Comparison of OMP and SOMP in the reconstruction of compressively sensed hyperspectral images

In this paper, we present a novel method for the acquisition and compression of hyperspectral images based on two concepts - distributed source coding and compressive sensing. Compressive sensing (CS) is a signal acquisition method that samples at sub Nyquist rates which is possible for signals that are sparse in some transform domain. Distributed source coding (DSC) is a method to encode correlated sources separately and decode them together in an attempt to shift complexity from the encoder to the decoder. Distributed compressive sensing (DCS) is a new framework suggested for jointly sparse signals which we apply to the correlated bands of hyperspectral images. We compressively sense each band of the hyperspectral image individually and can then recover the bands separately or using a joint recovery method. We use the Orthogonal Matching Pursuit (OMP) for individual recovery and Simultaneous Orthogonal Matching Pursuit (SOMP) for joint decoding and compare the two methods. The latter is shown to perform consistently better showing that the Distributed Compressive Sensing method that exploits the joint sparsity of the hyperspectral image is much better than individual recovery.