Support Recovery from Noisy Measurement via Orthogonal Multi-Matching Pursuit

In this paper, a new stopping rule is proposed for orthogonal multi-matching pursuit (OMMP). We show that, for l(2) bounded noise case, OMMP with the new stopping rule can recover the true support of any K-sparse signal x from noisy measurements y = Phi x + e in at most K iterations, provided that all the nonzero components of x and the elements of the matrix Phi satisfy certain requirements. The proposed method can improve the existing result. In particular, for the noiseless case, OMMP can exactly recover any K-sparse signal under the same RIP condition.