technique for designing symmetric short tap filters is presented, and it is shown that such filters can be easily implemented by using simple arithmetic operations (e.g. addition and multiplication). By applying the above filters, the input image is decomposed into four bands, which are then coded by using arithmetic coding in combination with discrete PCM coding of the lowest band and PCM coding of higher bands. Simulation results demonstrate that by using the method mentioned above good quality pictures can be obtained in the range of 0.7 to 0.8 bits/pel. >
---
paper_title: Lossless image compression using integer to integer wavelet transforms

paper_content:

Invertible wavelet transforms that map integers to integers are important for lossless representations. We present an approach to build integer to integer wavelet transforms based upon the idea of factoring wavelet transforms into lifting steps. This allows the construction of an integer version of every wavelet transform. We demonstrate the use of these transforms in lossless image compression.
---
paper_title: Wavelet transforms that map integers to integers

paper_content:

Abstract Invertible wavelet transforms that map integers to integers have important applications in lossless coding. In this paper we present two approaches to build integer to integer wavelet transforms. The first approach is to adapt the precoder of Laroiaet al.,which is used in information transmission; we combine it with expansion factors for the high and low pass band in subband filtering. The second approach builds upon the idea of factoring wavelet transforms into so-called lifting steps. This allows the construction of an integer version of every wavelet transform. Finally, we use these approaches in a lossless image coder and compare the results to those given in the literature.
---
paper_title: Image coding using wavelet transform

paper_content:

A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. This method involves two steps. First, a wavelet transform used in order to obtain a set of biorthogonal subclasses of images: the original image is decomposed at different scales using a pyramidal algorithm architecture. The decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image. Second, according to Shannon's rate distortion theory, the wavelet coefficients are vector quantized using a multiresolution codebook. To encode the wavelet coefficients, a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed. In order to allow the receiver to recognize a picture as quickly as possible at minimum cost, a progressive transmission scheme is presented. It is shown that the wavelet transform is particularly well adapted to progressive transmission. >
---
paper_title: A New Fast and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees

paper_content:

Embedded zerotree wavelet (EZW) coding, introduced by Shapiro (see IEEE Trans. Signal Processing, vol.41, no.12, p.3445, 1993), is a very effective and computationally simple technique for image compression. We offer an alternative explanation of the principles of its operation, so that the reasons for its excellent performance can be better understood. These principles are partial ordering by magnitude with a set partitioning sorting algorithm, ordered bit plane transmission, and exploitation of self-similarity across different scales of an image wavelet transform. Moreover, we present a new and different implementation based on set partitioning in hierarchical trees (SPIHT), which provides even better performance than our previously reported extension of EZW that surpassed the performance of the original EZW. The image coding results, calculated from actual file sizes and images reconstructed by the decoding algorithm, are either comparable to or surpass previous results obtained through much more sophisticated and computationally complex methods. In addition, the new coding and decoding procedures are extremely fast, and they can be made even faster, with only small loss in performance, by omitting entropy coding of the bit stream by the arithmetic code.
---
paper_title: The JPEG 2000 still image compression standard

paper_content:

One of the aims of the standardization committee has been the development of Part I, which could be used on a royalty- and fee-free basis. This is important for the standard to become widely accepted. The standardization process, which is coordinated by the JTCI/SC29/WG1 of the ISO/IEC has already produced the international standard (IS) for Part I. In this article the structure of Part I of the JPFG 2000 standard is presented and performance comparisons with established standards are reported. This article is intended to serve as a tutorial for the JPEG 2000 standard. The main application areas and their requirements are given. The architecture of the standard follows with the description of the tiling, multicomponent transformations, wavelet transforms, quantization and entropy coding. Some of the most significant features of the standard are presented, such as region-of-interest coding, scalability, visual weighting, error resilience and file format aspects. Finally, some comparative results are reported and the future parts of the standard are discussed.
---
paper_title: Compression of volumetric medical data based on cube splitting

paper_content:

The increasing use of three-dimensional imaging modalities triggers the need for efficient techniques to transport and store the related volumetric data. Desired properties like quality and resolution scalability, region-of-interest coding, lossy-to-lossless coding and excellent rate-distortion characteristics for as well low as high bit-rates are inherently supported by wavelet-based compression tools. In this paper a new 3D wavelet-based compression engine is proposed and compared against a classical 3D JPEG-based coder and a state-of-the-art 3D SPIHT coder for different medical imaging modalities. Furthermore, we evaluate the performance of a selected set of lossless integer lifting kernels. We demonstrate that the performance of the proposed coder is superior for lossless coding, and competitive with 3D SPIHT at lower bit-rates.
---
paper_title: Coding of ocean-temperature volumes using binary set splitting with k-d trees

paper_content:

An embedded wavelet-based coder for the shape-adaptive coding of ocean-temperature data is described. The proposed coder, 3D binary set splitting with k-d trees (3D-BISK), is based upon the popular bitplane-coding paradigm and is specifically designed for shape-adaptive coding. Other similar coding methods use octree-based set partitioning; however, 3D-BISK employs a simpler set decomposition based on k-d trees which makes it more flexible when considering shape-adaptive coding. The performance of 3D-BISK is compared to prominent shape-adaptive coders and superior performance is demonstrated for a variety of ocean-temperature datasets.
---
paper_title: Optimal 3-D Coefficient Tree Structure for 3-D Wavelet Video Coding

paper_content:

An optimal three-dimensional (3-D) coefficient tree structure for 3-D zerotree wavelet video coding is considered in this paper. The 3-D zerotree wavelet video coding is inspired by the success of the two-dimensional (2-D) zerotree wavelet image coding. Existing 3-D zerotree wavelet video codecs use the either symmetric or symmetric-alike 3-D tree structure, which is a straightforward extension of the symmetric 2-D tree structure in the zerotree wavelet image coding. In this paper, we show that the 3-D zerotree coding does not need to be applied symmetrically along all the directions, as the 2-D zerotree image coding does. We find that an asymmetric 3-D tree structure working with a more flexible asymmetric 3-D wavelet transform can produce a higher compression ratio than traditional symmetric approaches. The new 3-D tree structure can be used to improve the rate-distortion performance of many existing 3-D zerotree wavelet video codecs without sacrificing other features such as scalability and computational efficiency. The new tree structure is applied to the 3-D set partitioning in hierarchical trees method and receives convincing peak signal-to-noise ratio improvements in experiments.
---
paper_title: An overview of the JPEG2000 still image compression standard

paper_content:

In 1996, the JPEGcommittee began to investigate possibilities for a new still image compression standard to serve current and future applications. This initiative, which was named JPEG2000, has resulted in a comprehensive standard (ISO 154447ITU-T Recommendation T.800) that is being issued in six parts. Part 1, in the same vein as the JPEG baseline system, is aimed at minimal complexity and maximal interchange and was issued as an International Standard at the end of 2000. Parts 2–6 define extensions to both the compression technology and the file format and are currently in various stages of development. In this paper, a technical description of Part 1 of the JPEG2000 standard is provided, and the rationale behind the selected technologies is explained. Although the JPEG2000 standard only specifies the decoder and the codesteam syntax, the discussion will span both encoder and decoder issues to provide a better understanding of the standard in various applications. r 2002 Elsevier Science B.V. All rights reserved.
---
paper_title: Low bit-rate scalable video coding with 3-D set partitioning in hierarchical trees (3-D SPIHT)

paper_content:

We propose a low bit-rate embedded video coding scheme that utilizes a 3-D extension of the set partitioning in hierarchical trees (SPIHT) algorithm which has proved so successful in still image coding. Three-dimensional spatio-temporal orientation trees coupled with powerful SPIHT sorting and refinement renders 3-D SPIHT video coder so efficient that it provides comparable performance to H.263 objectively and subjectively when operated at the bit rates of 30 to 60 kbits/s with minimal system complexity. Extension to color-embedded video coding is accomplished without explicit bit allocation, and can be used for any color plane representation. In addition to being rate scalable, the proposed video coder allows multiresolutional scalability in encoding and decoding in both time and space from one bit stream. This added functionality along with many desirable attributes, such as full embeddedness for progressive transmission, precise rate control for constant bit-rate traffic, and low complexity for possible software-only video applications, makes the proposed video coder an attractive candidate for multimedia applications.
---
paper_title: JPEG2000 Image Compression Fundamentals, Standards and Practice

paper_content:

This is nothing less than a totally essential reference for engineers and researchers in any field of work that involves the use of compressed imagery. Beginning with a thorough and up-to-date overview of the fundamentals of image compression, the authors move on to provide a complete description of the JPEG2000 standard. They then devote space to the implementation and exploitation of that standard. The final section describes other key image compression systems. This work has specific applications for those involved in the development of software and hardware solutions for multimedia, internet, and medical imaging applications.
---
paper_title: Quantifying the parent-child coding gain in zero-tree-based coders

paper_content:

We attempt to quantify the coding gain due to parent-child dependencies in subband transforms. These dependencies are generally credited for the excellent mean square error (MSE) performances of zero-tree-based compression algorithms such as embedded zero-tree coding of wavelet coefficients (EZW) and set partitioning in hierarchical trees (SPIHT). Our experiments indicate that this gain is significantly smaller than what is widely believed at the time of this writing.
---
paper_title: Three-dimensional subband coding of video using the zero-tree method

paper_content:

In this paper, a simple yet highly effective video compression technique is presented. The zerotree method by Said, which is an improved version of Shapiro's original one, is applied and expanded to three-dimension to encode image sequences. A three-dimensional subband transformation on the image sequences is first performed, and the transformed information is then encoded using the zerotree coding scheme. The algorithm achieves results comparable to MPEG-2, without the complexity of motion compensation. The reconstructed image sequences have no blocking effects at very low rates, and the transmission is progressive.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
---
paper_title: 3D set partitioning coding methods in hyperspectral image compression

paper_content:

Hyperspectral images are generated by collecting hundreds of narrow and contiguously spaced spectral bands of data producing a highly correlated long sequence of images. Some application specific data compression techniques may be applied advantageously before we process, store or transmit hyperspectral images. This paper applies asymmetric tree 3DSPIHT (AT-3DSPIHT) for hyperspectral image compression; it also investigates and compares the performance of the AT-3DSPIHT, 3DSPIHT and 3DSPECK on hyperspectral image compression. Results show that the AT-3DSPIHT outperforms the other two by the approximate range of 0.2 to 0.9 dB PSNR. It guarantees over 4 dB PSNR improvement at all rates or rate savings at least a factor of 2.5 over 2D coding of separate spectral bands without axial transformation.
---
paper_title: Embedded and efficient low-complexity hierarchical image coder

paper_content:

We propose an embedded hierarchical image coding algorithm of low complexity. It exploits two fundamental characteristics of an image transform -- the well defined hierarchical structure, and energy clustering in frequency and in space. The image coding algorithm developed here, apart from being embedded and of low complexity, is very efficient and is comparable to the best known low-complexity image coding schemes available today.© (1998) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
---
paper_title: JPEG2000 coding strategies for hyperspectral data

paper_content:

In using JPEG2000 for the coding of multiple-component, or multiband, images such as hyperspectral imagery, one must consider spectral decorrelation and rate allocation between image components, issues that concern the design of the JPEG2000 encoder and are, consequently, outside the scope of the JPEG2000 standard. Spectral decorrelation via a wavelet transform, as well as three alternative strategies for extending to multiple components the optimal codeblock-bitstream-truncation process widely used for spatial rate allocation in JPEG2000 coding of single-component imagery, are considered. Results indicate that the strategy of simultaneously truncating all code-block bitstreams from all codeblocks from all image components coupled with wavelet-based spectral decorrelation significantly outperforms the other techniques considered in terms of not only rate-distortion performance but also accuracy of unsupervised classification.
---
paper_title: Compression of Multispectral Images by Three-Dimensional SPIHT Algorithm

paper_content:

The authors carry out low bit-rate compression of multispectral images by means of the Said and Pearlman's SPIHT algorithm, suitably modified to take into account the interband dependencies. Two techniques are proposed: in the first, a three-dimensional (3D) transform is taken (wavelet in the spatial domain, Karhunen-Loeve in the spectral domain) and a simple 3D SPIHT is used; in the second, after taking a spatial wavelet transform, spectral vectors of pixels are vector quantized and a gain-driven SPIHT is used. Numerous experiments on two sample multispectral images show very good performance for both algorithms.
---
paper_title: Three dimensional wavelet based approach for a scalable video conference system

paper_content:

In this paper a video coder based on a spatiotemporal multiresolution pyramid generated by a 3D separable wavelet transform (WT) is presented. The aim of the proposed coding scheme is to provide an effective scalability of the user profile by organizing the full resolution encoded bit stream into substreams, one for each temporal layer of the pyramid, which are then partitioned into substreams at increasing spatial resolution. This allows to simultaneously distribute, at different time and space resolutions, the same video to multiple users accessing the videoconference services through channels of different capacity, without multiple encoding.
---
paper_title: An embedded wavelet video coder using three-dimensional set partitioning in hierarchical trees (SPIHT)

paper_content:

The SPIHT (set partitioning in hierarchical trees) algorithm by Said and Pearlman (see IEEE Trans. on Circuits and Systems for Video Technology, no.6, p.243-250, 1996) is known to have produced some of the best results in still image coding. It is a fully embedded wavelet coding algorithm with precise rate control and low complexity. We present an application of the SPIHT algorithm to video sequences, using three-dimensional (3D) wavelet decompositions and 3D spatio-temporal dependence trees. A full 3D-SPIHT encoder/decoder is implemented in software and is compared against MPEG-2 in parallel simulations. Although there is no motion estimation or compensation in the 3D SPIHT, it performs measurably and visually better than MPEG-2, which employs complicated motion estimation and compensation.
---
paper_title: Error-resilient video coding with improved 3D SPIHT and error concealment

paper_content:

This paper first introduces an asymmetric tree structure for utilization with an error resilient form 3-D SPIHT, called ERC-SPIHT. Then, we present a fast error concealment scheme, borrowed from Rane et al.'s work with images, for embedded video bitstream using ERC-SPIHT. In addition to using simple averaging method in the root subband, we detect the presence or absence of edges in the lost block of every image. Then we use an interpolation scheme to recover the lost edge information.
---
paper_title: High performance scalable image compression with EBCOT

paper_content:

A new image compression algorithm is proposed, based on independent embedded block coding with optimized truncation of the embedded bit-streams (EBCOT). The algorithm exhibits state-of-the-art compression performance while producing a bit-stream with a rich feature set, including resolution and SNR scalability together with a random access property. The algorithm has modest complexity and is extremely well suited to applications involving remote browsing of large compressed images. The algorithm lends itself to explicit optimization with respect to MSE as well as more realistic psychovisual metrics, capable of modeling the spatially varying visual masking phenomenon.
---
paper_title: Three-dimensional wavelet-based compression of hyperspectral images

paper_content:

This chapter proposed a three dimensional set partitioned embedded block coder for hyperspectral image compression. The three dimensional wavelet transform automatically exploits inter-band dependence. Two versions of the algorithm were implemented. The integer filter implementation enables lossy-to-lossless compression, and the floating point filter implementation provides better performance for lossy representation. Wavelet packet structure and bit shifting were applied on the integer filter implementation to make the transform approximately unitary.
---
paper_title: Shape-adaptive coding using binary set splitting with k-d trees

paper_content:

The binary set splitting with k-d trees (BISK) algorithm is introduced. An embedded wavelet-based image coder based on the popular bitplane-coding paradigm, BISK is designed specifically for the coding of image objects with arbitrary shape. While other similar algorithms employ quadtree-based set partitioning to code significance-map information, BISK uses a simpler and more flexible, binary decomposition via k-d trees. Additionally, aggressive discarding of transparent regions is implemented by shrinking sets to the bounding box of their constituent opaque coefficients before further partitioning. Empirical results indicate that the proposed BISK coder consistently yields efficient performance when compared to a variety of other shape-adaptive coders.
---
paper_title: Shape-Adaptive Embedded Coding of Ocean-Temperature Imagery

paper_content:

An embedded wavelet-based coder for the shape-adaptive coding of ocean-temperature data is described. The proposed coder, 3D binary set splitting with k-A trees (3D-BISK), is based upon the popular bitplane-coding paradigm and is specifically designed for shape-adaptive coding. Other similar coding methods use octree-based set partitioning; however, 3D-BISK employs a simpler set decomposition based on k-A trees which makes it more flexible when considering shape-adaptive coding. The performance of 3D-BISK is compared to prominent shape-adaptive coders and superior performance is demonstrated for a variety of ocean-temperature datasets.
---
paper_title: Efficient, low-complexity image coding with a set-partitioning embedded block coder

paper_content:

We propose an embedded, block-based, image wavelet transform coding algorithm of low complexity. It uses a recursive set-partitioning procedure to sort subsets of wavelet coefficients by maximum magnitude with respect to thresholds that are integer powers of two. It exploits two fundamental characteristics of an image transform-the well-defined hierarchical structure, and energy clustering in frequency and in space. The two partition strategies allow for versatile and efficient coding of several image transform structures, including dyadic, blocks inside subbands, wavelet packets, and discrete cosine transform (DCT). We describe the use of this coding algorithm in several implementations, including reversible (lossless) coding and its adaptation for color images, and show extensive comparisons with other state-of-the-art coders, such as set partitioning in hierarchical trees (SPIHT) and JPEG2000. We conclude that this algorithm, in addition to being very flexible, retains all the desirable features of these algorithms and is highly competitive to them in compression efficiency.
---
paper_title: Coding of ocean-temperature volumes using binary set splitting with k-d trees

paper_content:

An embedded wavelet-based coder for the shape-adaptive coding of ocean-temperature data is described. The proposed coder, 3D binary set splitting with k-d trees (3D-BISK), is based upon the popular bitplane-coding paradigm and is specifically designed for shape-adaptive coding. Other similar coding methods use octree-based set partitioning; however, 3D-BISK employs a simpler set decomposition based on k-d trees which makes it more flexible when considering shape-adaptive coding. The performance of 3D-BISK is compared to prominent shape-adaptive coders and superior performance is demonstrated for a variety of ocean-temperature datasets.
---
paper_title: Microarray BASICA: background adjustment, segmentation, image compression and analysis of microarray images

paper_content:

This paper presents Microarray BASICA: an integrated image processing tool for background adjustment, segmentation, image compression and analysis of microarray images. BASICA uses the fast Mann-Whitney test-based algorithm introduced in J. Hua et al., (2002) to segment microarray images, and post-processing to eliminate the segmentation irregularities. The segmentation results, along with the foreground and background intensities obtained with background adjustment, are then used for the independent compression of foreground and background. We introduce a new distortion measure for microarray image compression and devise a coding scheme by modifying the object-based embedded block coding with optimized truncation (object-based EBCOT) algorithm J. Hua et al., (2002) to achieve optimal rate-distortion performance in lossy coding while still maintaining outstanding lossless compression performance. Experimental results show that BASICA can extract sufficiently accurate genetic information at bitrates as low as 43bpp.
---
paper_title: Embedded Wavelet-Based Coding of Three-Dimensional Oceanographic Images With Land Masses

paper_content:

We describe the wavelets around land masses (WAVAL) system for the embedded coding of three-dimensional (3-D) oceanographic images. These images differ from those arising in other applications in that valid data exists only at grid points corresponding to sea. Grid points that cover land or lie beyond the bathymetry have no associated data. For these images, the WAVAL system employs a 3-D lifting wavelet transform tailored specifically to the potentially sparse nature of the data by processing only the valid sea data points between land masses. We introduce successive-approximation runlength (SARL) coding, an embedded-coding procedure that adds successive-approximation properties to the well known stack-run (SR) algorithm. SARL is employed to code wavelet coefficients resulting from the 3-D transform in the WAVAL system. However, it is a general technique applicable to other coding tasks in which embedded coding is desired but for which zerotree techniques are impractical. Experimental results show that the WAVAL system achieves substantial improvement in rate-distortion performance over the technique currently used by the US Navy for compression of oceanographic imagery.
---
paper_title: 3-D wavelet coding of video with arbitrary regions of support

paper_content:

We examine 3-D wavelet coding of video with arbitrary regions of support (AROS). A critically sampled wavelet transform is applied to the AROS and a modified 3-D set partitioning in hierarchical trees (SPIHT) algorithm is used to quantize and code the wavelet coefficients in the AROS only. Experiments show that, for typical MPEG-4 pre-segmented sequences, our proposed method can achieve a gain of up to 5.6 dB in average PSNR at the same rate over 3-D SPIHT coding of regular volumes that embed the AROS of the given video sequences.
---
paper_title: Region-oriented compression of multispectral images by shape-adaptive wavelet transform and SPIHT

paper_content:

We present a new technique for the compression of remote-sensing hyperspectral images based on wavelet transform and zerotree coding of coefficients. In order to improve encoding efficiency, the image is first segmented in a small number of regions with homogeneous texture. Then, a shape-adaptive wavelet transform is carried out on each region and the resulting coefficients are finally encoded by a shape-adaptive version of SPIHT. Thanks to the segmentation map (sent as a side information) region boundaries are faithfully preserved and selective encoding strategies can be easily implemented. In addition, by-now homogeneous region textures can be more efficiently encoded.
---
paper_title: Wavelet-based coding of three-dimensional oceanographic images around land masses

paper_content:

We describe an algorithm for the embedded coding of 3D oceanographic images. These images differ from those arising in other applications in that valid data exist only at grid points corresponding to the sea; grid points that cover land or lie beyond the bathymetry have no associated data. For these images, we employ a 3D lifting wavelet transform tailored specifically to the potentially sparse nature of the data by processing only the valid sea data points in between land masses. In addition, we introduce successive-approximation runlength (SARL) coding, an embedded-coding procedure which adds successive-approximation properties to the well known stack-run (SR) algorithm. SARL is a general technique applicable to the oceanographic images considered here as well as to other coding tasks in which embedded coding is desired but for which zerotree-techniques are impractical.
---
paper_title: Shape-adaptive tarp coding

paper_content:

An embedded wavelet coder is proposed for arbitrarily shaped image objects. Contrary to the popular approach of considering transparent regions surrounding image objects as permanently insignificant, the proposed coder imposes no assumptions on the significance state of unknown transparent regions. Instead, the proposed shape-adaptive tarp coder employs a simple algorithm called tarp filtering to produce a probability estimate of coefficient significance which propagates unchanged across transparent regions. Experimental results show that the shape-adaptive tarp coder offers coding performance superior to a popular zerotree-based technique and equivalent to a popular method based on context conditioning.
---
paper_title: Region-based wavelet coding methods for digital mammography

paper_content:

Spatial resolution and contrast sensitivity requirements for some types of medical image techniques, including mammography, delay the implementation of new digital technologies, namely, computer-aided diagnosis, picture archiving and communications systems, or teleradiology. In order to reduce transmission time and storage cost, an efficient data-compression scheme to reduce digital data without significant degradation of medical image quality is needed. In this study, we have applied two region-based compression methods to digital mammograms. In both methods, after segmenting the breast region, a region-based discrete wavelet transform is applied, followed by an object-based extension of the set partitioning in hierarchical trees (OB-SPIHT) coding algorithm in one method, and an object-based extension of the set partitioned embedded block (OB-SPECK) coding algorithm in the other. We have compared these specific implementations against the original SPIHT and the new standard JPEG 2000, both using reversible and irreversible filters, on five digital mammograms compressed at rates ranging from 0.1 to 1.0 bit per pixel (bbp). Distortion was evaluated for all images and compression rates by the peak signal-to-noise ratio. For all images, OB-SPIHT and OB-SPECK performed substantially better than the traditional SPIHT and JPEG 2000, and a slight difference in performance was found between them. A comparison applying SPIHT and the standard JPEG 2000 to the same set of images with the background pixels fixed to zero was also carried out, obtaining similar implementation as region-based methods. For digital mammography, region-based compression methods represent an improvement in compression efficiency from full-image methods, also providing the possibility of encoding multiple regions of interest independently.
---
paper_title: A comparison of flat and object-based transform coding techniques for the compression of multispectral images

paper_content:

In this work we implement and compare several state-of-the-art transform coding schemes for the compression of multispectral images, in order to better understand which elements have a deeper impact on the overall performance, and which tools guarantee the best results. All schemes are based on Karhunen-Loeve transform and/or wavelet transform, in various combinations, and use SPIHT as the coding engine. Moreover, besides the ordinary techniques, their object-based counterparts are also examined, so as to study the viability of such approach [M. Cagnazzo et al., Oct 2004] for these images. Whenever possible, an optimal rate allocation strategy is applied. The experiments, performed on images acquired by two different sensors, highlight the superiority of KLT as spectral transform; the rough equivalence between object-based and ordinary techniques in terms of rate-distortion performance; and the importance of the optimal allocation.
---
paper_title: Lossy-to-lossless ROI coding of chromosome images using modified SPIHT and EBCOT

paper_content:

This paper proposes a lossy-to-lossless region of interest (ROI) compression scheme based on set partitioning in hierarchical trees (SPIHT) and embedded block coding with optimized truncation (EBCOT) (EBCOT is the base of the JPEG-2000 standard). However, SPIHT does not support ROI coding and JPEG-2000 does not allow lossy-to-lossless ROI compression. For our application, we modify the original SPIHT and EBCOT algorithms for lossy-to-lossless ROI coding of both the foreground and the background of chromosome images. Experiments show that our implementations offer better compression performance with exact ROI support than other image coders.
---
paper_title: Shape-adaptive coding using binary set splitting with k-d trees

paper_content:

The binary set splitting with k-d trees (BISK) algorithm is introduced. An embedded wavelet-based image coder based on the popular bitplane-coding paradigm, BISK is designed specifically for the coding of image objects with arbitrary shape. While other similar algorithms employ quadtree-based set partitioning to code significance-map information, BISK uses a simpler and more flexible, binary decomposition via k-d trees. Additionally, aggressive discarding of transparent regions is implemented by shrinking sets to the bounding box of their constituent opaque coefficients before further partitioning. Empirical results indicate that the proposed BISK coder consistently yields efficient performance when compared to a variety of other shape-adaptive coders.
---
paper_title: Shape-Adaptive Embedded Coding of Ocean-Temperature Imagery

paper_content:

An embedded wavelet-based coder for the shape-adaptive coding of ocean-temperature data is described. The proposed coder, 3D binary set splitting with k-A trees (3D-BISK), is based upon the popular bitplane-coding paradigm and is specifically designed for shape-adaptive coding. Other similar coding methods use octree-based set partitioning; however, 3D-BISK employs a simpler set decomposition based on k-A trees which makes it more flexible when considering shape-adaptive coding. The performance of 3D-BISK is compared to prominent shape-adaptive coders and superior performance is demonstrated for a variety of ocean-temperature datasets.
---
paper_title: All-phase motion compensated prediction in the wavelet domain for high performance video coding

paper_content:

This paper presents a novel framework of motion compensated prediction (MCP) techniques in the wavelet domain for high performance video coding. Our analysis reveals fundamental limitations with previous ad-hoc wavelet-based video coders from the motion accuracy point of view. We demonstrate that the phase associated with any wavelet transform carries critical information of the motion accuracy and we propose to restore the motion accuracy by considering the wavelet coefficients of the previous frame with all different phases. Our all-phase MCP approach can be viewed as predicting the wavelet coefficients from an over-complete expansion of the previous frame. Experimental results have shown that restoration of motion accuracy in the wavelet domain can dramatically improve the efficiency of MCP. The video coder (MCP-WT) built upon the MCP of wavelet coefficients has achieved 2 to 3 dB gain over existing the MPEG-2 coder at the bit rate of 1 to 9 Mbps. Moreover, MCP techniques in the wavelet domain offer a promising new ground for developing efficient scalable video coders.
---
paper_title: Multihypothesis motion compensation in the redundant wavelet domain

paper_content:

Multihypothesis motion compensation is extended into the transform domain by using a redundant wavelet transform to produce multiple predictions that are diverse in transform phase. The corresponding inverse transform implicitly combines the multihypothesis predictions into a single spatial-domain prediction for motion compensation such that no side information is needed to describe the combination weights. Additionally, we use a hierarchical search to tailor the motion-vector field to individual phases. Substantial gains in rate-distortion performance are obtained in comparison to an equivalent system using single-phase prediction.
---
paper_title: Motion Compensation Via Redundant-Wavelet Multihypothesis

paper_content:

Multihypothesis motion compensation has been widely used in video coding with previous attention focused on techniques employing predictions that are diverse spatially or temporally. In this paper, the multihypothesis concept is extended into the transform domain by using a redundant wavelet transform to produce multiple predictions that are diverse in transform phase. The corresponding multiple-phase inverse transform implicitly combines the phase-diverse predictions into a single spatial-domain prediction for motion compensation. The performance advantage of this redundant-wavelet-multihypothesis approach is investigated analytically, invoking the fact that the multiple-phase inverse involves a projection that significantly reduces the power of a dense-motion residual modeled as additive noise. The analysis shows that redundant-wavelet multihypothesis is capable of up to a 7-dB reduction in prediction-residual variance over an equivalent single-phase, single-hypothesis approach. Experimental results substantiate the performance advantage for a block-based implementation
---
paper_title: A zerotree wavelet video coder

paper_content:

This paper describes a hybrid motion-compensated wavelet transform coder designed for encoding video at very low bit rates. The coder and its components have been submitted to MPEG-4 to support the functionalities of compression efficiency and scalability. Novel features of this coder are the use of overlapping block motion compensation in combination with a discrete wavelet transform followed by adaptive quantization and zerotree entropy coding, plus rate control. The coder outperforms the VM of MPEG-4 for coding of I-frames and matches the performance of the VM for P-frames while providing a path to spatial scalability, object scalability, and bitstream scalability.
---
paper_title: Motion compensation and multiresolution coding

paper_content:

Abstract Multiresolution techniques have become more and more appealing in current image coding. Image multispectral representation produces many important features such as spectral shaping of coding noise according to human eye perception, good image energy compaction, coder tuning with respect to any band characteristics, and allows for multilevel layered transmission that is one of the main targets pursued by the broadcaster. Despite these appealing capabilities, multiresolution techniques have failed to give the expected results. One of the reasons for this failure is the difficulty of exploiting the temporal redudancy present in image sequences. This paper addresses the problem of motion compensation in a multiresolution environment, considering both QMF-SBC and wavelet transform approaches. Different motion compensation schemes are derived and their efficiency is considered with regard to scalability and to the lengths of subband analysis and synthesis filters. Simulation results are used to support relevant conclusions where needed.
---
paper_title: Motion-compensated generic coding of video based on a multiresolution data structure

paper_content:

We present a generic video codec, which is able to compress image sequences efficiently regardless of their input formats. In addition, this codec supports a wide range of bit rates, without significant changes in its main architecture. A multiresolution representation of the data is generated by a Gabor-like wavelet transform. The motion estimation is performed by a locally adaptive multigrid block-matching technique. This codec can handle both interlaced and progressive input sequences, the temporal redundancies being exploited by interframe/interfield coding. A perceptual quantization of the resulting coefficients is then performed, followed by adaptive entropy coding. Simulations using different test sequences demonstrate a reconstructed signal of good quality for a wide range of bit rates. Thereby demonstrating that this codec can perform generic coding with reduced complexity and high efficiency.
---
paper_title: An Implementation of the “algorithme à trous” to Compute the Wavelet Transform

paper_content:

The computation of the wavelet transform involves the computation of the convolution product of the signal to be analysed by the analysing wavelet. It will be shown that the computation load grows with the scale factor of the analysis. We are interested in musical sounds lasting a few seconds. Using a straightforward algorithm leads to a prohibitive computation time, so we need a more effective computation procedure.
---
paper_title: A Real-Time Algorithm for Signal Analysis with the Help of the Wavelet Transform

paper_content:

The purpose of this paper is to present a real-time algorithm for the analysis of time-varying signals with the help of the wavelet transform. We shall briefly describe this transformation in the following. For more details, we refer to the literature [1].
---
paper_title: Motion-compensated wavelet transform coding for color video compression

paper_content:

A video compression scheme based on the wavelet representation and multi-resolution motion estimation (MRME) is presented in this paper. The multiresolution/multifrequency nature of the discrete wavelet transform lends itself as an ideal tool for representing images and video signals. Wavelet transform decomposes a video frame into a set of sub-frames with different resolutions corresponding to different frequency bands. These multiresolution frames also provide a representation of the global motion structure of the video signals at different scales. The motion activities for a particular sub-frame in different resolutions are hence highly correlated since they actually specify the same motion structure at different scales. In the MRMC described the Section 4, motion vectors in higher resolution are predicted by the motion vectors in the lower resolution, and are refined at each step. In particular, we propose a variable block-size MRMC scheme in which the size of a block is adapted to its level in the pyramid. This scheme not only considerably reduces the searching and matching time but also provides a meaningful characterization of the intrinsic motion structure. The variable-size MRMC approach also avoids the drawback of the constant-size MRMC in describing small object motion activities. After wavelet decomposition, each scaled wavelet tends to have different statistical properties. An adaptive truncation process similar to [CHEN 84] was implemented and a bit allocation scheme similar to that in the transform coding is examined by adapting to the local variance distribution in each scaled wavelet. Based on the wavelet representation, variable-size MRMC approach and a uniform quantization scheme, four variations of the proposed motion-compensated wavelet video compression system are presented in Section 6. It is shown that the motion-compensated wavelet transform coding approach out-performs the conventional transform coding scheme in terms of the signal-to- noise ratio as well as the subjective performance.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
---
paper_title: Scalable video compression via overcomplete motion compensated wavelet coding

paper_content:

Recently, there have been a flurry of works on overcomplete motion compensated wavelet coding (OMCWC). In this paper, we address the importance of phase and focus on the design of scalable video coding algorithms within the OMCWC framework. Specifically, our new contributions consist of the following three components: (1) efficient block motion estimation techniques in the wavelet domain including hierarchical and fractional-pel block matching, (2) extend overcomplete motion compensated prediction (MCP) into overcomplete motion compensated temporal filtering (MCTF) to achieve temporal scalability (3) context modeling strategies for embedded quantization and entropy coding of 3D wavelet coefficients. Experiment results are used to demonstrate that the class of overomplete MCP/MCTF coders are capable of achieving comparable performance to other competing interframe wavelet coders.
---
paper_title: Video coding based on motion estimation in the wavelet detail images

paper_content:

This work proposes a new block based motion estimation and compensation technique applied on the detail images of the wavelet pyramidal decomposition. The algorithm uses two matching criteria, namely the absolute difference and the absolute sum. For a wavelet decomposed one-dimensional step function, it is shown that for odd translations of the step, the absolute sum reaches a smaller minimum than the absolute difference. We also derive in this case a constraint on the highpass filter coefficients so that a zero prediction error can be reached by using the absolute sum. Although this cannot be easily generalized for an arbitrary signal profile, experimental results obtained with photorealistic image sequences indicate that the prediction error can be reduced with respect to techniques that only use the absolute difference as matching criterion.
---
paper_title: High-performance resolution-scalable video coding via all-phase motion-compensated prediction of wavelet coefficients

paper_content:

How to develop a multi-resolution representation of video signals for both efficient and scalable coding? What are fundamental advantages and limitations of a resolution scalable video coder? How to make use of the scalability features of a video codec to compromise other requirements (e.g. delay)? These are the central issues we address in this paper. We first demonstrate the importance of resolving the phase uncertainty on the efficiency of motion-compensated prediction (MCP) in the wavelet domain. Improved understanding of the relationship between phase associated with any wavelet transform (WT) and motion accuracy of MCP motivates us to develop a novel multi-resolution representation for video signals. The salient feature of our new representation is that MCP can be performed both effectively and independently at different resolutions. We apply previous theoretical results on fractional-pel MCP to analyze the sacrifice of coding efficiency due to the resolution scalability constraint. We also investigate the issue of delay in video coding and propose a framework of trading delay with spatial resolution. A video decoder can display a low-resolution frame with low delay first and then gracefully enhance the frame resolution as the delay increases. The low-delay resolution-scalable MCP-WT coder built upon our new wavelet-based multi-resolution representation of video signals has achieved significant Rate-Distortion improvements over previously-reported scalable coders in the literature and even outperforms non-scalable MPEG-2 coder by 1-2dB at the bit rate of 2-9Mbps.
---
paper_title: The discrete wavelet transform: wedding the a trous and Mallat algorithms

paper_content:

Two separately motivated implementations of the wavelet transform are brought together. It is observed that these algorithms are both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by the choice of filters. In fact, the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, it is shown that the commonly used Lagrange a trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support. A systematic framework for the discrete wavelet transform is provided, and conditions are derived under which it computes the continuous wavelet transform exactly. Suitable filter constraints for finite energy and boundedness of the discrete transform are also derived. Relevant signal processing parameters are examined, and it is observed that orthonormality is balanced by restrictions on resolution. >
---
paper_title: Mesh-based motion estimation and compensation in the wavelet domain using a redundant transform

paper_content:

A technique is presented that incorporates an irregular triangle mesh into wavelet-domain motion-estimation and motion-compensation using a shift-invariant redundant wavelet transform. Triangle vertices are identified by a simple correlation operator locating image edges in the wavelet subbands, while motion compensation takes place through an affine transformation mapping triangles from one frame to the next. The motion-compensated residual is downsampled to a non-redundant form which is then coded using any wavelet-based still-image coder. Experimental results indicate that the combined approach outperforms either technique applied separately,, in addition, the proposed method outperforms a variety of motion-estimation and motion-compensation approaches operating in both the spatial and wavelet domains.
---
paper_title: Motion estimation and compensation in the redundant-wavelet domain using triangle meshes

paper_content:

In this paper, a technique is presented that incorporates an irregular triangle mesh into wavelet-domain motion estimation and compensation using a shift-invariant redundant-wavelet transform. The main contribution of this work resides in a demonstration that triangle-mesh motion estimation and compensation can be deployed more effectively in the redundant-wavelet domain thanks to a simple correlation operator that is robust to the prediction residual, a noise-like signal that hinders spatial-domain gradient-based efforts to locate image edges which persist from frame to frame. In the proposed technique, motion compensation takes place through an affine transform mapping triangles from one frame to the next, while the motion-compensated residual is downsampled to a non-redundant form which is then coded using any wavelet-based still-image coder. Experimental results indicate that the proposed technique significantly outperforms not only the usual spatial-domain approach to mesh-based motion estimation and compensation, but also the emerging wavelet-based coders that employ traditional block-based structures, particularly for sequences with fast or complex motion.
---
paper_title: Scalable wavelet video-coding with in-band prediction - implementation and experimental results

paper_content:

In this paper we elaborate on a recently proposed approach for scalable video-coding based on in-band prediction in the overcomplete wavelet domain. It is shown that, through a new calculation scheme for the level-by-level complete to overcomplete discrete wavelet transform (DWT) that exploits certain symmetries, important reductions in the multiplication budget are obtained in comparison to the fastest-known algorithm of the literature. Based on the derived overcomplete transform-domain coefficients, a pixel-accurate motion estimation and compensation (ME/MC) algorithm is proposed, which provides a hybrid-coding framework that supports full scalability in resolution, quality and frame rate. To give an indication of the coding performance of such a system, some preliminary results are reported.
---
paper_title: Wavelet-based moving-picture coding using shift-invariant motion estimation in wavelet domain

paper_content:

Abstract The shift-variant property of the discrete wavelet transform (DWT) makes the motion estimation and compensation inefficient in the wavelet domain. In order to overcome the shift-variant property of the DWT, a low-band-shift (LBS) method has been developed. Using the LBS method in the wavelet domain, two motion estimation and compensation schemes are developed and evaluated. One scheme is the motion estimation and compensation using the LBS method with wavelet-block basis and the other is with band-by-band basis. Both schemes using the LBS method have superior performances to the conventional motion estimation methods in spatial domain or wavelet domain with respect to peak-noise-to-signal ratio (PSNR). The experiment results show that the proposed schemes have PSNR improvements of above 1.0 dB to the full-search method in spatial domain.
---
paper_title: 3-band motion-compensated temporal structures for scalable video coding

paper_content:

Recent breakthroughs in motion-compensated temporal wavelet filtering have finally enabled implementation of highly efficient scalable and error-resilient video codecs. These new wavelet codecs provide numerous advantages over nonscalable conventional solutions techniques based on motion-compensated prediction, such as no recursive predictive loop, separation of noise and sampling artifacts from the content through use of longer temporal filters, removal of long range as well as short range temporal redundancies, etc. Moreover, these wavelet video coding schemes can provide flexible spatial, temporal, signal-to-noise ratio and complexity scalability with fine granularity over a large range of bit rates, while maintaining a very high coding efficiency. However, most motion-compensated wavelet video schemes are based on classical two-band decompositions that offer only dyadic factors of temporal scalability. In this paper, we propose a three-band temporal structure that extends the concept of motion-compensated temporal filtering (MCTF) that was introduced in the classical lifting framework. These newly introduced structures provide higher temporal scalability flexibility, as well as improved compression performance compared with dyadic Haar MCTF
---
paper_title: Scalable video compression using longer motion compensated temporal filters

paper_content:

Three-dimensional (3-D) subband/wavelet coding using a motion compensated temporal filter (MCTF) is emerging as a very effective structure for highly scalable video coding. Most previous work has used two-tap Haar filters for the temporal analysis/synthesis. To make better use of the temporal redundancies, we are proposing an MCTF scheme based on longer biorthogonal filters. We show a lifting based coder capable of subpixel accurate motion compensation. If we retain the fixed size GOP structure of the Haar filter MCTFs, we need to use symmetric extensions at both ends of the GOP. This gives rise to loss of coding efficiency at the GOP boundaries resulting in significant PSNR drops there. This performance can be considerably improved by using a 'sliding window,' in place of the GOP block. We employ the 5/3 filter and its non-orthogonality causes PSNR variation, which can be reduced by employing filter-based weighting coefficients. Overall the longer filters have a higher coding gain than the Haar filters and show significant improvement in average PSNR at high bit rates. However, a doubling in the number of motion vectors to be transmitted, translates to a drop in PSNR at the lower video bit rates.© (2003) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
---
paper_title: Successive refinement of video: fundamental issues, past efforts, and new directions

paper_content:

The paper provides an overview of the fundamental issues confronting scalable video compression, together with some of the most promising general approaches to addressing these issues. For motivation, the paper sketches a compelling application in remote browsing of video, whose realization is not possible without efficient highly scalable video compression technology. The paper outlines some of the most important structural alternatives for wavelet-based scalable video compression systems, together with experimental findings in support of particular alternatives. In particular, the paper describes novel spatio-temporal decomposition structures, a novel finely embedded motion coding structure, and a complete compression system which addresses the needs of a wide range of potential applications. Preliminary compression performance results are provided together with information on an implementation which is capable of real-time decoding at CIF resolutions and beyond.
---
paper_title: 3-D video coding with redundant-wavelet multihypothesis

paper_content:

Multihypothesis with phase diversity is introduced into motion-compensated temporal filtering by deploying the latter in the domain of a spatially redundant wavelet transform. The centerpiece of this redundant-wavelet approach to multihypothesis temporal filtering is a multiple-phase inverse transform that involves an implicit projection significantly reducing noise not captured by the motion model of the temporal filtering. The primary contribution of the work is a derivation that establishes analytically the advantage of the redundant-wavelet approach as compared to equivalent temporal filtering taking place in the spatial domain. For practical implementation, a regular triangle mesh is used to track motion between frames, and an affine transform between mesh triangles implements motion compensation within a lifting-based temporal transform. Experimental results reveal that the incorporation of phase-diversity multihypothesis into motion-compensated temporal filtering improves rate-distortion performance, and state-of-the-art scalable performance is observed.
---
paper_title: 3D video coding using redundant-wavelet multihypothesis and motion-compensated temporal filtering

paper_content:

A video coder is presented that combines mesh-based motion-compensated temporal filtering, phase-diversity multihypothesis motion compensation, and an embedded 3D wavelet-coefficient coder. The key contribution of this work is the introduction of the phase-diversity multihypothesis paradigm into motion-compensated temporal filtering, which is achieved by deploying temporal filtering in the domain of a spatially redundant wavelet transform. A regular triangle mesh is used to track motion between frames, and an affine transform between mesh triangles implements motion compensation within a lifting-based temporal transform. Experimental results reveal that the incorporation of pulse-diversity multihypothesis into mesh-based motion-compensated temporal filtering significantly improves the rate-distortion performance of the 3D video coder.
---
paper_title: 3D, 3-band, 3-tap temporal lifting for scalable video coding

paper_content:

Recently, a new generation of video compression techniques gained the interest of the research engineering community, by proposing state-of-the-art compression performance in addition to temporal/spatial/SNR scalability features. They exploit interframe redundancy through a temporal wavelet transform in the motion direction. While classical two-band decompositions offer dyadic factors of scalability, in this paper we present a three-band temporal lifting structure providing a factor 3 of scalability in a motion-compensated subband video coding scheme. More flexibility is thus available in order to adapt the bitstream to the bandwidth variations in heterogeneous networks. We also show improved compression performance compared with a dyadic Haar MCTF analysis.
---
paper_title: Motion-compensated 3-D subband coding of video

paper_content:

This paper describes a video coding system based on motion-compensated three-dimensional (3-D) subband/wavelet coding (MC-3DSBC), which can overcome the limits of both 3-D SBC and MC prediction-based coding. In this new system, spatio-temporal subbands are generated by MC temporal analysis and a spatial wavelet transform, and then encoded by 3-D subband-finite state scalar quantization (3DSB-FSSQ). The rate allocation from the GOP level to each class of subbands is optimized by utilizing the structural property of MC-3DSBC that additive superposition approximately holds for both rate and distortion. The proposed video coding system is applied to several test video clips. Its performance exceeds that of both a known MPEG-1 implementation and a similar subband MC predictive coder while maintaining modest computational complexity and memory size.
---
paper_title: Advances in Scalable Video Coding

paper_content:

Scalable video coding is attractive due to the capability of reconstructing lower resolution or lower quality signals from partial bit streams. This allows for simple solutions in adaptation to network and terminal capabilities. Different modalities of scalability are specified by video coding standards like MPEG-2 and MPEG-4. This paper gives a short overview over these techniques and analyzes in more detail the encoder/decoder drift problem, which is the major reason why scalable coding has been significantly less efficient than single-layer coding in most of these implementations. Only recently, new scalable video coding technology has evolved, which seems to close the gap of compression performance compared to state of the art single-layer video coding. New methods of efficient enhancement layer prediction were developed to improve traditional (motion-compensated hybrid) scalable coders, providing more flexible compromises on the drift problem. As a new technology trend, motion-compensated spatiotemporal wavelet coding has matured which entirely discards the drift and allows most flexible combinations of spatial, temporal, and signal-to-noise ratio (SNR) scalability with fine granularity over a broad range of data rates.
---
paper_title: Advanced motion threading for 3D wavelet video coding

paper_content:

Abstract This paper presents an advanced motion threading technique for improved performance in 3D wavelet coding. First, we extend an original motion threading idea of ours to a lifting- based implementation. Methods for enabling fractional-pixel alignment in motion threading and for processing many-to-one pixel mapping and non-referred pixels are proposed to reduce the wavelet boundary effects. Second, we devise an advanced motion threading technique, in which one set of motion vectors is generated for each temporal layer of wavelet coefficients for temporal scalability. In order to reduce the motion overhead information, especially at low bit rates, several correlated motion prediction modes at the macroblock level are defined to exploit the intra/inter layer correlation in motion vector coding. Finally, rate-distortion optimization is utilized in motion estimation to select the best motion prediction mode for each macroblock. With the new motion threading technique, we are able to achieve 1.5–6.0 dB gain in average PSNR in 3D wavelet coding over our previous implementation of motion threading.
---
paper_title: MOTION-COMPENSATED HIGHLY SCALABLE VIDEO COMPRESSION USING AN ADAPTIVE 3 D WAVELET TRANSFORM BASED ON LIFTING

paper_content:

This paper proposes a new framework for the construction of motion compensated wavelet transforms, with application to efficient highly scalable video compression. Motion compensated transform techniques, as distinct from motion compensated predictive coding, represent a key tool in the development of highly scalable video compression algorithms. The proposed framework overcomes a variety of limitations exhibited by existing approaches. This new method overcomes the failure of frame warping techniques to preserve perfect reconstruction when tracking complex scene motion. It also overcomes some of the limitations of block displacement methods. Specifically, the lifting framework allows the transform to exploit inter-frame redundancy without any dependence on the model selected for estimating and representing motion. A preliminary implementation of the proposed approach was tested in the context of a scalable video compression system, yielding PSNR performance competitive with other results reported in the literature.
---
paper_title: Improvements to the MC-EZBC scalable video coder

paper_content:

MC-EZBC is a fully scalable video coder using a motion-compensated 3-D subband/wavelet decomposition. Temporal filtering is performed along estimated motion trajectories to remove temporal redundancy. To get greatly increased motion compensation (MC) accuracy and increased coding efficiency, we use the lifting filter implementation. Additionally, we introduce unconnected blocks and spatial lowpass transition filtering (SLTF). This results in improved lower frame rate data for the scalable MC-EZBC coder. Finally, an optimized quantization strategy is introduced to compensate for variations in synthesis filtering for connected and unconnected pixels.
---
paper_title: Scalable video compression via overcomplete motion compensated wavelet coding

paper_content:

Recently, there have been a flurry of works on overcomplete motion compensated wavelet coding (OMCWC). In this paper, we address the importance of phase and focus on the design of scalable video coding algorithms within the OMCWC framework. Specifically, our new contributions consist of the following three components: (1) efficient block motion estimation techniques in the wavelet domain including hierarchical and fractional-pel block matching, (2) extend overcomplete motion compensated prediction (MCP) into overcomplete motion compensated temporal filtering (MCTF) to achieve temporal scalability (3) context modeling strategies for embedded quantization and entropy coding of 3D wavelet coefficients. Experiment results are used to demonstrate that the class of overomplete MCP/MCTF coders are capable of achieving comparable performance to other competing interframe wavelet coders.
---
paper_title: A 5-band Temporal Lifting Scheme for Video Surveillance

paper_content:

Three-dimensional (3D) wavelet coding schemes have been demonstrated to be efficient techniques for video compression applications. The scalability property of such schemes is one of the most important issues for video surveillance systems. In this paper we introduce a new lifting-based method of temporal decomposition which provides a scalability factor of 5 in a motion-compensated subband video coding scheme. Depending on the sequence characteristics, motion model etc., this structure can provide high coding performance. Also, it gives a better coding efficiency for the temporal approximation subbands, thus leading to an improved temporal scalability. It addresses video surveillance applications, where the motion is very low in most cases.
---
paper_title: Lifting-based invertible motion adaptive transform (LIMAT) framework for highly scalable video compression

paper_content:

We propose a new framework for highly scalable video compression, using a lifting-based invertible motion adaptive transform (LIMAT). We use motion-compensated lifting steps to implement the temporal wavelet transform, which preserves invertibility, regardless of the motion model. By contrast, the invertibility requirement has restricted previous approaches to either block-based or global motion compensation. We show that the proposed framework effectively applies the temporal wavelet transform along a set of motion trajectories. An implementation demonstrates high coding gain from a finely embedded, scalable compressed bit-stream. Results also demonstrate the effectiveness of temporal wavelet kernels other than the simple Haar, and the benefits of complex motion modeling, using a deformable triangular mesh. These advances are either incompatible or difficult to achieve with previously proposed strategies for scalable video compression. Video sequences reconstructed at reduced frame-rates, from subsets of the compressed bit-stream, demonstrate the visually pleasing properties expected from low-pass filtering along the motion trajectories. The paper also describes a compact representation for the motion parameters, having motion overhead comparable to that of motion-compensated predictive coders. Our experimental results compare favorably to others reported in the literature, however, our principal objective is to motivate a new framework for highly scalable video compression.
---
paper_title: Complete-to-overcomplete discrete wavelet transforms for scalable video coding with MCTF

paper_content:

Techniques for full scalability with motion-compensated temporal filtering (MCTF) in the wavelet-domain (in-band) are presented in this paper. The application of MCTF in the wavelet domain is performed after the production of the overcomplete discrete wavelet transform from the critically-sampled decomposition, a process that occurs at both the encoder and decoder side. This process, which is a complete-to-overcomplete discrete wavelet transform, is critical for the efficiency of the system with respect to scalability, coding performance and complexity. We analyze these aspects of the system and set the necessary constraints for drift-free video coding with in-band MCTF. As a result, the proposed architecture permits the independent operation of MCTF within different resolution levels or even different subbands of the transform and allows the successive refinement of the video information in resolution, frame-rate and quality.
---
paper_title: HIGHLY SCALABLE VIDEO COMPRESSION USING A LIFTING-BASED 3 D WAVELET TRANSFORM WITH DEFORMABLE MESH MOTION COMPENSATION

paper_content:

This paper continues the development of a new framework for the construction of motion-compensated wavelet transforms for highly scalable video compression. The current authors recently proposed a motion adaptive wavelet transform based on motion-compensated lifting steps. This approach overcomes several limitations of existing methods. In particular, frame warping and block displacement methods cannot efficiently exploit complex motion without sacrificing invertibility. By contrast, the motion-compensated lifting transform remains invertible regardless of the motion model. The previous work was primarily in the context of a block motion model. However, block motion models inevitably yield discontinuous motion fields, which poorly represent complex motion in real video sequences. In this paper we consider the benefits of a continuous motion field, by incorporating a deformable mesh motion model into the existing framework. Experimental results show that this leads to improved compression performance. In addition, we show that the invertibility of continuous motion fields allows greater potential for compactly representing the motion information.
---
paper_title: A flexible structure for fully scalable motion-compensated 3-D DWT with emphasis on the impact of spatial scalability

paper_content:

We investigate the implications of the conventional " 2-D" motion-compensated (MC) three-dimensional (3-D) discrete wavelet/subband transform structure for spatial scal- ability and propose a novel flexible structure for fully scalable video compression. In this structure, any number of levels of "pretemporal" spatial wavelet decomposition are performed on the original full resolution frames, followed by MC temporal decomposition of the subbands within each spatial resolution level. Further levels of "posttemporal" spatial decomposition may be performed on the spatiotemporal subbands to provide additional levels of spatial scalability and energy compaction. This structure allows us to trade energy compaction against the potential for artifacts at reduced spatial resolutions. More importantly, the structure permits extensive study of the interaction between spatial aliasing, scalability and energy compaction. We show that where the motion model fails, the " 2-D" structure inevitably produces misaligned spatial aliasing artifacts in reduced resolution sequences. These artifacts can be removed by using pretemporal spatial decomposition. On the other hand, we also show that the " 2-D" structure necessarily maximizes compression efficiency. We propose different schemes to minimize the loss of compression efficiency associated with pretemporal spatial decomposition. Highly scalable encoders must operate with no knowledge of the actual decoded quality or resolution. The predictive feedback paradigm inherent in traditional motion-compensated (MC) video compression algorithms is incompatible with the requirement of highly scalable compression, as the encoder must duplicate the decoder's behavior during the encoding process to avoid the problem of error drift. Indeed, the preferred paradigm is that of feed-forward compression, in which a spatiotemporal transform is followed by embedded quantization and coding. At the same time, to efficiently exploit interframe redundancy, it is important that the transform estimates the motion between frames and compensates for it in the temporal decomposition. Three-dimensional (3-D) discrete wavelet/subband trans- forms (DWTs) are highly desirable for scalable video compres-
---
paper_title: Directional spatial I-blocks for the MC-EZBC video coder

paper_content:

In subband/wavelet interframe video compression, motion-compensated coders make use of estimated motion paths to compress the data. When these motion paths are not valid, due to either occlusion or difficulty in their estimation, artifacts can sometimes be created in the embedded lower frame rate video. Since these coders are intended for scalable application, it is important that the lower frame rate video be as free of artifacts as possible. The incorporation of I-blocks in the context of hierarchical variable size block matching (HVSBM) allows for inevitable occasional poorly connected motion blocks. Directional spatial interpolation/prediction can then be employed to minimize such a block's energy in a temporal high frame. Results are provided for the MC-EZBC (motion compensated embedded zeroblock coding) coder that has been recently under investigation at MPEG.
---
paper_title: Three-dimensional lifting schemes for motion compensated video compression

paper_content:

Three-dimensional wavelet decompositions are efficient tools for scalable video coding. We show a lifting formulation for these decompositions. The temporal wavelet transform is inherently nonlinear, due to the motion estimation step, and the lifting formalism allows us to provide several improvements to the scheme initially proposed by Choi and Woods: a better processing of the uncovered areas is proposed and an overlapped motion-compensated temporal filtering method is introduced in the multiresolution decomposition. As shown by simulations, the proposed method results in higher coding efficiency, while keeping the scalability functionalities.
---
paper_title: Overview of the Scalable H.264/MPEG4-AVC Extension

paper_content:

The scalable extension of H.264/MPEG4-AVC is a current standardization project of the joint video team of the ITU-T Video Coding Experts Group and the ISO/IEC moving picture experts group. This paper gives an overview of the design of the scalable H.264/MPEG4-AVC extension and describes the basic concepts for supporting temporal, spatial, and SNR scalability. The efficiency of the described concepts for providing spatial and SNR scalability is analyzed by means of simulation results and compared to H.264/MPEG4-AVC compliant single layer coding.
---
paper_title: New results of phase shifting in the wavelet space

paper_content:

This paper investigates the relationship between even-phase coefficients and odd-phase coefficients in a two-channel perfect reconstruction filter bank. We demonstrate that they are linked to each other by a unique phase-shifting matrix. In the case of multilevel wavelet decomposition, we present an efficient recursive solution to directly perform phase shifting in the wavelet space. Our proposed solution can also be easily generalized into the case of two-dimensional wavelet transform. Direct phase-shifting methods in the wavelet space have potential applications in wavelet-based image/video coding and compressed domain processing.
---
paper_title: Bidirectional MC-EZBC with lifting implementation

paper_content:

In conventional motion-compensated three-dimensional subband/wavelet coding, where the motion compensation is unidirectional, incorrect classification of connected and unconnected pixels caused by incorrect motion vectors (MVs) has resulted in some coding inefficiency and visual artifacts in the embedded low-frame-rate video. In this paper, we introduce bidirectional motion compensated temporal filtering with unconnected pixel detection and I blocks. We also incorporate a recently suggested lifting implementation of the subband/wavelet filter for improved MV accuracy in an MC-EZBC coder. Simulation results compare PSNR performance of this new version of MC-EZBC versus H.26L under the constraint of equal groups of pictures size, and show a general parity with this state-of-the-art nonscalable coder on several test clips.
---
paper_title: 3D based video coding in the overcomplete discrete wavelet transform domain with reduced delay requirements

paper_content:

In this work, we propose a new temporal filter set to minimize delay in 3D wavelet based video coding, which gives a performance at par with existing longer filters. Our filter set will not have any boundary effects at the group of frames (GOF). The length of the GOF can vary from five to any number of frames depending on delay requirements. We also propose a novel technique of assigning priorities to temporal subbands at different levels to control distortion fluctuation inside a GOF. Experimental results are presented and conclusions are drawn.
---
paper_title: Unconstrained motion compensated temporal filtering (UMCTF) for efficient and flexible interframe wavelet video coding

paper_content:

We introduce an efficient and flexible framework for temporal filtering in wavelet-based scalable video codecs called unconstrained motion compensated temporal filtering (UMCTF). UMCTF allows for the use of different filters and temporal decomposition structures through a set of controlling parameters that may be easily modified during the coding process, at different granularities and levels. The proposed framework enables the adaptation of the coding process to the video content, network and end-device characteristics, allows for enhanced scalability, content-adaptivity and reduced delay, while improving the coding efficiency as compared to state-of-the-art motion-compensated wavelet video coders. Additionally, a mechanism for the control of the distortion variation in video coding based on UMCTF employing only the predict step is proposed. The control mechanism is formulated by expressing the distortion in an arbitrary decoded frame, at any temporal level in the pyramid, as a function of the distortions in the reference frames at the same temporal level. All the different scenarios proposed in the paper are experimentally validated through a coding scheme that incorporates advanced features (such as rate-distortion optimized variable block-size multihypothesis prediction and overlapped block motion compensation). Experiments are carried out to determine the relative efficiency of different UMCTF instantiations, as well as to compare against the current state-of-the-art in video coding.
---
paper_title: A resolution and frame-rate scalable subband/wavelet video coder

paper_content:

A source coding algorithm is presented which delivers a spatiotemporal scalable encoded bitstream. Motion compensated temporal filtering is combined with a spatial subband/wavelet pyramid to provide an efficient 3-D multiresolution representation. Error-feedback hierarchical coding permits near-optimal results for each subvideo. The proposed ordering of refinement addresses the noncommutative property of motion compensated temporal filtering and spatial subband/wavelet analysis. Finally, adaptive conditional arithmetic coding of quantizer significance maps increases coding efficiency. Experimental results demonstrate a significant improvement in performance over earlier published algorithms. The code-and-refine nature of our hierarchical algorithm makes it possible to use the algorithm as a scalable extension to other source coding algorithms. Finally, the complexity of the algorithm is modest and is well suited to parallel implementation.
---
paper_title: Fully scalable 3D overcomplete wavelet video coding using adaptive motion compensated temporal filtering

paper_content:

In this paper, we present a fully scalable 3-D overcomplete wavelet video coder that employs a new and highly efficient 3-D lifting structure for adaptive motion compensated temporal filtering (MCTF). Unlike the conventional interframe wavelet video techniques that apply MCTF on the spatial domain video data and then encode the resulting temporally filtered frames using critical sampled wavelet transforms, the scheme proposed in this paper performs first the spatial domain wavelet transform and subsequently applies MCTF for each wavelet band. To overcome the inefficiency of motion estimation in the wavelet domain, the low band shifting method (LBS) is used at both the encoder and decoder to generate an overcomplete representation of the temporal reference frames. A novel interleaving algorithm for the overcomplete wavelet coefficient is proposed that enables optimal sub-pixel accuracy motion estimation implementations. Furthermore, to achieve arbitrary accuracy motion estimation and compensation in the overcomplete wavelet domain with perfect reconstruction, a novel 3-D lifting structure is also introduced. Simulation results shows that the proposed fully scalable 3-D overcomplete wavelet video coder has comparable or better performance (up to 0.5dB) than the previously proposed interframe wavelet coders under the same coding conditions. Several techniques that can further improve the performance of the proposed overcomplete wavelet coding scheme are also discussed.
---
paper_title: Complete-to-overcomplete discrete wavelet transforms: theory and applications

paper_content:

A new transform is proposed that derives the overcomplete discrete wavelet transform (ODWT) subbands from the critically sampled DWT subbands (complete representation). This complete-to-overcomplete DWT (CODWT) has certain advantages in comparison to the conventional approach that performs the inverse DWT to reconstruct the input signal, followed by the a/spl grave/-trous or the lowband shift algorithm. Specifically, the computation of the input signal is not required. As a result, the minimum number of downsampling operations is performed and the use of upsampling is avoided. The proposed CODWT computes the ODWT subbands by using a set of prediction-filter matrices and filtering-and-downsampling operators applied to the DWT. This formulation demonstrates a clear separation between the single-rate and multirate components of the transform. This can be especially significant when the CODWT is used in resource-constrained environments, such as resolution-scalable image and video codecs. To illustrate the applicability of the proposed transform in these emerging applications, a new scheme for the transform-calculation is proposed, and existing coding techniques that benefit from its usage are surveyed. The analysis of the proposed CODWT in terms of arithmetic complexity and delay reveals significant gains as compared with the conventional approach.
---
paper_title: Video Coding with Motion-Compensated Lifted Wavelet Transforms

paper_content:

This article explores the efficiency of motion-compensated three-dimensional transform coding, a compression scheme that employs a motion-compensated transform for a group of pictures. We investigate this coding scheme experimentally and theoretically. The practical coding scheme employs in temporal direction a wavelet decomposition with motion-compensated lifting steps. Further, we compare the experimental results to that of a predictive video codec with single-hypothesis motion compensation and comparable computational complexity. The experiments show that the 5/3 wavelet kernel outperforms both the Haar kernel and, in many cases, the reference scheme utilizing single-hypothesis motion-compensated predictive coding. The theoretical investigation models this motion-compensated subband coding scheme for a group of K pictures with a signal model for K motion-compensated pictures that are decorrelated by a linear transform. We utilize the Karhunen-Loeve Transform to obtain theoretical performance bounds at high bit-rates and compare to both optimum intra-frame coding of individual motion-compensated pictures and single-hypothesis motion-compensated predictive coding. The investigation shows that motion-compensated three-dimensional transform coding can outperform predictive coding with single-hypothesis motion compensation by up to 0.5 bits/sample.
---
paper_title: An efficient content-adaptive motion-compensated 3-D DWT with enhanced spatial and temporal scalability

paper_content:

We propose a novel, content adaptive method for motion-compensated three-dimensional wavelet transformation (MC 3-D DWT) of video. The proposed method overcomes problems of ghosting and nonaligned aliasing artifacts which can arise in regions of motion model failure, when the video is reconstructed at reduced temporal or spatial resolutions. Previous MC 3-D DWT structures either take the form of MC temporal DWT followed by a spatial transform ("t+2D"), or perform the spatial transform first ("2D+t"), limiting the spatial frequencies which can be jointly compensated in the temporal transform, and hence limiting the compression efficiency. When the motion model fails, the "t+2D" structure causes nonaligned aliasing artifacts in reduced spatial resolution sequences. Essentially, the proposed transform continuously adapts itself between the "t+2D" and "2D+t" structures, based on information available within the compressed bit stream. Ghosting artifacts may also appear in reduced frame-rate sequences due to temporal low-pass filtering along invalid motion trajectories. To avoid the ghosting artifacts, we continuously select between different low-pass temporal filters, based on the estimated accuracy of the motion model. Experimental results indicate that the proposed adaptive transform preserves high compression efficiency while substantially improving the quality of reduced spatial and temporal resolution sequences.
---
paper_title: Motion Compensation and Scalability in Lifting-Based Video Coding

paper_content:

Abstract Motion-compensated temporal filtering subband video codecs have attracted recently a lot of attention, due to their compression performance comparable with that of state-of-the-art hybrid codecs and due to their additional scalability features. In this paper, we present a scalable video codec based on a 5/3 adaptive temporal lifting decomposition. Different adaptation criteria for coping with the occluded areas are discussed and new criteria for optimizing the temporal prediction are introduced. For our simulations, we use a memory-constraint “on-the-fly” implementation. We also evaluate the temporal scalability properties of this video coding structure.
---
paper_title: JPEG2000-compatible scalable scheme for wavelet-based video coding

paper_content:

We present a simple yet efficient scalable scheme for wavelet-based video coders, able to provide on-demand spatial, temporal, and SNR scalability, and fully compatible with the still-image coding standard JPEG2000. Whereas hybrid video coders must undergo significant changes in order to support scalability, our coder only requires a specific wavelet filter for temporal analysis, as well as an adapted bit allocation procedure based on models of rate-distortion curves. Our study shows that scalably encoded sequences have the same or almost the same quality than nonscalably encoded ones, without a significant increase in complexity. A full compatibility with Motion JPEG2000, which tends to be a serious candidate for the compression of high-definition video sequences, is ensured.
---
paper_title: A fully scalable 3D subband video codec

paper_content:

Multimedia transmissions over heterogeneous networks require a high degree of flexibility from video compression systems. They are expected to be fully scalable, that is to say to be able to partly decode a video bitstream and to get a reconstruction quality proportional to the received amount of information. To achieve this functionality, we propose a video codec based on 2D+t subband decomposition. Groups of frames are first temporally filtered using motion compensation and then spatially decomposed with wavelets. The spatiotemporal coefficients are further scanned and compressed using a new SPIHT-like strategy, namely fully scalable zerotree coding, together with arithmetic encoding, which provides a combination of temporal, spatial and SNR scalability. In addition, scalable motion vector coding ensures a fully progressive bitstream.
---
paper_title: Shape-Adaptive Embedded Coding of Ocean-Temperature Imagery

paper_content:

An embedded wavelet-based coder for the shape-adaptive coding of ocean-temperature data is described. The proposed coder, 3D binary set splitting with k-A trees (3D-BISK), is based upon the popular bitplane-coding paradigm and is specifically designed for shape-adaptive coding. Other similar coding methods use octree-based set partitioning; however, 3D-BISK employs a simpler set decomposition based on k-A trees which makes it more flexible when considering shape-adaptive coding. The performance of 3D-BISK is compared to prominent shape-adaptive coders and superior performance is demonstrated for a variety of ocean-temperature datasets.
---
paper_title: Overcomplete image coding using iterative projection-based noise shaping

paper_content:

Overcomplete transforms, like the dual-tree complex wavelet transform, offer more flexible signal representations than critically-sampled transforms. Large numbers of transform coefficients can be discarded without much reconstruction quality loss by forcing compensatory changes in the remaining coefficients. We develop and demonstrate a new and unique system for achieving these transform coding aims of coefficient elimination and compensation. The system is based on iterative projection of signals between the image domain and transform domain.
---
paper_title: Coding of ocean-temperature volumes using binary set splitting with k-d trees

paper_content:

An embedded wavelet-based coder for the shape-adaptive coding of ocean-temperature data is described. The proposed coder, 3D binary set splitting with k-d trees (3D-BISK), is based upon the popular bitplane-coding paradigm and is specifically designed for shape-adaptive coding. Other similar coding methods use octree-based set partitioning; however, 3D-BISK employs a simpler set decomposition based on k-d trees which makes it more flexible when considering shape-adaptive coding. The performance of 3D-BISK is compared to prominent shape-adaptive coders and superior performance is demonstrated for a variety of ocean-temperature datasets.
---
paper_title: An investigation of 3D dual-tree wavelet transform for video coding

paper_content:

This paper examines the properties of a recently introduced 3D dual-tree discrete wavelet transform (DDWT) for video coding. The 3D DDWT is an attractive video representation because it isolates motion along different directions in separate subbands. However, it is an overcomplete transform with 8:1 redundancy. We examine the effectiveness of the iterative projection-based noise shaping scheme proposed by Kingsbury et al., (2002) on reducing the number of coefficients. We also investigate the correlation between subbands at the same spatial/temporal location, both in the significance map and in actual coefficient values.
---
paper_title: Complex Wavelets for Shift Invariant Analysis and Filtering of Signals

paper_content:

Abstract This paper describes a form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. This introduces limited redundancy (2m:1 for m-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective filters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational efficiency with good well-balanced frequency responses. Here we analyze why the new transform can be designed to be shift invariant and describe how to estimate the accuracy of this approximation and design suitable filters to achieve this. We discuss two different variants of the new transform, based on odd/even and quarter-sample shift (Q-shift) filters, respectively. We then describe briefly how the dual tree may be extended for images and other multi-dimensional signals, and finally summarize a range of applications of the transform that take advantage of its unique properties.
---
paper_title: Low bit-rate scalable video coding with 3-D set partitioning in hierarchical trees (3-D SPIHT)

paper_content:

We propose a low bit-rate embedded video coding scheme that utilizes a 3-D extension of the set partitioning in hierarchical trees (SPIHT) algorithm which has proved so successful in still image coding. Three-dimensional spatio-temporal orientation trees coupled with powerful SPIHT sorting and refinement renders 3-D SPIHT video coder so efficient that it provides comparable performance to H.263 objectively and subjectively when operated at the bit rates of 30 to 60 kbits/s with minimal system complexity. Extension to color-embedded video coding is accomplished without explicit bit allocation, and can be used for any color plane representation. In addition to being rate scalable, the proposed video coder allows multiresolutional scalability in encoding and decoding in both time and space from one bit stream. This added functionality along with many desirable attributes, such as full embeddedness for progressive transmission, precise rate control for constant bit-rate traffic, and low complexity for possible software-only video applications, makes the proposed video coder an attractive candidate for multimedia applications.
---
paper_title: An embedded wavelet video coder using three-dimensional set partitioning in hierarchical trees (SPIHT)

paper_content:

The SPIHT (set partitioning in hierarchical trees) algorithm by Said and Pearlman (see IEEE Trans. on Circuits and Systems for Video Technology, no.6, p.243-250, 1996) is known to have produced some of the best results in still image coding. It is a fully embedded wavelet coding algorithm with precise rate control and low complexity. We present an application of the SPIHT algorithm to video sequences, using three-dimensional (3D) wavelet decompositions and 3D spatio-temporal dependence trees. A full 3D-SPIHT encoder/decoder is implemented in software and is compared against MPEG-2 in parallel simulations. Although there is no motion estimation or compensation in the 3D SPIHT, it performs measurably and visually better than MPEG-2, which employs complicated motion estimation and compensation.
---
paper_title: Three dimensional sub-band coding of video

paper_content:

A novel coding scheme has been developed which is based on multidimensional subband coding. The digital video signal is filtered and sub-sampled in all three dimensions (temporally, horizontally and vertically) to yield the subbands, from which the input signal can be losslessly reconstructed in the absence of coding loss. The subbands can be more efficiently coded than the input signal in terms of compression and quality, because the restricted information in each band allows well-tailored encoding. The computational complexity of this coding scheme compares favorably to DCT with interframe prediction and inter/intra frame DPCM. The scheme has an architectural structure suitable for parallel implementation, and it yields high compression with sustained good quality. >
---
paper_title: Video Coding Using a Complex Wavelet Transform and Set Partitioning

paper_content:

A video-coding system that exploits the motion-selective characteristics of the 3-D complex dual-tree discrete wavelet transform is presented. The proposed system does not perform explicit motion compensation but instead relies on the dual-tree transform to isolate moving features. Although the dual-tree transform is redundant, a noise-shaping process increases the sparsity of the transform coefficients, resulting in a high degree of spatiotemporally coherent regions of insignificant coefficients. The transform coefficients are coded with binary set-partitioning using k-d trees in an algorithm that exploits both within-subband spatiotemporal coherency as well as cross-subband correlation to achieve efficient coding. Experimental results demonstrate that the proposed system outperforms other coders that also do not perform explicit motion estimation or compensation.
---
paper_title: Shape-adaptive coding using binary set splitting with k-d trees

paper_content:

The binary set splitting with k-d trees (BISK) algorithm is introduced. An embedded wavelet-based image coder based on the popular bitplane-coding paradigm, BISK is designed specifically for the coding of image objects with arbitrary shape. While other similar algorithms employ quadtree-based set partitioning to code significance-map information, BISK uses a simpler and more flexible, binary decomposition via k-d trees. Additionally, aggressive discarding of transparent regions is implemented by shrinking sets to the bounding box of their constituent opaque coefficients before further partitioning. Empirical results indicate that the proposed BISK coder consistently yields efficient performance when compared to a variety of other shape-adaptive coders.
---
paper_title: Shape-Adaptive Embedded Coding of Ocean-Temperature Imagery

paper_content:

An embedded wavelet-based coder for the shape-adaptive coding of ocean-temperature data is described. The proposed coder, 3D binary set splitting with k-A trees (3D-BISK), is based upon the popular bitplane-coding paradigm and is specifically designed for shape-adaptive coding. Other similar coding methods use octree-based set partitioning; however, 3D-BISK employs a simpler set decomposition based on k-A trees which makes it more flexible when considering shape-adaptive coding. The performance of 3D-BISK is compared to prominent shape-adaptive coders and superior performance is demonstrated for a variety of ocean-temperature datasets.
---
paper_title: Video denoising using 2D and 3D dual-tree complex wavelet transforms

paper_content:

The denoising of video data should take into account both temporal and spatial dimensions, however, true 3D transforms are rarely used for video denoising. Separable 3-D transforms have artifacts that degrade their performance in applications. This paper describes the design and application of the non-separable oriented 3-D dual-tree wavelet transform for video denoising. This transform gives a motion-based multi-scale decomposition for video - it isolates in its subbands motion along different directions. In addition, we investigate the denoising of video using the 2-D and 3-D dual-tree oriented wavelet transforms, where the 2-D transform is applied to each frame individually.
---
paper_title: Nonlinear Wavelet Transforms for Image Coding via Lifting

paper_content:

We investigate central issues such as invertibility, stability, synchronization, and frequency characteristics for nonlinear wavelet transforms built using the lifting framework. The nonlinearity comes from adaptively choosing between a class of linear predictors within the lifting framework. We also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood of pixels. Preliminary compression results for model and real-world images demonstrate the promise of our techniques.
---
paper_title: Lifting scheme: a new philosophy in biorthogonal wavelet constructions

paper_content:

In this paper we present the basic idea behind the lifting scheme, a new construction of biorthogonal wavelets which does not use the Fourier transform. In contrast with earlier papers we introduce lifting purely from a wavelet transform point of view and only consider the wavelet basis functions in a later stage. We show how lifting leads to a faster, fully in- plane implementation of the wavelet transform. Moreover, it can be used in the construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one function. A typical example of the latter are wavelets on the sphere.
---
paper_title: Combining Seminorms in Adaptive Lifting Schemes and Applications to Image Analysis and Compression

paper_content:

In this paper, we present some adaptive wavelet decompositions that can capture the directional nature of images. Our method exploits the properties of seminorms to build lifting structures able to choose between different update filters, the choice being triggered by the local gradient-type features of the input. In order to deal with the variety and wealth of images, one has to be able to use multiple criteria, giving rise to multiple choice of update filters. We establish the conditions under these decisions can be recovered at synthesis, without the need for transmitting overhead information. Thus, we are able to design invertible and non-redundant schemes that discriminate between different geometrical information to efficiently represent images for lossless compression methods.
---
paper_title: Adaptive Wavelets for Image Compression Using Update Lifting-Quantization and Error Analysis

paper_content:

Classical linear wavelet representations of images have the drawback that they are not optimally suited to represent edge information. To overcome this problem, nonlinear multiresolution decompositions have been designed that can take into account the characteristics of the input signal or image. The adaptive update lifting framework is introduced that does not require bookkeeping but has the property that it processes edges and homogeneous image regions in different fashion. The effect of scalar uniform quantization in an adaptive multiresolution analysis based on lifting implementation is analyzed. Such an analysis is essential for the application of these adaptive decompositions in image compression. Conditions are provided for recovering the original decisions at the synthesis and show how to estimate the reconstruction error in terms of the quantization error.
---
paper_title: Gradient-driven update lifting for adaptive wavelets

paper_content:

Abstract Over the past few years, wavelets have become extremely popular in signal and image processing applications. The classical linear wavelet transform, however, performs a homogeneous smoothing of the signal contents which, in some cases, is not desirable. This has led to a growing interest in (nonlinear) wavelet representations that can preserve discontinuities, such as transitions and edges. In this paper, we present the construction of adaptive wavelets by means of an extension of the lifting scheme. The basic idea is to choose the update filters according to some decision criterion which depends on the local characteristics of the input signal. We show that these adaptive schemes yield lower entropies than schemes with fixed update filters, a property that is highly relevant in the context of compression . Moreover, we analyze the effect of a scalar uniform quantization and the stability in such adaptive wavelet decompositions.
---
paper_title: Nonlinear wavelet transforms for image coding

paper_content:

We examine the central issues of invertibility, stability, artifacts, and frequency-domain characteristics in the construction of nonlinear analogs of the wavelet transform. The lifting framework for wavelet construction motivates our analysis and provides new insight into the problem. We describe a new type of nonlinearity for use in constructing nonlinear transforms: a set of linear predictors that are chosen adaptively using a nonlinear selection function. We also describe how earlier families of nonlinear filter banks can be extended through the use of prediction functions operating on a causal neighborhood. We present preliminary results for a synthetic test image.
---
paper_title: Adaptive update lifting with a decision rule based on derivative filters

paper_content:

This letter treats a class of adaptive update-lifting schemes that do not require bookkeeping for perfect reconstruction. The choice of the update-lifting filter is triggered by a binary threshold criterion based on a generalized gradient that is chosen in such a way that it only smooths homogeneous regions. This criterion can be chosen so that it ignores portions of a signal that are polynomial up to a given order. The update-lifting filter modifies the signal in these polynomial regions but leaves other portions unaffected.
---
paper_title: Optimized lifting scheme for two-dimensional quincunx sampling images

paper_content:

This paper introduces the problem of designing a quincunx lifting scheme well-adapted to lossy compression applications. The main goal is to design quincunx filters adapted to the statistical properties of the input signal in order to perform a better signal reconstruction after deterioration due to a lossy coding. To perform such a filtering, the basic idea is to combine optimization methods and a lifting scheme. The latter is an attractive tool to perform wavelet transforms.
---
paper_title: Quantization of adaptive 2D wavelet decompositions

paper_content:

Classical linear wavelet representations of images have the drawback that they are not well suited to represent edge information. To overcome this problem, nonlinear multiresolution decompositions are being designed that can take into account the characteristics of the input signal/image. In our previous work [(G. Piella et al., July 2002), (H.J.A.M. Heijmans et al., 2002)] we have introduced an adaptive lifting framework that does not require bookkeeping but has the property that it processes edges and homogeneous regions in an image in a different fashion. The current paper discusses the effects of quantization in such adaptive wavelet decomposition. We provide conditions for recovering the original decisions at the synthesis and for relating the reconstruction error to the quantization error. Such an analysis is essential for the application of these adaptive decompositions in image compression algorithms.
---
paper_title: A 2-D orientation-adaptive prediction filter in lifting structures for image coding

paper_content:

Lifting-style implementations of wavelets are widely used in image coders. A two-dimensional (2-D) edge adaptive lifting structure, which is similar to Daubechies 5/3 wavelet, is presented. The 2-D prediction filter predicts the value of the next polyphase component according to an edge orientation estimator of the image. Consequently, the prediction domain is allowed to rotate +/-45 degrees in regions with diagonal gradient. The gradient estimator is computationally inexpensive with additional costs of only six subtractions per lifting instruction, and no multiplications are required.
---
paper_title: Building adaptive 2D wavelet decompositions by update lifting

paper_content:

The paper discusses a method for the construction of nonlinear 2D wavelet decompositions using an adaptive update lifting scheme. A very interesting aspect is that the decomposition does not require any bookkeeping, i.e., it is nonredundant, but that it, nevertheless, allows perfect reconstruction. The major ingredient of the construction is the so-called decision map which triggers the choice of the update filter. Another interesting point is the possibility of better preserving edges, even at low resolutions.
---
paper_title: An adaptive update lifting scheme with perfect reconstruction

paper_content:

The lifting scheme provides a general and flexible tool for the construction of wavelet decompositions and perfect reconstruction filter banks. We propose an adaptive version of this scheme which has the intriguing property that it allows perfect reconstruction without any overhead cost. We restrict ourselves to the update lifting step which affects the approximation signal only. The update lifting filter is assumed to depend pointwise on the norm of the associated gradient vector, in such a way that a large gradient induces a weak update filter. Thus, sharp transitions in a signal (eg, edges in an image) will not be smoothed to the same extent as regions which are more homogeneous.
---
paper_title: Adaptive lifting for multicomponent image coding through quadtree partitioning

paper_content:

The objective of this paper is the design of adaptive quincunx lifting schemes for lossless compression of multiband images. More precisely, the operators of the lifting scheme are modified according to the local activity of the multivariate input signal. To this respect, a block-based adaptive strategy is adopted: the image is partitioned into a quadtree structure and a couple of optimal operators is assigned to each resulting volumetric segmented block. Our main contribution consists of a suitable quadtree partitioning rule that takes into account simultaneously the spatial and spectral redundancies. Simulations performed on real satellite images show that the proposed adaptive method outperforms the conventional non-adaptive lifting schemes.
---
paper_title: Adaptive Lifting Schemes With Perfect Reconstruction

paper_content:

textabstractIn this paper, we propose a framework for constructing adaptive wavelet decompositions using the lifting scheme. A major requirement is that perfect reconstruction is possible without any overhead cost. In this paper we restrict ourselves to the update lifting stage. It is assumed that the update filter utilises local gradient information to adapt itself to the signal in the sense that smaller gradients `evoke' stronger update filters. As a result, sharp transitions in a signal will not be smoothed to the same extent as regions which are more homogeneous. The approach taken in this paper differs from other adaptive schemes found in the literature in the sense that that no bookkeeping is required in order to have perfect reconstruction.
---
paper_title: Adaptive update lifting with gradient criteria modeling high-order differences

paper_content:

This paper treats a class of adaptive update lifting schemes which do not require bookkeeping for perfect reconstruction. The choice of the update lifting filter is triggered by a binary threshold criterion based on a generalised gradient which is chosen in such a way that it only smoothes homogeneous regions. More precisely, the criterion can be chosen so that it ‘recognises’ signals that are polynomial up to a given order. The lifting filter updates the signal in these polynomial regions but leaves other parts unaffected.
---
paper_title: Factoring wavelet transforms into lifting steps

paper_content:

This article is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is well-known to algebraists (and expressed by the formulaSL(n;R[z, z−1])=E(n;R[z, z−1])); it is also used in linear systems theory in the electrical engineering community. We present here a self-contained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering. This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the biorthogonal, i.e., non-unitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a wavelet-like transform that maps integers to integers.
---
paper_title: Lossless image compression using integer to integer wavelet transforms

paper_content:

Invertible wavelet transforms that map integers to integers are important for lossless representations. We present an approach to build integer to integer wavelet transforms based upon the idea of factoring wavelet transforms into lifting steps. This allows the construction of an integer version of every wavelet transform. We demonstrate the use of these transforms in lossless image compression.
---
paper_title: Signal-Adapted Multiresolution Transform for Image Coding

paper_content:

Wavelet-type multiresolution transforms have recently been introduced in digital image coding, and have been shown to offer some advantages over classical block transform techniques such as the discrete cosine transform (DCT). This correspondence is mainly concerned with the problem of designing suitable multiresolution transforms that are adapted to the given image signal, in the sense that they maximize the coding gain at each resolution level. A simple alternating optimization algorithm is derived for solving this problem in the framework of the lattice realization of para-unitary quadrature mirror filters (QMF). The resulting image coding scheme is discussed in some detail, and its
---
paper_title: Quincunx lifting scheme for lossy image compression

paper_content:

Quincunx sampling is of large interest for image coding applications. Recent remote sensors of satellites return quincunx sampled images. Moreover, a quincunx sampling allows the decomposition of the image into two channels and a twice as accurate multiresolution analysis as the dyadic one. This paper introduces a new construction of the quincunx wavelet transform. This new transform is a bidimensional extension of the factorization of a wavelet transform into a lifting scheme for finite and symmetrical low pass filters. The aim of this method is to deal with quincunx images with appropriate transforms while using advantages offered by the lifting scheme. This method allows us to find new efficient quincunx wavelet filters.
---
paper_title: Wavelet transforms that map integers to integers

paper_content:

Abstract Invertible wavelet transforms that map integers to integers have important applications in lossless coding. In this paper we present two approaches to build integer to integer wavelet transforms. The first approach is to adapt the precoder of Laroiaet al.,which is used in information transmission; we combine it with expansion factors for the high and low pass band in subband filtering. The second approach builds upon the idea of factoring wavelet transforms into so-called lifting steps. This allows the construction of an integer version of every wavelet transform. Finally, we use these approaches in a lossless image coder and compare the results to those given in the literature.
---
paper_title: Reversible multiresolution image coding based on adaptive lifting

paper_content:

We first calculate the optimal predictors of a lifting scheme in the general n-dimensional case. Then, we apply these optimal predictor filters with corresponding update filters for the lossless compression of still images using simple row-column sampling. The efficiency of the linear predictor is enhanced by nonlinear means, namely by adaptive-length postprocessing. The resulting filter bank in effect adapts to the features of the area of the image being processed and in this way it is shown to achieve superior performance than even the most efficient known lossless compression methods capable of progressive transmission.
---
paper_title: Adaptively quadratic (AQua) image interpolation

paper_content:

Image interpolation is a key aspect of digital image processing. This paper presents a novel interpolation method based on optimal recovery and adaptively determining the quadratic signal class from the local image behavior. The advantages of the new interpolation method are the ability to interpolate directly by any factor and to model properties of the data acquisition system into the algorithm itself. Through comparisons with other algorithms it is shown that the new interpolation is not only mathematically optimal with respect to the underlying image model, but visually it is very efficient at reducing jagged edges, a place where most other interpolation algorithms fail.
---
paper_title: Lossless image compression based on optimal prediction, adaptive lifting, and conditional arithmetic coding

paper_content:

The optimal predictors of a lifting scheme in the general n-dimensional case are obtained and applied for the lossless compression of still images using first quincunx sampling and then simple row-column sampling. In each case, the efficiency of the linear predictors is enhanced nonlinearly. Directional postprocessing is used in the quincunx case, and adaptive-length postprocessing in the row-column case. Both methods are seen to perform well. The resulting nonlinear interpolation schemes achieve extremely efficient image decorrelation. We further investigate context modeling and adaptive arithmetic coding of wavelet coefficients in a lossless compression framework. Special attention is given to the modeling contexts and the adaptation of the arithmetic coder to the actual data. Experimental evaluation shows that the best of the resulting coders produces better results than other known algorithms for multiresolution-based lossless image coding.
---
paper_title: Adaptive polyphase subband decomposition structures for image compression

paper_content:

Subband decomposition techniques have been extensively used for data coding and analysis. In most filter banks, the goal is to obtain subsampled signals corresponding to different spectral regions of the original data. However, this approach leads to various artifacts in images having spatially varying characteristics, such as images containing text, subtitles, or sharp edges. In this paper, adaptive filter banks with perfect reconstruction property are presented for such images. The filters of the decomposition structure which can be either linear or nonlinear vary according to the nature of the signal. This leads to improved image compression ratios. Simulation examples are presented.
---
paper_title: The Lifting Scheme: A Construction Of Second Generation Wavelets

paper_content:

We present the lifting scheme, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to a faster, in-place calculation of the wavelet transform. Several examples are included.
---
paper_title: Adaptive, non-separable lifting transforms for image compression

paper_content:

In the context of high performance image compression algorithms, such as that emerging as the JPEG 2000 standard, the wavelet transform has demonstrated excellent compression performance with natural images. Like all waveform coding techniques, however, performance suffers in the neighbourhood of oriented edges clad with artificial imagery such as text and graphics. In this paper, we explore some of the opportunities offered by the framework of lifting for developing adaptive wavelet transforms to improve performance under these conditions.
---
paper_title: Design of signal-adapted multidimensional lifting scheme for lossy coding

paper_content:

This paper proposes a new method for the design of lifting filters to compute a multidimensional nonseparable wavelet transform. Our approach is stated in the general case, and is illustrated for the 2-D separable and for the quincunx images. Results are shown for the JPEG2000 database and for satellite images acquired on a quincunx sampling grid. The design of efficient quincunx filters is a difficult challenge which has already been addressed for specific cases. Our approach enables the design of less expensive filters adapted to the signal statistics to enhance the compression efficiency in a more general case. It is based on a two-step lifting scheme and joins the lifting theory with Wiener's optimization. The prediction step is designed in order to minimize the variance of the signal, and the update step is designed in order to minimize a reconstruction error. Application for lossy compression shows the performances of the method.
---
paper_title: Resolution enhancement of images using wavelet transform extrema extrapolation

paper_content:

One problem of image interpolation refers to magnifying a small image without loss in image clarity. We propose a wavelet based method which estimates the higher resolution information needed to sharpen the image. This method extrapolates the wavelet transform of the higher resolution based on the evolution of the wavelet transform extrema across the scales. By identifying three constraints that the higher resolution information needs to obey, we enhance the reconstructed image through alternating projections onto the sets defined by these constraints.
---
paper_title: Image interpolation using wavelet based hidden Markov trees

paper_content:

Hidden Markov trees in the wavelet domain are capable of accurately modeling the statistical behavior of real world signals by exploiting relationships between coefficients in different scales. The model is used to interpolate images by predicting coefficients at finer scales. Various optimizations and post-processing steps are also investigated to determine their effect on the performance of the interpolation. The interpolation algorithm was found to produce noticeably sharper images with PSNR values which outperform many other interpolation techniques on a variety of images.
---
paper_title: Locally adaptive wavelet-based image interpolation

paper_content:

We describe a spatially adaptive algorithm for image interpolation. The algorithm uses a wavelet transform to extract information about sharp variations in the low-resolution image and then implicitly applies interpolation which adapts to the image local smoothness/singularity characteristics. The proposed algorithm yields images that are sharper compared to several other methods that we have considered in this paper. Better performance comes at the expense of higher complexity.
---
paper_title: The foundations of set theoretic estimation

paper_content:

Explains set theoretic estimation, which is governed by the notion of feasibility and produces solutions whose sole property is to be consistent with all information arising from the observed data and a priori knowledge. Each piece of information is associated with a set in the solution space, and the intersection of these sets, the feasibility set, represents the acceptable solutions. The practical use of the set theoretic framework stems from the existence of efficient techniques for finding these solutions. Many scattered problems in systems science and signal processing have been approached in set theoretic terms over the past three decades. The author synthesizes a single, general framework from these various approaches, examines its fundamental philosophy, goals, and analytical techniques, and relates it to conventional methods. >
---
paper_title: Prediction of image detail

paper_content:

In the problem of image interpolation, most of the difficulties arise in areas around edges and sharp changes. Around edges, many interpolation methods tend to smooth and blur image detail. Fortunately, most of the signal information is often carried around edges and areas of sharp changes and can be used to predict these missing details from a sampled image. A method for adding image detail based on the cone of influence, the evolution of the wavelet coefficients across scales, is presented.
---
paper_title: Image interpolation based on inter-scale dependency in wavelet domain

paper_content:

Image interpolation in the wavelet domain can be considered as the estimation of wavelet coefficients in the highest frequency subband. In this paper, a novel image interpolation method based on inter-scale dependency in the wavelet domain is proposed. In our method, the Gaussian mixture model (GMM) is used to estimate the magnitude of the wavelet coefficient, and the parameters of the GMM are derived from subbands with no training. The sign of the estimated wavelet coefficient is also obtained by using the inter-scale dependency of wavelet subbands. In the simulation results, the proposed method shows an improved PSNR and subjective quality compared with conventional bicubic method and the statistical method (K. Kinebuchi et al., May, 2001) that exploits the hidden Markov tree (HMT) model with training.
---
paper_title: Wavelet domain image interpolation via statistical estimation

paper_content:

We propose a new wavelet domain image interpolation scheme based on statistical signal estimation. A linear composite MMSE estimator is constructed to synthesize the detailed wavelet coefficients as well as to minimize the mean squared error for high-resolution signal recovery. Based on a discrete time edge model, we use low-resolution information to characterize local intensity changes and perform resolution enhancement accordingly. A linear MMSE estimator follows to minimize the estimation error. Local image statistics are involved in determining the spatially adaptive optimal estimator. With knowledge of edge behavior and local signal statistics, the composite estimation is able to enhance important edges and to maintain the intensity consistency along edges. Strong improvement in both the visual quality and the PSNRs of the interpolated images has been achieved by the proposed estimation scheme.
---
paper_title: Characterization of Signals from Multiscale Edges

paper_content:

A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. The authors study the properties of multiscale edges through the wavelet theory. For pattern recognition, one often needs to discriminate different types of edges. They show that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures. Numerical descriptors of edge types are derived. The completeness of a multiscale edge representation is also studied. The authors describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges. For images, the reconstruction errors are below visual sensitivity. As an application, a compact image coding algorithm that selects important edges and compresses the image data by factors over 30 has been implemented. >
---
paper_title: On a source-coding problem with two channels and three receivers

paper_content:

This paper treats the problem of communicating a memoryless unit-variance Gaussian source to three receivers. Two channels are available, each with a separate receiver. A third receiver has the outputs of both channels available. We obtain an expression for the simultaneously achievable distortions (mean-squared error). This problem applies to the following situation: Assume that high-quality reproduction of a source is desired at a single receiver which is connected to the source over a pair of links operating in parallel. Further assume that the links are unreliable in that either may fail, and that the source encoder is unaware of the failures. One can then ask how “robust” a system designed for this situation can be. That is, what are the limits on the fidelity achievable when both links are functioning if graceful degradation is required during the failure of either link? An inverse relation between performance in the two modes is obtained in the sense that, as performance in the presence of both links approaches its theoretical optimum, average distortion during failures becomes large. Conversely, if near-ideal performance during link failures is desired, then the distortion achieved when both links operate is far from its optimum value.
---
paper_title: Filter bank frame expansions with erasures

paper_content:

We study frames for robust transmission over the Internet. In our previous work, we used quantized finite-dimensional frames to achieve resilience to packet losses; here, we allow the input to be a sequence in l/sub 2/(Z) and focus on a filter-bank implementation of the system. We present results in parallel, R/sup N/ or C/sup N/ versus l/sub 2/(Z), and show that uniform tight frames, as well as newly introduced strongly uniform tight frames, provide the best performance.
---
paper_title: Design of entropy-constrained multiple-description scalar quantizers

paper_content:

The problem of entropy-constrained multiple-description scalar quantizer design is posed as an optimization problem, necessary conditions for optimality are derived, and an iterative design algorithm is presented. Performance results are presented for a Gaussian source, along with comparisons to the multiple-description rate distortion bound and a reference system. >
---
paper_title: Design of multiple description scalar quantizers

paper_content:

The design of scalar quantizers for communication systems that use diversity to overcome channel impairments is considered. The design problem is posed as an optimization problem and necessary conditions for optimality are derived. A design algorithm, a generalization of S.P. Lloyd's (1962) algorithm for quantizer design, is developed. Unlike a single channel scalar quantizer, the performance of a multiple description scalar quantizer is dependent on the index assignment. The problem of index assignment is addressed. Good index assignments, performance results, and sample quantizer designs are presented for a memoryless Gaussian source. Comparisons are made with rate distortion bounds for the multiple description problem. >
---
paper_title: Quantized frame expansions as source-channel codes for erasure channels

paper_content:

Quantized frame expansions are proposed as a method for generalized multiple description coding, where each quantized coefficient is a description. Whereas previous investigations have revealed the robustness of frame expansions to additive noise and quantization, this represents a new application of frame expansions. The performance of a system based on quantized frame expansions is compared to that of a system with a conventional block channel code. The new system performs well when the number of lost descriptions (erasures on an erasure channel) is hard to predict.
---
paper_title: Reliable video communication over lossy packet networks using multiple state encoding and path diversity

paper_content:

Video communication over lossy packet networks such as the Internet is hampered by limited bandwidth and packet loss. This paper presents a system for providing reliable video communication over these networks, where the system is composed of two subsystems: (1) multiple state video encoder/decoder and (2) a path diversity transmission system. Multiple state video coding combats the problem of error propagation at the decoder by coding the video into multiple independently decodable streams, each with its own prediction process and state. If one stream is lost the other streams can still be decoded to produce usable video, and furthermore, the correctly received streams provide bidirectional (previous and future) information that enables improved state recovery for the corrupted stream. This video coder is a form of multiple description coding (MDC), and its novelty lies in its use of information from the multiple streams to perform state recovery at the decoder. The path diversity transmission system explicitly sends different subsets of packets over different paths, as opposed to the default scenarios where the packets proceed along a single path, thereby enabling the end- to-end video application to effectively see an average path behavior. We refer to this as path diversity. Generally, seeing this average path behavior provides better performance than seeing the behavior of any individual random path. For example, the probability that all of the multiple paths are simultaneously congested is much less than the probability that a single path is congested. The resulting path diversity provides the multiple state video decoder with an appropriate virtual channel to assist in recovering from lost packets, and can also simplify system design, e.g. FEC design. We propose two architectures for achieving path diversity, and examine the effectiveness of path diversity in communicating video over a lossy packet network.
---
paper_title: Quantized Frame Expansions with Erasures

paper_content:

Abstract Frames have been used to capture significant signal characteristics, provide numerical stability of reconstruction, and enhance resilience to additive noise. This paper places frames in a new setting, where some of the elements are deleted. Since proper subsets of frames are sometimes themselves frames, a quantized frame expansion can be a useful representation even when some transform coefficients are lost in transmission. This yields robustness to losses in packet networks such as the Internet. With a simple model for quantization error, it is shown that a normalized frame minimizes mean-squared error if and only if it is tight. With one coefficient erased, a tight frame is again optimal among normalized frames, both in average and worst-case scenarios. For more erasures, a general analysis indicates some optimal designs. Being left with a tight frame after erasures minimizes distortion, but considering also the transmission rate and possible erasure events complicates optimizations greatly.
---
paper_title: Optimal pairwise correlating transforms for multiple description coding

paper_content:

Multiple description coding (MDC) addresses the problem of encoding a source into two (or more) bitstreams such that a high-quality reconstruction is decodable from the two bitstreams together, while a lower, but still acceptable, quality reconstruction is decodable if either of the two bitstreams is lost. Recent research has proposed using transforms to introduce a controlled amount of correlation between the two bitstreams in order to achieve MDC objectives. This paper considers several optimality issues related to such transform based MDC methods. Redundancy rate-distortion (RRD) performance of a general class of transforms is derived and used to identify the optimal transform for achieving any given amount of redundancy. Then, the paper introduces a more general transform-based MDC framework incorporating both the transform mode of redundancy and a second mode of redundancy. The optimal allocation of redundancy among these two modes is analyzed.
---
paper_title: Multiple Description Coding with Many Channels

paper_content:

An achievable region for the L-channel multiple description coding problem is presented. This region generalizes two-channel results of El Gamal and Cover (1982) and of Zhang and Berger (1987). It further generalizes three-channel results of Gray and Wyner (1974) and of Zhang and Berger. A source that is successively refinable on chains is shown to be successively refinable on trees. A new outer bound on the rate-distortion (RD) region for memoryless Gaussian sources with mean squared error distortion is also derived. The achievable region meets this outer bound for certain symmetric cases.
---
paper_title: Optimal multiple description subband coding

paper_content:

Multiple description coding refers to encoding an information source into multiple bitstreams, in a way that various levels of tradeoff between decoding quality and channel protection can be supported. This paper addresses the design of two-channel orthonormal filter banks to optimize the redundancy rate-distortion performance of multiple description subband coding. The problem is formulated in a Lagrangian optimization framework, and is solved directly in the frequency domain to produce the optimal filter responses. By varying the Lagrangian parameter, our design obtains all points on the information redundancy rate-distortion curve for Gaussian wide sense stationary input processes. Application of the proposed algorithm to the popular AR(1) model yields very interesting and insightful results. Comparisons with popularly deployed filter banks reveal large gaps from the theoretical performance bound.
---
paper_title: Multiple description image coding for noisy channels by pairing transform coefficients

paper_content:

Multiple description coding (MDC) is a way of trading off coding gain with robustness to channel errors. This paper presents a new method for MDC using the framework of transform coding. Instead of using the Karhunen-Loeve transform (KLT) that decorrelates all the coefficients, we choose the transform bases so that the coefficients are correlated pair-wise. This is accomplished by rotating every two basis vectors in the KLT. Each pair of correlated coefficients are then split between two descriptions. Only 45/spl deg/ rotation is considered which leads to two balanced streams. In the actual implementation, the DCT is employed in place of the KLT and the rotation of transform bases is accomplished by rotating the DCT coefficients. Experimental results show that this method can lead to satisfactory image reconstruction from any one description with a relatively small (20% for "lena") overhead over a standard JPEG coder.
---
paper_title: Multiple description coding via polyphase transform and selective quantization

paper_content:

In this paper, we present an efficient Multiple Description Coding (MDC) technique to achieve robust communication over unreliable channels such as a lossy packet network. We first model such unreliable channels as erasure channels and then we present a MDC system using polyphase transform and selective quantization to recover channel erasures. Different from previous MDC work, our system explicitly separates description generation and redundancy addition which greatly reduces the implementation complexity specially for systems with more than two descriptions. Our system also realizes a Balanced Multiple Description Coding (BMDC) framework which can generate descriptions of statistically equal rate and importance. This property is well matched to communication systems with no priority mechanisms for data delivery, such as today's Internet. We then study, for a given total coding rate, the problem of optimal bit allocation between source coding and redundancy coding to achieve the minimum average distortion for different channel failure rates. With high resolution quantization assumption, we give optimal redundancy bit rate allocations for both scalar i.i.d sources and vector i.i.d sources for independent channel failures. To evaluate the performance of our system, we provide an image coding application with two descriptions and our simulation results are better than the best MDC image coding results reported to date. We also provide image coding examples with 16 descriptions to illustrate the simplicity and effectiveness of our proposed MDC system.
---
paper_title: Multiple Description Coding: Compression Meets the Network

paper_content:

This article focuses on the compressed representations of pictures. The representation does not affect how many bits get from the Web server to the laptop, but it determines the usefulness of the bits that arrive. Many different representations are possible, and there is more involved in their choice than merely selecting a compression ratio. The techniques presented represent a single information source with several chunks of data ("descriptions") so that the source can be approximated from any subset of the chunks. By allowing image reconstruction to continue even after a packet is lost, this type of representation can prevent a Web browser from becoming dormant.
---
paper_title: Multiple Description Coding Using Pairwise Correlating Transforms

paper_content:

The objective of multiple description coding (MDC) is to encode a source into multiple bitstreams supporting multiple quality levels of decoding. In this paper, we only consider the two-description case, where the requirement is that a high-quality reconstruction should be decodable from the two bitstreams together, while lower, but still acceptable, quality reconstructions should be decodable from either of the two individual bitstreams. This paper describes techniques for meeting MDC objectives in the framework of standard transform-based image coding through the design of pairwise correlating transforms. The correlation introduced by the transform helps to reduce the distortion when only a single description is received, but it also increases the bit rate beyond that prescribed by the rate-distortion function of the source. We analyze the relation between the redundancy (i.e., the extra bit rate) and the single description distortion using this transform-based framework. We also describe an image coder that incorporates the pairwise transform and show its redundancy-rate-distortion performance for real images.
---
paper_title: Multiple-description wavelet based image coding

paper_content:

We consider the problem of image coding for communication systems that use diversity to overcome channel impairments. We focus on the special case in which there are two channels of equal capacity between a transmitter and a receiver. Our designs are based on a combination of techniques successfully applied to the construction of some of the most efficient wavelet based image coding algorithms, with multiple description scalar quantizers (MDSQs). For a given image, we produce two bitstreams, to be transmitted over each channel. Should one of the channels fail, each individual description guarantees a minimum image quality specified by the user. However, if both descriptions arrive at destination, they are combined to produce a higher quality image than that achievable based on individual descriptions. We formulate a discrete optimization problem, whose solution gives parameters of the proposed encoder yielding optimal performance in an operational sense. Simulation results are presented.
---
paper_title: Optimal subband filter banks for multiple description coding

paper_content:

Multiple description coding refers to the encoding of an information source into multiple bit streams, in a manner that each bit stream independently represents a "coarse" description of the source, while multiple descriptions jointly convey a higher fidelity source representation. Thus multiple description coding allows enhanced resilience to loss of individual descriptions, and can be viewed as a form of source-based diversity coding. This paper addresses the design of subband filter banks to optimize the rate-distortion performance of multiple description subband coding. The problem is formulated in a Lagrangian optimization framework, and is solved directly in the frequency domain to produce the optimal filter spectral responses. By varying the Lagrangian parameter, our design obtains all points on the redundancy-distortion curve for Gaussian wide-sense stationary input processes. We consider the cases of both orthonormal and more general biorthogonal filter banks. We also analyze the connections between these two solutions, and quantify the gap in their optimal performance. Application of the proposed methods to the popular first-order autoregressive (AR(1)) model yields very interesting and insightful results. In the two extreme cases of maximum and minimum redundancy, our solutions degenerate to previously known results. Finally, comparisons with popularly deployed filter banks reveal large gaps from the theoretical performance bound.
---
paper_title: Achievable Rates for Multiple Descriptions

paper_content:

Consider a sequence of independent identically distributed (i.i.d.) random variables X_{l},X_{2}, \cdots, X_{n} and a distortion measure d(X_{i},X_{i}) on the estimates X_{i} of X_{i} . Two descriptions i(X)\in \{1,2, \cdots ,2^{nR_{1}\} and j(X)\in \{1,2, \cdots,2^{nR_{2}\} are given of the sequence X=(X_{1}, X_{2}, \cdots ,X_{n}) . From these two descriptions, three estimates (i(X)), X2(j(X)) , and \hat{X}_{O}(i(X),j(X)) are formed, with resulting expected distortions E \frac{1/n} \sum^{n}_{k=1} d(X_{k}, \hat{X}_{mk})=D_{m}, m=0,1,2. We find that the distortion constraints D_{0}, D_{1}, D_{2} are achievable if there exists a probability mass distribution p(x)p(\hat{x}_{1},\hat{x}_{2},\hat{x}_{0}|x) with Ed(X,\hat{x}_{m})\leq D_{m} such that R_{1}>I(X;\hat{X}_{1}), R_{2}>I(X;\hat{X}_{2}), where I(\cdot) denotes Shannon mutual information. These rates are shown to be optimal for deterministic distortion measures.
---
paper_title: Optimal multiple description transform coding of Gaussian vectors

paper_content:

Multiple description coding (MDC) is source coding for multiple channels such that a decoder which receives an arbitrary subset of the channels may produce a useful reconstruction. Orchard et al. (1997) proposed a transform coding method for MDC of pairs of independent Gaussian random variables. This paper provides a general framework which extends multiple description transform coding (MDTC) to any number of variables and expands the set of transforms which are considered. Analysis of the general case is provided, which can be used to numerically design optimal MDTC systems. The case of two variables sent over two channels is analytically optimized in the most general setting where channel failures need not have equal probability or be independent. It is shown that when channel failures are equally probable and independent, the transforms used in Orchard et al. are in the optimal set, but many other choices are possible. A cascade structure is presented which facilitates low-complexity design, coding, and decoding for a system with a large number of variables.
---
paper_title: Multiple-description vector quantization with lattice codebooks: Design and analysis

paper_content:

The problem of designing a multiple-description vector quantizer with lattice codebook /spl Lambda/ is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance results are obtained for quantizers based on the lattices A/sub 2/ and Z/sup i/, i=1, 2, 4, 8, that make use of this labeling algorithm. The high-rate squared-error distortions for this family of L-dimensional vector quantizers are then analyzed for a memoryless source with probability density function (PDF) p and differential entropy h(p)</spl infin/. For any a /spl epsiv/ (0, 1) and rate pair (R, R), it is shown that the two-channel distortion d~/sub o/ and the channel 1 (or channel 2) distortion d~/sub s/ satisfy lim/sub R/spl rarr//spl infin//d~/sub o/2/sup 2R(1+a)/= 1/4 G(/spl Lambda/)2/sup 2h(p)/ and lim/sub R/spl rarr//spl infin//d~/sub s/2/sup 2R(1-a)/=G(S/sub L/)2/sup 2h(p)/ where G(/spl Lambda/) is the normalized second moment of a Voronoi cell of the lattice /spl Lambda/ and G(S/sub L/) is the normalized second moment of a sphere in L dimensions.
---
paper_title: Multiple description lattice vector quantization: variations and extensions

paper_content:

Multiple description lattice vector quantization (MDLVQ) is a technique for two-channel multiple description coding. We observe that MDLVQ, in the form introduced by Servetto et al. (1999), is inherently optimized for the central decoder; i.e., for zero probability of a lost description. With a nonzero probability of description loss, performance is improved by modifying the encoding rule (using nearest neighbors with respect to "multiple description distance") and by perturbing the lattice codebook. The perturbation maintains many symmetries and hence does not significantly affect encoding or decoding complexity. An extension to more than two descriptions with attractive decoding properties is outlined.
---
paper_title: Design of entropy-constrained multiple-description scalar quantizers

paper_content:

The problem of entropy-constrained multiple-description scalar quantizer design is posed as an optimization problem, necessary conditions for optimality are derived, and an iterative design algorithm is presented. Performance results are presented for a Gaussian source, along with comparisons to the multiple-description rate distortion bound and a reference system. >
---
paper_title: Design of multiple description scalar quantizers

paper_content:

The design of scalar quantizers for communication systems that use diversity to overcome channel impairments is considered. The design problem is posed as an optimization problem and necessary conditions for optimality are derived. A design algorithm, a generalization of S.P. Lloyd's (1962) algorithm for quantizer design, is developed. Unlike a single channel scalar quantizer, the performance of a multiple description scalar quantizer is dependent on the index assignment. The problem of index assignment is addressed. Good index assignments, performance results, and sample quantizer designs are presented for a memoryless Gaussian source. Comparisons are made with rate distortion bounds for the multiple description problem. >
---
paper_title: Multiple description lattice vector quantization

paper_content:

We consider the problem of designing a lattice-based multiple description vector quantizer for a two-channel diversity system. The design of such a quantizer can be reduced to the problem of assigning pair labels to points of a vector quantizer codebook. A general labeling procedure based on the structure of the lattice is presented, along with detailed results for the hexagonal lattice: algorithms, asymptotic performance, and numerical simulations. Asymptotically, when compared with the lattice Z, the resulting quantizer achieves the standard second-moment gain of the hexagonal lattice for the central distortion, and, surprisingly, achieves the two-dimensional sphere gain for the side distortion.
---
paper_title: Multiple Description Vector Quantization With a Coarse Lattice

paper_content:

A multiple description (MD) lattice vector quantization technique for two descriptions was previously introduced in which fine and coarse codebooks are both lattices. The encoding begins with quantization to the nearest point in the fine lattice. This encoding is an inherent optimization for the decoder that receives both descriptions; performance can be improved with little increase in complexity by considering all decoders in the initial encoding step. The altered encoding relies only on the symmetries of the coarse lattice. This allows us to further improve performance without a significant increase in complexity by replacing the fine lattice codebook with a nonlattice codebook that respects many of the symmetries of the coarse lattice. Examples constructed with the two-dimensional (2-D) hexagonal lattice demonstrate large improvement over time sharing between previously known quantizers.
---
paper_title: Multiple description coding via polyphase transform and selective quantization

paper_content:

In this paper, we present an efficient Multiple Description Coding (MDC) technique to achieve robust communication over unreliable channels such as a lossy packet network. We first model such unreliable channels as erasure channels and then we present a MDC system using polyphase transform and selective quantization to recover channel erasures. Different from previous MDC work, our system explicitly separates description generation and redundancy addition which greatly reduces the implementation complexity specially for systems with more than two descriptions. Our system also realizes a Balanced Multiple Description Coding (BMDC) framework which can generate descriptions of statistically equal rate and importance. This property is well matched to communication systems with no priority mechanisms for data delivery, such as today's Internet. We then study, for a given total coding rate, the problem of optimal bit allocation between source coding and redundancy coding to achieve the minimum average distortion for different channel failure rates. With high resolution quantization assumption, we give optimal redundancy bit rate allocations for both scalar i.i.d sources and vector i.i.d sources for independent channel failures. To evaluate the performance of our system, we provide an image coding application with two descriptions and our simulation results are better than the best MDC image coding results reported to date. We also provide image coding examples with 16 descriptions to illustrate the simplicity and effectiveness of our proposed MDC system.
---
paper_title: On the optimality of block orthogonal transforms for multiple description coding of Gaussian vector sources

paper_content:

In this work, we consider the application of unitary filter banks for multiple description coding of independent, identically distributed Gaussian vector sources. We derive the redundancy-rate-distortion bound for this class of signals. It is shown that for two-dimensional (2-D) Gaussian vector sources (resulting in a two-description system), 2/spl times/2 block transforms give all the achievable optimal points in the redundancy-rate-distortion function among the class of all unitary filter banks. Similar results can be obtained for higher-dimensional transforms.
---
paper_title: 3D WAVELET-BASED COMPRESSION OF HYPERSPECTRAL IMAGERY

paper_content:

Since hyperspectral imagery is generated by collecting hundreds of contiguous bands, uncompressed hyperspectral imagery can be very large, with a single image potentially occupying hundreds of megabytes. For instance, the Airborne Visible InfraRed Imaging Spectrometer (AVIRIS) sensor is capable of collecting several gigabytes of data per day. Compression is thus necessary to facilitate both the storage and the transmission of hyperspectral images. Since hyperspectral imagery is typically collected on remote acquisition platforms, such as satellites, the transmission of such data to central, often terrestrial, reception sites can be a critical issue. Thus, compression schemes oriented to the task of remote transmission are becoming increasingly of interest in hyperspectral applications. Although there have been a number of approaches to the compression of hyperspectral imagery proposed in recent years—prominent techniques would include vector quantization (VQ) (e.g., [1, 2]) or principal component analysis (PCA) (e.g., [3, 4]) applied to spectral pixel vectors, as well as 3D extensions of common image-compression methods such as the discrete cosine transform (DCT) (e.g., [5])—most of the approaches as proposed are not particularly well-suited to the image-transmission task. That is, in many applications involving the communication of images, progressive transmission is desired in that successive reconstructions of the image are possible. In such a scenario, the receiver can produce a low-quality representation of the image after having received only a small portion of the transmitted bitstream, and this “preview” representation can be successively refined in
---
paper_title: Rate‐Distortion Theory

paper_content:

Rate-distortion theory is the branch of information theory that treats compressing the data produced by an information source down to a specified encoding rate that is strictly less than the source's entropy. This necessarily entails some lossiness, or distortion, between the original source data and the best approximation thereto that can be produced on the basis of the encoder's output bits. Rate-distortion theory was introduced in the seminal works written in 1948 and 1959 by C. E. Shannon, the founder of information theory. We describe Shannon's contribution and then trace its subsequent development worldwide. Heavier than usual emphasis is placed on the concept of “matching” a channel to a source in the rate-distortion sense, and also on the analogous matching of a source to a channel. Experimental evidence has been mounting in support of the hypothesis that living organisms often simultaneously achieve both of these matchings when processing their sensory inputs, thereby eliminating the need for the complex encoding and decoding operations that are needed in order to produce an information-theoretically optimum system in the absence of such double matching. ::: ::: ::: Keywords: ::: ::: rate-distortion; ::: lossy source coding; ::: distortion measure; ::: Shannon; ::: joint source-channel coding; ::: bioinformation theory
---
paper_title: Optimal pairwise correlating transforms for multiple description coding

paper_content:

Multiple description coding (MDC) addresses the problem of encoding a source into two (or more) bitstreams such that a high-quality reconstruction is decodable from the two bitstreams together, while a lower, but still acceptable, quality reconstruction is decodable if either of the two bitstreams is lost. Recent research has proposed using transforms to introduce a controlled amount of correlation between the two bitstreams in order to achieve MDC objectives. This paper considers several optimality issues related to such transform based MDC methods. Redundancy rate-distortion (RRD) performance of a general class of transforms is derived and used to identify the optimal transform for achieving any given amount of redundancy. Then, the paper introduces a more general transform-based MDC framework incorporating both the transform mode of redundancy and a second mode of redundancy. The optimal allocation of redundancy among these two modes is analyzed.
---
paper_title: Optimal multiple description subband coding

paper_content:

Multiple description coding refers to encoding an information source into multiple bitstreams, in a way that various levels of tradeoff between decoding quality and channel protection can be supported. This paper addresses the design of two-channel orthonormal filter banks to optimize the redundancy rate-distortion performance of multiple description subband coding. The problem is formulated in a Lagrangian optimization framework, and is solved directly in the frequency domain to produce the optimal filter responses. By varying the Lagrangian parameter, our design obtains all points on the information redundancy rate-distortion curve for Gaussian wide sense stationary input processes. Application of the proposed algorithm to the popular AR(1) model yields very interesting and insightful results. Comparisons with popularly deployed filter banks reveal large gaps from the theoretical performance bound.
---
paper_title: Multiple description image coding for noisy channels by pairing transform coefficients

paper_content:

Multiple description coding (MDC) is a way of trading off coding gain with robustness to channel errors. This paper presents a new method for MDC using the framework of transform coding. Instead of using the Karhunen-Loeve transform (KLT) that decorrelates all the coefficients, we choose the transform bases so that the coefficients are correlated pair-wise. This is accomplished by rotating every two basis vectors in the KLT. Each pair of correlated coefficients are then split between two descriptions. Only 45/spl deg/ rotation is considered which leads to two balanced streams. In the actual implementation, the DCT is employed in place of the KLT and the rotation of transform bases is accomplished by rotating the DCT coefficients. Experimental results show that this method can lead to satisfactory image reconstruction from any one description with a relatively small (20% for "lena") overhead over a standard JPEG coder.
---
paper_title: Elements of Information Theory

paper_content:

Preface to the Second Edition. Preface to the First Edition. Acknowledgments for the Second Edition. Acknowledgments for the First Edition. 1. Introduction and Preview. 1.1 Preview of the Book. 2. Entropy, Relative Entropy, and Mutual Information. 2.1 Entropy. 2.2 Joint Entropy and Conditional Entropy. 2.3 Relative Entropy and Mutual Information. 2.4 Relationship Between Entropy and Mutual Information. 2.5 Chain Rules for Entropy, Relative Entropy, and Mutual Information. 2.6 Jensen's Inequality and Its Consequences. 2.7 Log Sum Inequality and Its Applications. 2.8 Data-Processing Inequality. 2.9 Sufficient Statistics. 2.10 Fano's Inequality. Summary. Problems. Historical Notes. 3. Asymptotic Equipartition Property. 3.1 Asymptotic Equipartition Property Theorem. 3.2 Consequences of the AEP: Data Compression. 3.3 High-Probability Sets and the Typical Set. Summary. Problems. Historical Notes. 4. Entropy Rates of a Stochastic Process. 4.1 Markov Chains. 4.2 Entropy Rate. 4.3 Example: Entropy Rate of a Random Walk on a Weighted Graph. 4.4 Second Law of Thermodynamics. 4.5 Functions of Markov Chains. Summary. Problems. Historical Notes. 5. Data Compression. 5.1 Examples of Codes. 5.2 Kraft Inequality. 5.3 Optimal Codes. 5.4 Bounds on the Optimal Code Length. 5.5 Kraft Inequality for Uniquely Decodable Codes. 5.6 Huffman Codes. 5.7 Some Comments on Huffman Codes. 5.8 Optimality of Huffman Codes. 5.9 Shannon-Fano-Elias Coding. 5.10 Competitive Optimality of the Shannon Code. 5.11 Generation of Discrete Distributions from Fair Coins. Summary. Problems. Historical Notes. 6. Gambling and Data Compression. 6.1 The Horse Race. 6.2 Gambling and Side Information. 6.3 Dependent Horse Races and Entropy Rate. 6.4 The Entropy of English. 6.5 Data Compression and Gambling. 6.6 Gambling Estimate of the Entropy of English. Summary. Problems. Historical Notes. 7. Channel Capacity. 7.1 Examples of Channel Capacity. 7.2 Symmetric Channels. 7.3 Properties of Channel Capacity. 7.4 Preview of the Channel Coding Theorem. 7.5 Definitions. 7.6 Jointly Typical Sequences. 7.7 Channel Coding Theorem. 7.8 Zero-Error Codes. 7.9 Fano's Inequality and the Converse to the Coding Theorem. 7.10 Equality in the Converse to the Channel Coding Theorem. 7.11 Hamming Codes. 7.12 Feedback Capacity. 7.13 Source-Channel Separation Theorem. Summary. Problems. Historical Notes. 8. Differential Entropy. 8.1 Definitions. 8.2 AEP for Continuous Random Variables. 8.3 Relation of Differential Entropy to Discrete Entropy. 8.4 Joint and Conditional Differential Entropy. 8.5 Relative Entropy and Mutual Information. 8.6 Properties of Differential Entropy, Relative Entropy, and Mutual Information. Summary. Problems. Historical Notes. 9. Gaussian Channel. 9.1 Gaussian Channel: Definitions. 9.2 Converse to the Coding Theorem for Gaussian Channels. 9.3 Bandlimited Channels. 9.4 Parallel Gaussian Channels. 9.5 Channels with Colored Gaussian Noise. 9.6 Gaussian Channels with Feedback. Summary. Problems. Historical Notes. 10. Rate Distortion Theory. 10.1 Quantization. 10.2 Definitions. 10.3 Calculation of the Rate Distortion Function. 10.4 Converse to the Rate Distortion Theorem. 10.5 Achievability of the Rate Distortion Function. 10.6 Strongly Typical Sequences and Rate Distortion. 10.7 Characterization of the Rate Distortion Function. 10.8 Computation of Channel Capacity and the Rate Distortion Function. Summary. Problems. Historical Notes. 11. Information Theory and Statistics. 11.1 Method of Types. 11.2 Law of Large Numbers. 11.3 Universal Source Coding. 11.4 Large Deviation Theory. 11.5 Examples of Sanov's Theorem. 11.6 Conditional Limit Theorem. 11.7 Hypothesis Testing. 11.8 Chernoff-Stein Lemma. 11.9 Chernoff Information. 11.10 Fisher Information and the Cram-er-Rao Inequality. Summary. Problems. Historical Notes. 12. Maximum Entropy. 12.1 Maximum Entropy Distributions. 12.2 Examples. 12.3 Anomalous Maximum Entropy Problem. 12.4 Spectrum Estimation. 12.5 Entropy Rates of a Gaussian Process. 12.6 Burg's Maximum Entropy Theorem. Summary. Problems. Historical Notes. 13. Universal Source Coding. 13.1 Universal Codes and Channel Capacity. 13.2 Universal Coding for Binary Sequences. 13.3 Arithmetic Coding. 13.4 Lempel-Ziv Coding. 13.5 Optimality of Lempel-Ziv Algorithms. Compression. Summary. Problems. Historical Notes. 14. Kolmogorov Complexity. 14.1 Models of Computation. 14.2 Kolmogorov Complexity: Definitions and Examples. 14.3 Kolmogorov Complexity and Entropy. 14.4 Kolmogorov Complexity of Integers. 14.5 Algorithmically Random and Incompressible Sequences. 14.6 Universal Probability. 14.7 Kolmogorov complexity. 14.9 Universal Gambling. 14.10 Occam's Razor. 14.11 Kolmogorov Complexity and Universal Probability. 14.12 Kolmogorov Sufficient Statistic. 14.13 Minimum Description Length Principle. Summary. Problems. Historical Notes. 15. Network Information Theory. 15.1 Gaussian Multiple-User Channels. 15.2 Jointly Typical Sequences. 15.3 Multiple-Access Channel. 15.4 Encoding of Correlated Sources. 15.5 Duality Between Slepian-Wolf Encoding and Multiple-Access Channels. 15.6 Broadcast Channel. 15.7 Relay Channel. 15.8 Source Coding with Side Information. 15.9 Rate Distortion with Side Information. 15.10 General Multiterminal Networks. Summary. Problems. Historical Notes. 16. Information Theory and Portfolio Theory. 16.1 The Stock Market: Some Definitions. 16.2 Kuhn-Tucker Characterization of the Log-Optimal Portfolio. 16.3 Asymptotic Optimality of the Log-Optimal Portfolio. 16.4 Side Information and the Growth Rate. 16.5 Investment in Stationary Markets. 16.6 Competitive Optimality of the Log-Optimal Portfolio. 16.7 Universal Portfolios. 16.8 Shannon-McMillan-Breiman Theorem (General AEP). Summary. Problems. Historical Notes. 17. Inequalities in Information Theory. 17.1 Basic Inequalities of Information Theory. 17.2 Differential Entropy. 17.3 Bounds on Entropy and Relative Entropy. 17.4 Inequalities for Types. 17.5 Combinatorial Bounds on Entropy. 17.6 Entropy Rates of Subsets. 17.7 Entropy and Fisher Information. 17.8 Entropy Power Inequality and Brunn-Minkowski Inequality. 17.9 Inequalities for Determinants. 17.10 Inequalities for Ratios of Determinants. Summary. Problems. Historical Notes. Bibliography. List of Symbols. Index.
---
paper_title: Optimal subband filter banks for multiple description coding

paper_content:

Multiple description coding refers to the encoding of an information source into multiple bit streams, in a manner that each bit stream independently represents a "coarse" description of the source, while multiple descriptions jointly convey a higher fidelity source representation. Thus multiple description coding allows enhanced resilience to loss of individual descriptions, and can be viewed as a form of source-based diversity coding. This paper addresses the design of subband filter banks to optimize the rate-distortion performance of multiple description subband coding. The problem is formulated in a Lagrangian optimization framework, and is solved directly in the frequency domain to produce the optimal filter spectral responses. By varying the Lagrangian parameter, our design obtains all points on the redundancy-distortion curve for Gaussian wide-sense stationary input processes. We consider the cases of both orthonormal and more general biorthogonal filter banks. We also analyze the connections between these two solutions, and quantify the gap in their optimal performance. Application of the proposed methods to the popular first-order autoregressive (AR(1)) model yields very interesting and insightful results. In the two extreme cases of maximum and minimum redundancy, our solutions degenerate to previously known results. Finally, comparisons with popularly deployed filter banks reveal large gaps from the theoretical performance bound.
---
paper_title: Optimal multiple description transform coding of Gaussian vectors

paper_content:

Multiple description coding (MDC) is source coding for multiple channels such that a decoder which receives an arbitrary subset of the channels may produce a useful reconstruction. Orchard et al. (1997) proposed a transform coding method for MDC of pairs of independent Gaussian random variables. This paper provides a general framework which extends multiple description transform coding (MDTC) to any number of variables and expands the set of transforms which are considered. Analysis of the general case is provided, which can be used to numerically design optimal MDTC systems. The case of two variables sent over two channels is analytically optimized in the most general setting where channel failures need not have equal probability or be independent. It is shown that when channel failures are equally probable and independent, the transforms used in Orchard et al. are in the optimal set, but many other choices are possible. A cascade structure is presented which facilitates low-complexity design, coding, and decoding for a system with a large number of variables.
---
paper_title: Quantized frame expansions as source-channel codes for erasure channels

paper_content:

Quantized frame expansions are proposed as a method for generalized multiple description coding, where each quantized coefficient is a description. Whereas previous investigations have revealed the robustness of frame expansions to additive noise and quantization, this represents a new application of frame expansions. The performance of a system based on quantized frame expansions is compared to that of a system with a conventional block channel code. The new system performs well when the number of lost descriptions (erasures on an erasure channel) is hard to predict.
---
paper_title: Quantized Frame Expansions with Erasures

paper_content:

Abstract Frames have been used to capture significant signal characteristics, provide numerical stability of reconstruction, and enhance resilience to additive noise. This paper places frames in a new setting, where some of the elements are deleted. Since proper subsets of frames are sometimes themselves frames, a quantized frame expansion can be a useful representation even when some transform coefficients are lost in transmission. This yields robustness to losses in packet networks such as the Internet. With a simple model for quantization error, it is shown that a normalized frame minimizes mean-squared error if and only if it is tight. With one coefficient erased, a tight frame is again optimal among normalized frames, both in average and worst-case scenarios. For more erasures, a general analysis indicates some optimal designs. Being left with a tight frame after erasures minimizes distortion, but considering also the transmission rate and possible erasure events complicates optimizations greatly.
---
paper_title: Quantized Overcomplete Expansions in R^N: Analysis, Synthesis, and Algorithms

paper_content:

Coefficient quantization has peculiar qualitative effects on representations of vectors in IR with respect to overcomplete sets of vectors. These effects are investigated in two settings: frame expansions (representations obtained by forming inner products with each element of the set) and matching pursuit expansions (approximations obtained by greedily forming linear combinations). In both cases, based on the concept of consistency, it is shown that traditional linear reconstruction methods are suboptimal, and better consistent reconstruction algorithms are given. The proposed consistent reconstruction algorithms were in each case implemented, and experimental results are included. For frame expansions, results are proven to bound distortion as a function of frame redundancy r and quantization step size for linear, consistent, and optimal reconstruction methods. Taken together, these suggest that optimal reconstruction methods will yield O(1/r/sup 2/) mean-squared error (MSE), and that consistency is sufficient to insure this asymptotic behavior. A result on the asymptotic tightness of random frames is also proven. Applicability of quantized matching pursuit to lossy vector compression is explored. Experiments demonstrate the likelihood that a linear reconstruction is inconsistent, the MSE reduction obtained with a nonlinear (consistent) reconstruction algorithm, and generally competitive performance at low bit rates.
---
paper_title: Domain-based multiple description coding of images and video

paper_content:

In this paper we present a method of creating domain-based multiple descriptions of images and video. Descriptions are created by partitioning the domain of the signal into sets whose points are maximally separated from each other. This property enables simple error concealment methods to produce good estimates of lost signal samples. We present the approach in the context of Internet transmission of subband-coded images and scalable motion compensated 3-D subband-coded video, but applications are not limited to these scenarios.
---
paper_title: Multiple descriptions scalable video coding

paper_content:

Multiple description coding (MDC) is a joint source-channel coding technique specifically designed for real-time multimedia applications over best effort switched packet networks (such as Internet), in order to cope with packet losses due to transmission errors or network congestion. Error resilience of transmitted bitstreams is thus significantly increased, but this does not solve problems like bitstream adaptation to bandwidth variations or receiver characteristics, which are in turn addressed by scalable coding techniques. In this paper, we present a new method of multiple description coding of scalable video, combining the scalability features with MDC. It is based on a motion-compensated spatio-temporal subband decomposition, where the redundancy is tunable in a frame-like non-linear temporal representation.
---
paper_title: Multiple Description Coding for Video Delivery

paper_content:

Multiple description coding (MDC) is an effective means to combat bursty packet losses in the Internet and wireless networks. MDC is especially promising for video applications where retransmission is unacceptable or infeasible. When combined with multiple path transport (MPT), MDC enables traffic dispersion and hence reduces network congestion. This work describes principles in designing MD video coders employing temporal prediction and presents several predictor structures that differ in their tradeoffs between mismatch-induced distortion and coding efficiency. The paper also discusses example video communication systems integrating MDC and MPT.
---
paper_title: Multiple description video coding for scalable and robust transmission over IP

paper_content:

In this paper, we address the problem of video transmission over unreliable networks, such as the Internet, where packet losses occur. The most recent literature indicates multiple description (MD) as a promising coding approach to handle this issue. Moreover, it has been shown also how important the use of motion compensation prediction is in an MD-coding scheme. This paper proposes two architectures for multiple description video coding, both of them are based on the motion compensation prediction loop. The common characteristic of the two architectures is the use of a polyphase down-sampling technique to create the MDs and to introduce cross-redundancy among the descriptions. The first scheme, that we call drift-compensation multiple description video coder (DC-MDVC) appears very robust when used in an error-prone environment, but it can provide only two descriptions. The second architecture, called independent flow multiple description video coder (IF-MDVC), generates multiple sets of data before the motion compensation loop; in this case, there are no severe limitations in the selection of the number of descriptions used by the coder.
---
paper_title: Error-resilient video coding using multiple description motion compensation

paper_content:

A new approach for multiple description video coding is proposed. It employs a second-order predictor for motion-compensation, which predicts a current frame from two previously coded frames. The coder generates two descriptions, containing the coded even and odd frames, respectively. When only a single description (say, that containing even frames) is received, the decoder can only use previous even frames for prediction. The mismatch between the predicted frames at the encoder and decoder is explicitly coded to avoid error propagation in the ideal MD channels, where a description is either received intact or lost completely. By using the second-order predictor and coding the mismatch signal, one can also suppress error propagation in packet lossy networks where packets in either description can be lost. The predictor and the mismatch signal quantizer can be varied to achieve a wide range of tradeoffs between coding efficiency and error resilience.
---
paper_title: Multiple description scalable coding using wavelet-based motion compensated temporal filtering

paper_content:

Packet delay jitter and loss due to network congestion pose significant challenges for designing and deploying delay sensitive multimedia applications over the best effort packet switched networks such as the Internet. Recent studies indicate that using multiple descriptions coding (MDC) in conjunction with path or server diversity can mitigate these effects. However, the proposed MDC coding and streaming techniques are based on non-scalable coding techniques. A key disadvantages of these techniques is that they can only improve the error resilience of the transmitted video, but are not able to address two other important challenges associated with the robust transmission of video over unreliable networks: adaptation to bandwidth variations and receiving device characteristics. In this paper, we present a new paradigm, referred to as multiple description scalable coding (MDSC), that is able to address all the previously mentioned challenges by combining the advantages of scalable coding and MDC. This framework enables tradeoffs between throughput, redundancy and complexity at transmission time, unlike previous non-scalable MDC schemes. Furthermore, we also propose a novel MDSC scheme based on motion compensated temporal filtering (MCTF), denominated multiple description motion compensated temporal filtering (MD-MCTF). We use the inherent ability of current MCTF schemes, using the lifting implementation of temporal filtering. We show how tradeoffs between throughput, redundancy and complexity can easily be achieved by adaptively partitioning the video into several descriptions after MCTF. Based on our simulations using different network conditions, the proposed MD-MCTF framework outperforms existing MDC schemes over a variety of network conditions.
---
paper_title: Error-resilient compression and transmission of scalable video

paper_content:

Compressed video bitstreams require protection from channel errors in a wireless channel and protection from packet loss in a wired ATM channel. The three-dimensional (3-D) SPIHT coder has proved its efficiency and its real-time capability in compression of video. A forward-error-correcting (FEC) channel (RCPC) code combined with a single ARQ (automatic- repeat-request) proved to be an effective means for protecting the bitstream. There were two problems with this scheme: the noiseless reverse channel ARQ may not be feasible in practice; and, in the absence of channel coding and ARQ, the decoded sequence was hopelessly corrupted even for relatively clean channels. In this paper, we first show how to make the 3-D SPIHT bitstream more robust to channel errors by breaking the wavelet transform into a number of spatio-temporal tree blocks which can be encoded and decoded independently. This procedure brings the added benefit of parallelization of the compression and decompression algorithms. Then we demonstrate the packetization of the bit stream and the reorganization of these packets to achieve scalability in bit rate and/or resolution in addition to robustness. Then we encode each packet with a channel code. Not only does this protect the integrity of the packets in most cases, but it also allows detection of packet decoding failures, so that only the cleanly recovered packets are reconstructed. This procedure obviates ARQ, because the performance is only about 1 dB worse than normal 3-D SPIHT with FEC and ARQ. Furthermore, the parallelization makes possible real-time implementation in hardware and software.
---
paper_title: Multiple Description Video Coding Using Motion-Compensated Temporal Prediction

paper_content:

We propose multiple description (MD) video coders which use motion-compensated predictions. Our MD video coders utilize MD transform coding and three separate prediction paths at the encoder to mimic the three possible scenarios at the decoder: both descriptions received or either of the single descriptions received. We provide three different algorithms to control the mismatch between the prediction loops at the encoder and decoder. We present simulation results comparing the three approaches to two standards-based approaches to MD video coding. We show that when the main prediction loop at the encoder uses a two-channel reconstruction, it is important to have side prediction loops and transmit some redundancy information to control mismatch. We also examine the performance of our MD video coder with partial mismatch control in the presence of random packet loss, and demonstrate a significant improvement compared to more traditional approaches.
---
paper_title: Network-adaptive video streaming using multiple description coding and path diversity

paper_content:

This paper presents a TCP-friendly rate allocation algorithm for multiple description coding combined with path diversity. A 3-D SPIHT-based multiple description coding is used to generate two independent substreams and each substream is protected with an FEC-based unequal error protection algorithm. In the proposed video streaming framework, two senders simultaneously stream complementary substreams to the receiver over different paths. The proposed rate allocation algorithm coordinates distributed video streaming from multiple senders to a single receiver to minimize the overall distortion. Simulation results show that the proposed algorithm increases tolerance to packet loss due to network congestion and achieves higher visual quality compared to non-adaptive methods.
---
paper_title: A Robust Codec for Transmission of Very Low Bit-rate Video over Channels with Bursty Errors

paper_content:

We describe a robust codec for the transmission of very low bit-rate video over channels with a variety of errors, including random and bursty bit errors and packet loss. The codec exploits adaptivity to give good performance with a low overhead. By only protecting macroblocks which would otherwise be poorly concealed by the decoder the codec allows adaptive selection of the parts of video to protect. For protection, it uses multiple description codes which indirectly provide frequency-based adaptivity by protecting the more significant DCT coefficients. Simulations show significant improvements in the performance of the codec when compared to codecs which use intra macroblock updating (raster scan and random) at the same overhead. The codec is efficient in its use of bits and has good error resilience properties both objectively and subjectively over a wide range of conditions. Further, transcoding of the received bit stream to the standard H.263 syntax is relatively easy.
---
paper_title: Balanced interframe multiple description video compression

paper_content:

A balanced twin-description interframe video coder is designed and performance results are presented for video transmission aver packet networks with packet losses. The coder is based on a predictive multiple description quantizer structure called mutually-refining DPCM (MR-DPCM). The novel feature of this predictive quantizer is that the decoder and encoder filter states trade in either of the two single-channel modes as well as in the two-channel mode. The performance and indeed the suitability of the multiple description approach for a network with packet lasses depends an the packetization method. Two packetization methods are considered-a "correct" one and a low latency but "incorrect" one. Performance results are presented for synthetic sources as well as for a video sequence under a variety of conditions.
---
paper_title: A Full-Featured, Error Resilient, Scalable Wavelet Video Codec Based on the Set Partitioning in Hierarchical Trees (SPIHT) Algorithm

paper_content:

Compressed video bitstreams require protection from channel errors in a wireless channel. The 3-D set partitioning in hierarchical trees (SPIHT) coder has proved its efficiency and its real-time capability in the compression of video. A forward-error-correcting (FEC) channel (RCPC) code combined with a single automatic-repeat request (ARQ) proved to be an effective means for protecting the bitstream. There were two problems with this scheme: (1) the noiseless reverse channel ARQ may not be feasible in practice and (2) in the absence of channel coding and ARQ, the decoded sequence was hopelessly corrupted even for relatively clean channels. We eliminate the need for ARQ by making the 3-D SPIHT bitstream more robust and resistant to channel errors. We first break the wavelet transform into a number of spatio-temporal tree blocks which can be encoded and decoded independently by the 3-D SPIHT algorithm. This procedure brings the added benefit of parallelization of the compression and decompression algorithms, and enables implementation of region-based coding. We demonstrate the packetization of the bitstream and the reorganization of these packets to achieve scalability in bit rate and/or resolution in addition to robustness. Then we encode each packet with a channel code. Not only does this protect the integrity of the packets in most cases, but it also allows detection of packet-decoding failures, so that only the cleanly recovered packets are reconstructed. In extensive comparative tests, the reconstructed video is shown to be superior to that of MPEG-2, with the margin of superiority growing substantially as the channel becomes noisier. Furthermore, the parallelization makes possible real-time implementation in hardware and software.
---
paper_title: Progressive source-channel coding of video for unknown noisy channels

paper_content:

Numerous techniques have been developed over the last several decades to efficiently transmit video across noisy channel. In this paper, we propose an unequal error protection scheme for the progressive video compression through cascading a bit-sensitive-based error control channel coding with an embedded multiresolutional 3D-SPIHT scalable video coder. It provides an efficient manner for the joint source-channel coding system to trade off the rate-distortion (RD) performance and the error-resilient performance for the unknown uncontrollable noisy channels at a given available transmission rate. This coding system is easy to implement and has acceptable complexity. The performance of the joint source-channel coding approach under various channel conditions is evaluated.
---
paper_title: Channel coding and transmission aspects for wireless multimedia

paper_content:

Multimedia transmission has to handle a variety of compressed and uncompressed source signals such as data, text, image, audio, and video. On wireless channels the error rates are high and joint source/channel coding and decoding methods are advantageous. Also, the system architecture has to adapt to the bad channel conditions. Several examples of a joint design are given. We especially advocate the use of rate-compatible punctured systematic recursive convolutional (RCPRSC) codes which are show to lead to a straightforward and versatile unequal error protection (UEP) design. In addition, the high-end receiver could use soft outputs and source-controlled channel decoding for even better performance.
---
paper_title: Low bit-rate scalable video coding with 3-D set partitioning in hierarchical trees (3-D SPIHT)

paper_content:

We propose a low bit-rate embedded video coding scheme that utilizes a 3-D extension of the set partitioning in hierarchical trees (SPIHT) algorithm which has proved so successful in still image coding. Three-dimensional spatio-temporal orientation trees coupled with powerful SPIHT sorting and refinement renders 3-D SPIHT video coder so efficient that it provides comparable performance to H.263 objectively and subjectively when operated at the bit rates of 30 to 60 kbits/s with minimal system complexity. Extension to color-embedded video coding is accomplished without explicit bit allocation, and can be used for any color plane representation. In addition to being rate scalable, the proposed video coder allows multiresolutional scalability in encoding and decoding in both time and space from one bit stream. This added functionality along with many desirable attributes, such as full embeddedness for progressive transmission, precise rate control for constant bit-rate traffic, and low complexity for possible software-only video applications, makes the proposed video coder an attractive candidate for multimedia applications.
---
paper_title: Bit Allocation for Joint Source/Channel Coding of Scalable Video

paper_content:

We propose an efficient bit allocation algorithm for a joint source/channel video codec over noisy channels. The approach is to distribute the available source and channel coding bits among the subbands in such a way that the expected distortion is minimized. The constructed distortion curves bound the performance degradation should the channel be estimated incorrectly. The algorithm can be used in other similar distortion minimization problems with two constraints, such as power or complexity.
---
paper_title: Joint source/channel coding of scalable video over noisy channels

paper_content:

We propose an optimal bit allocation strategy for a joint source/channel video codec over noisy channel when the channel state is assumed to be known. Our approach is to partition source and channel coding bits in such a way that the expected distortion is minimized. The particular source coding algorithm we use is rate scalable and is based on 3D subband coding with multi-rate quantization. We show that using this strategy, transmission of video over very noisy channels still renders acceptable visual quality, and outperforms schemes that use equal error protection only. The flexibility of the algorithm also permits the bit allocation to be selected optimally when the channel state is in the form of a probability distribution instead of a deterministic state.
---
paper_title: Dependent source and channel rate allocation for video transmission

paper_content:

A general joint source-channel rate allocation scheme for a dependent video coding environment is presented. It is assumed that the source coders rely on motion-compensated prediction, and thus error propagation will contribute significantly to the degradation of the reconstructed video. The rate allocation methodology is based upon generation of operational distortion-rate characteristics. In order to reduce computational complexity, these surfaces and the channel code performance are modeled. An analytic method for computing optimal rate allocation across frames in a video sequence is then introduced. Comparisons are made between equal error protection and unequal error protection over video frames. Results are shown for H.263 compressed video used in conjunction with rate-compatible punctured convolutional codes.
---
paper_title: Adaptive Source-Channel Subband Video Coding for Wireless Channels

paper_content:

This paper presents a general framework for combined source-channel coding within the context of subband coding. The unequal importance of subbands in reconstruction of the source is exploited by an appropriate allocation of source and channel coding rates for the coding and transmission of subbands over a noisy channel. For each subband, the source coding rate as well as the level of protection (quantified by the channel coding rate) are jointly chosen to minimize the total end-to-end mean-squared distortion suffered by the source. This allocation of source and channel coding rates is posed as a constrained optimization problem, and solved using a generalized bit allocation algorithm. The optimal choice of source and channel coding rates depends on the state of the physical channel. These results are extended to transmission over fading channels using a finite state model, where every state corresponds to an additive white Gaussian noise (AWGN) channel. A coding strategy is also developed that minimizes the average distortion when the channel state is unavailable at the transmitter. Experimental results are provided that demonstrate application of these combined source-channel coding strategies on video sequences.
---
paper_title: Progressive Video Coding for Noisy Channels

paper_content:

Abstract We extend the work of Sherwood and Zeger to progressive video coding for noisy channels. By utilizing a three-dimensional (3D) extension of the set partitioning in hierarchical trees (SPIHT) algorithm, we cascade the resulting 3D SPIHT video coder with the rate-compatible punctured convolutional channel coder for transmission of video over a binary symmetric channel. Progressive coding is achieved by increasing the target rate of the 3D embedded SPIHT video coder as the channel condition improves. The performance of our proposed coding system is acceptable at low transmission rate and bad channel conditions.
---
paper_title: An embedded wavelet video coder using three-dimensional set partitioning in hierarchical trees (SPIHT)

paper_content:

The SPIHT (set partitioning in hierarchical trees) algorithm by Said and Pearlman (see IEEE Trans. on Circuits and Systems for Video Technology, no.6, p.243-250, 1996) is known to have produced some of the best results in still image coding. It is a fully embedded wavelet coding algorithm with precise rate control and low complexity. We present an application of the SPIHT algorithm to video sequences, using three-dimensional (3D) wavelet decompositions and 3D spatio-temporal dependence trees. A full 3D-SPIHT encoder/decoder is implemented in software and is compared against MPEG-2 in parallel simulations. Although there is no motion estimation or compensation in the 3D SPIHT, it performs measurably and visually better than MPEG-2, which employs complicated motion estimation and compensation.
---
paper_title: Good error-correcting codes based on very sparse matrices

paper_content:

We report theoretical and empirical properties of Gallager's (1963) low density parity check codes on Gaussian channels. It can be proved that, given an optimal decoder, these codes asymptotically approach the Shannon limit. With a practical 'belief propagation' decoder, performance substantially better than that of standard convolutional and concatenated codes can be achieved; indeed the performance is almost as close to the Shannon limit as that of turbo codes.
---
paper_title: Image coding using wavelet transform

paper_content:

A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. This method involves two steps. First, a wavelet transform used in order to obtain a set of biorthogonal subclasses of images: the original image is decomposed at different scales using a pyramidal algorithm architecture. The decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image. Second, according to Shannon's rate distortion theory, the wavelet coefficients are vector quantized using a multiresolution codebook. To encode the wavelet coefficients, a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed. In order to allow the receiver to recognize a picture as quickly as possible at minimum cost, a progressive transmission scheme is presented. It is shown that the wavelet transform is particularly well adapted to progressive transmission. >
---
paper_title: Optimal quantizer design for noisy channels: An approach to combined source - channel coding

paper_content:

We present an analysis of the zero-memory quantization of memoryless sources when the quantizer output is to be encoded and transmitted across a noisy channel. Necessary conditions for the joint optimization of the quantizer and the encoder/decoder pair are presented, and an iterative algorithm for obtaining a locally optimum system is developed. The performance of this locally optimal system, obtained for the class of generalized Gaussian distributions and the binary symmetric channel, is compared against the optimum performance theoretically attainable (using rate-distortion theoretic arguments), as well as against the performance of Lloyd-Max quantizers encoded using the natural binary code and the folded binary code. It is shown that this optimal design could result in substantial performance improvements. The performance improvements are more noticeable at high bit rates and for broad-tailed densities.
---

Title: An Overview on Wavelets in Source Coding, Communications, and Networks

Section 1: INTRODUCTION
Description 1: This section introduces the concept of wavelets and their significant role in signal processing, particularly in the contexts of image and video coding.

Section 2: WAVELETS IN SIGNAL REPRESENTATION AND SOURCE CODING
Description 2: This section overviews the role of wavelets in signal representation and source coding, focusing on image and video coding, image-adaptive wavelet transforms, and interpolation.

Section 3: Image coding
Description 3: This subsection discusses the implementation of wavelets in 2D and 3D image coding, including multidimensional wavelet transforms and coding procedures.

Section 4: Multidimensional wavelet transforms
Description 4: This subsection explains the methodology of applying wavelet transforms independently along each dimension of an image dataset for effective image decomposition.

Section 5: Coding procedures
Description 5: This subsection provides an overview of the various coding procedures that efficiently encode wavelet-transformed image data.

Section 6: Coding of arbitrarily shaped imagery
Description 6: This subsection addresses the challenges and techniques involved in coding images with arbitrary shapes using wavelets.

Section 7: Video coding
Description 7: This subsection discusses the application of wavelets in video coding and the different strategies such as redundant transforms and motion-compensated temporal filtering (MCTF).

Section 8: Image-adaptive lifting transforms
Description 8: This subsection explores adaptive lifting transforms that respond to local signal characteristics to enhance wavelet decompositions.

Section 9: Image interpolation
Description 9: This subsection covers the use of wavelet-based signal representations for image interpolation, aimed at magnifying images while preserving sharpness.

Section 10: WAVELETS IN COMMUNICATIONS AND NETWORKING
Description 10: This section surveys the use of wavelets in redundancy creation for robust image and video communication across networks, including multiple-description coding and joint source-channel coding techniques.

Section 11: Multiple-description coding
Description 11: This subsection overviews the multiple-description coding (MDC) strategy that creates multiple correlated but independently decodable image or video bitstreams.

Section 12: Joint source-channel coding
Description 12: This subsection explores the strategies for designing joint source-channel coding systems optimized for the specific channel conditions to improve error resilience and overall system performance.

Section 13: CONCLUSION
Description 13: This section summarizes the key points discussed in the paper, highlighting the broad applicability and continued relevance of wavelets in image and video processing.