Coherence-based sufficient condition for support recovery using block generalized orthogonal matching pursuit

Abstract

Challenge is to find the support vectors of the unknown block sparse vector with compressed measurements in an underdetermined system where the number of unknowns is more than that of measurements. To recover unknown block sparse vector, restricted isometry property (RIP) is a sufficient condition need to be satisfied. Finding the restricted isometric constant is a non-polynomial hard problem for large values of n. In this paper coherence-based recovery guarantee has been proposed to recover the support vectors using block generalized orthogonal matching pursuit (BGOMP). It is proved that BGOMP can able to recover the support vectors with lesser number of iteration than block orthogonal matching pursuit (BOMP) by selecting multiple block support elements per iteration. Simulation results show detection performance of BGOMP is better than BOMP, block subspace pursuit (BSP) and block compressive sampling matching pursuit (BCoSaMP) for different block sparsity and block length. In most of the cases for different block sparsity and block length computation time for BGOMP is lesser than BCoSaMP, BSP and BOMP due to the multiple selection of elements in each iteration.