On Recovery of Block Sparse Signals via Block Compressive Sampling Matching Pursuit

Compressive sampling matching pursuit (CoSaMP) is an efficient reconstruction algorithm for sparse signal. When the signal is block sparse, i.e., the non-zero elements are presented in clusters, some block sparse reconstruction algorithms have been proposed accordingly. In this paper, we present a new block algorithm based on CoSaMP, called block compressive sampling matching pursuit (BlockCoSaMP). Compared with CoSaMP algorithm, the proposed algorithm shows improved performance when sparse signal is presented in block form. Restricted isometry property (RIP) of measurement matrix is an effective tool for analyzing the performance of the CS algorithm, and Block restricted isometry property (Block RIP) is the extension of traditional RIP. Based on the Block RIP, we derive the sufficient condition to guarantee the convergence of Block-CoSaMP algorithm. In addition, the number of required iterations is obtained. Finally, simulation experiments show that with the increase of block length, the performance of Block-CoSaMP algorithm approaches to that of block subspace pursuit (Block-SP) algorithm. When the block length and sparsity are small, the performance of Block-CoSaMP algorithm is better than that of the CoSaMP, l
₂
/l
₁
norm and block orthogonal matching pursuit (BOMP) algorithms. Especially, when compared with CoSaMP and l
₂
/l
₁
norm algorithms, the proposed algorithm exhibits more obvious performance gain.