Jpeg Image Compression Using Discrete Cosine Transform - A Survey
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paper_title: Introduction to Data Compression

paper_content:

Preface 1 Introduction 1.1 Compression Techniques 1.1.1 Lossless Compression 1.1.2 Lossy Compression 1.1.3 Measures of Performance 1.2 Modeling and Coding 1.3 Organization of This Book 1.4 Summary 1.5 Projects and Problems 2 Mathematical Preliminaries 2.1 Overview 2.2 A Brief Introduction to Information Theory 2.3 Models 2.3.1 Physical Models 2.3.2 Probability Models 2.3.3. Markov Models 2.3.4 Summary 2.5 Projects and Problems 3 Huffman Coding 3.1 Overview 3.2 "Good" Codes 3.3. The Huffman Coding Algorithm 3.3.1 Minimum Variance Huffman Codes 3.3.2 Length of Huffman Codes 3.3.3 Extended Huffman Codes 3.4 Nonbinary Huffman Codes 3.5 Adaptive Huffman Coding 3.5.1 Update Procedure 3.5.2 Encoding Procedure 3.5.3 Decoding Procedure 3.6 Applications of Huffman Coding 3.6.1 Lossless Image Compression 3.6.2 Text Compression 3.6.3 Audio Compression 3.7 Summary 3.8 Projects and Problems 4 Arithmetic Coding 4.1 Overview 4.2 Introduction 4.3 Coding a Sequence 4.3.1 Generating a Tag 4.3.2 Deciphering the Tag 4.4 Generating a Binary Code 4.4.1 Uniqueness and Efficiency of the Arithmetic Code 4.4.2 Algorithm Implementation 4.4.3 Integer Implementation 4.5 Comparison of Huffman and Arithmetic Coding 4.6 Applications 4.6.1 Bi-Level Image Compression-The JBIG Standard 4.6.2 Image Compression 4.7 Summary 4.8 Projects and Problems 5 Dictionary Techniques 5.1 Overview 5.2 Introduction 5.3 Static Dictionary 5.3.1 Diagram Coding 5.4 Adaptive Dictionary 5.4.1 The LZ77 Approach 5.4.2 The LZ78 Approach 5.5 Applications 5.5.1 File Compression-UNIX COMPRESS 5.5.2 Image Compression-the Graphics Interchange Format (GIF) 5.5.3 Compression over Modems-V.42 bis 5.6 Summary 5.7 Projects and Problems 6 Lossless Image Compression 6.1 Overview 6.2 Introduction 6.3 Facsimile Encoding 6.3.1 Run-Length Coding 6.3.2 CCITT Group 3 and 4-Recommendations T.4 and T.6 6.3.3 Comparison of MH, MR, MMR, and JBIG 6.4 Progressive Image Transmission 6.5 Other Image Compression Approaches 6.5.1 Linear Prediction Models 6.5.2 Context Models 6.5.3 Multiresolution Models 6.5.4 Modeling Prediction Errors 6.6 Summary 6.7 Projects and Problems 7 Mathematical Preliminaries 7.1 Overview 7.2 Introduction 7.3 Distortion Criteria 7.3.1 The Human Visual System 7.3.2 Auditory Perception 7.4 Information Theory Revisted 7.4.1 Conditional Entropy 7.4.2 Average Mutual Information 7.4.3 Differential Entropy 7.5 Rate Distortion Theory 7.6 Models 7.6.1 Probability Models 7.6.2 Linear System Models 7.6.3 Physical Models 7.7 Summary 7.8 Projects and Problems 8 Scalar Quantization 8.1 Overview 8.2 Introduction 8.3 The Quantization Problem 8.4 Uniform Quantizer 8.5 Adaptive Quantization 8.5.1 Forward Adaptive Quantization 8.5.2 Backward Adaptive Quantization 8.6 Nonuniform Quantization 8.6.1 pdf-Optimized Quantization 8.6.2 Companded Quantization 8.7 Entropy-Coded Quantization 8.7.1 Entropy Coding of Lloyd-Max Quantizer Outputs 8.7.2 Entropy-Constrained Quantization 8.7.3 High-Rate Optimum Quantization 8.8 Summary 8.9 Projects and Problems 9 Vector Quantization 9.1 Overview 9.2 Introduction 9.3 Advantages of Vector Quantization over Scalar Quantization 9.4 The Linde-Buzo-Gray Algorithm 9.4.1 Initializing the LBG Algorithm 9.4.2 The Empty Cell Problem 9.4.3 Use of LBG for Image Compression 9.5 Tree-Structured Vector Quantizers 9.5.1 Design of Tree-Structured Vector Quantizers 9.6 Structured Vector Quantizers 9.6.1 Pyramid Vector Quantization 9.6.2 Polar and Spherical Vector Quantizers 9.6.3 Lattice Vector Quantizers 9.7 Variations on the Theme 9.7.1 Gain-Shape Vector Quantization 9.7.2 Mean-Removed Vector Quantization 9.7.3 Classified Vector Quantization 9.7.4 Multistage Vector Quantization 9.7.5 Adaptive Vector Quantization 9.8 Summary 9.9 Projects and Problems 10 Differential Encoding 10.1 Overview 10.2 Introduction 10.3 The Basic Algorithm 10.4 Prediction in DPCM 10.5 Adaptive DPCM (ADPCM) 10.5.1 Adaptive Quantization in DPCM 10.5.2 Adaptive Prediction in DPCM 10.6 Delta Modulation 10.6.1 Constant Factor Adaptive Delta Modulation (CFDM) 10.6.2 Continuously Variable Slope Delta Modulation 10.7 Speech Coding 10.7.1 G.726 10.8 Summary 10.9 Projects and Problems 11 Subband Coding 11.1 Overview 11.2 Introduction 11.3 The Frequency Domain and Filtering 11.3.1 Filters 11.4 The Basic Subband Coding Algorithm 11.4.1 Bit Allocation 11.5 Application to Speech Coding-G.722 11.6 Application to Audio Coding-MPEG Audio 11.7 Application to Image Compression 11.7.1 Decomposing an Image 11.7.2 Coding the Subbands 11.8 Wavelets 11.8.1 Families of Wavelets 11.8.2 Wavelets and Image Compression 11.9 Summary 11.10 Projects and Problems 12 Transform Coding 12.1 Overview 12.2 Introduction 12.3 The Transform 12.4 Transforms of Interest 12.4.1 Karhunen-Loeve Transform 12.4.2 Discrete Cosine Transform 12.4.3 Discrete Sine Transform 12.4.4 Discrete Walsh-Hadamard Transform 12.5 Quantization and Coding of Transform Coefficients 12.6 Application to Image Compression-JPEG 12.6.1 The Transform 12.6.2 Quantization 12.6.3 Coding 12.7 Application to Audio Compression 12.8 Summary 12.9 Projects and Problems 13 Analysis/Synthesis Schemes 13.1 Overview 13.2 Introduction 13.3 Speech Compression 13.3.1 The Channel Vocoder 13.3.2 The Linear Predictive Coder (Gov.Std.LPC-10) 13.3.3 Code Excited Linear Prediction (CELP) 13.3.4 Sinusoidal Coders 13.4 Image Compression 13.4.1 Fractal Compression 13.5 Summary 13.6 Projects and Problems 14 Video Compression 14.1 Overview 14.2 Introduction 14.3 Motion Compensation 14.4 Video Signal Representation 14.5 Algorithms for Videoconferencing and Videophones 14.5.1 ITU_T Recommendation H.261 14.5.2 Model-Based Coding 14.6 Asymmetric Applications 14.6.1 The MPEG Video Standard 14.7 Packet Video 14.7.1 ATM Networks 14.7.2 Compression Issues in ATM Networks 14.7.3 Compression Algorithms for Packet Video 14.8 Summary 14.9 Projects and Problems A Probability and Random Processes A.1 Probability A.2 Random Variables A.3 Distribution Functions A.4 Expectation A.5 Types of Distribution A.6 Stochastic Process A.7 Projects and Problems B A Brief Review of Matrix Concepts B.1 A Matrix B.2 Matrix Operations C Codes for Facsimile Encoding D The Root Lattices Bibliography Index
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paper_title: Applied Linear Algebra

paper_content:

Chapter 1. Linear Algebraic Systems 1.1. Solution of Linear Systems 1.2. Matrices and Vectors 1.3. Gaussian Elimination - Regular Case 1.4. Pivoting and Permutations 1.5. Matrix Inverses 1.6. Transposes and Symmetric Matrices 1.7. Practical Linear Algebra 1.8. General Linear Systems 1.9. Determinants Chapter 2. Vector Spaces and Bases 2.1. Vector Spaces 2.2. Subspaces 2.3. Span and Linear Independence 2.4. Bases 2.5. The Fundamental Matrix Subspaces 2.6. Graphs and Incidence Matrices Chapter 3. Inner Products and Norms 3.1. Inner Products 3.2. Inequalities 3.3. Norms 3.4. Positive Definite Matrices 3.5. Completing the Square 3.6. Complex Vector Spaces Chapter 4. Minimization and Least Squares Approximation 4.1. Minimization Problems 4.2. Minimization of Quadratic Functions 4.3. Least Squares and the Closest Point 4.4. Data Fitting and Interpolation Chapter 5. Orthogonality 5.1. Orthogonal Bases 5.2. The Gram-Schmidt Process 5.3. Orthogonal Matrices 5.4. Orthogonal Polynomials 5.5. Orthogonal Projections and Least Squares 5.6. Orthogonal Subspaces Chapter 6. Equilibrium 6.1. Springs and Masses 6.2. Electrical Networks 6.3. Structures Chapter 7. Linearity 7.1. Linear Functions 7.2. Linear Transformations 7.3. Affine Transformations and Isometries 7.4. Linear Systems 7.5. Adjoints Chapter 8. Eigenvalues 8.1. Simple Dynamical Systems 8.2. Eigenvalues and Eigenvectors 8.3. Eigenvector Bases and Diagonalization 8.4. Eigenvalues of Symmetric Matrices 8.5. Singular Values 8.6. Incomplete Matrices and the Jordan Canonical Form Chapter 9. Linear Dynamical Systems 9.1. Basic Solution Methods 9.2. Stability of Linear Systems 9.3. Two-Dimensional Systems 9.4. Matrix Exponentials 9.5. Dynamics of Structures 9.6. Forcing and Resonance Chapter 10. Iteration of Linear Systems 10.1. Linear Iterative Systems 10.2. Stability 10.3. Matrix Norms 10.4. Markov Processes 10.5. Iterative Solution of Linear Systems 10.6. Numerical Computation of Eigenvalues Chapter 11. Boundary Value Problems in One Dimension 11.1. Elastic Bars 11.2. Generalized Functions and the Green's Function 11.3. Adjoints and Minimum Principles 11.4. Beams and Splines 11.5. Sturm-Liouville Boundary Value Problems 11.6. Finite Elements
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Title: Jpeg Image Compression Using Discrete Cosine Transform - A Survey

Section 1: INTRODUCTION
Description 1: Write about the significance of image compression in the digital age and explain the necessity for efficient digital information management.

Section 2: Principles Behind Compression
Description 2: Discuss the key principles behind image compression techniques, including spatial redundancy, spectral redundancy, and psycho-visual redundancy, and describe various compression categorizations.

Section 3: Atypical Image Coder
Description 3: Describe the components of a typical lossy image compression system, including the source encoder, quantizer, and entropy encoder.

Section 4: Performance Criteria in Image Compression
Description 4: Introduce the performance criteria for image compression, focusing on compression ratio (CR) and quality measurement of the reconstructed image (PSNR).

Section 5: DCT TRANSFORMATION
Description 5: Explain the Discrete Cosine Transform (DCT) and its importance in image compression, including its applications and advantages.

Section 6: JPEG COMPRESSION
Description 6: Detail the JPEG compression process, its steps, and the significance of JPEG as a standard for image compression using the DCT.

Section 7: Discrete Cosine Transform
Description 7: Describe the transformation of image data into frequency components using DCT and the subsequent steps in the JPEG process.

Section 8: Quantization in JPEG
Description 8: Explain the quantization step in JPEG compression, including the process of data reduction and the role of frequency components.

Section 9: Huffman Encoding
Description 9: Describe the entropy encoding process in JPEG compression, particularly Huffman coding, and its effectiveness in compressing data.

Section 10: Decompression
Description 10: Outline the steps involved in the decompression process, reversing the compression steps, and restoring the image data.

Section 11: CONCLUSION & FUTURE WORK
Description 11: Summarize the survey's findings on JPEG image compression using DCT and discuss future work, including comparisons with other compression techniques like Discrete Wavelet Transform.