Greedy Orthogonal Matching Pursuit algorithm for sparse signal recovery in compressive sensing

The sparse signal recovery problem has been the subject of extensive research in several different communities. Tractable recovery algorithm is a crucial and fundamental theme of compressive sensing (CS), which has drawn significant interests in the last few years. In this paper, we firstly analyze the iterative residual in Orthogonal Matching Pursuit (OMP) algorithm. Secondly, a greedier algorithm is introduced, which is called Greedy OMP (GOMP) algorithm. This algorithm iteratively identifies more than one atoms using greedy atom identification, and then discards some atoms, which are of high similarity with the optimal atom. Compared with OMP algorithm, the experiments conducted on Gaussian and Zero-one sparse signal demonstrate that the proposed GOMP algorithm can provide better recovery performance. Finally, we experimentally investigate the effect of greedy constant in GOMP upon the recovery performance.