Study of the gOMP Algorithm for Recovery of Compressed Sensed
  Hyperspectral Images
Jon Alvarez Justo Milica Orlandic
Hyperspectral Imaging (HSI) is used in a wide range of applications such as
remote sensing, yet the transmission of the HS images by communication data
links becomes challenging due to the large number of spectral bands that the HS
images contain together with the limited data bandwidth available in real
applications. Compressive Sensing reduces the images by randomly subsampling
the spectral bands of each spatial pixel and then it performs the image
reconstruction of all the bands using recovery algorithms which impose sparsity
in a certain transform domain. Since the image pixels are not strictly sparse,
this work studies a data sparsification pre-processing stage prior to
compression to ensure the sparsity of the pixels. The sparsified images are
compressed $2.5\times$ and then recovered using the Generalized Orthogonal
Matching Pursuit algorithm (gOMP) characterized by high accuracy, low
computational requirements and fast convergence. The experiments are performed
in five conventional hyperspectral images where the effect of different
sparsification levels in the quality of the uncompressed as well as the
recovered images is studied. It is concluded that the gOMP algorithm
reconstructs the hyperspectral images with higher accuracy as well as faster
convergence when the pixels are highly sparsified and hence at the expense of
reducing the quality of the recovered images with respect to the original
images.