Recovery of block sparse signals by a block version of StOMP

It is in general NP-hard to pursue the sparsest solution of an underdetermined system of linear equations. The Stagewise Orthogonal Matching Pursuit (StOMP) algorithm has been proposed in Donoho et al. [1] to recover sparse signals from compressed measurements, which is a greedy algorithm with low computational complexity and has some particularly interesting theoretical properties. On the other hand, problems of block sparse signal recovery have arisen in fields like signal processing and systems biology, under which a block sparse signal recovery algorithm with low computational complexity and theoretical guarantees is needed. In this paper, a block version of StOMP is proposed, termed Block Stagewise Orthogonal Matching Pursuit (Block-StOMP). Block-StOMP combines advantages of StOMP and block structure of signals for a high-efficiency recovery of the block sparse signal. Moreover, a rigorous theoretical analysis for Block-StOMP is given in this paper. Compared with StOMP and other algorithms, Block-StOMP has excellent recovery performance when the measurement noise level is moderate.