In this paper, a new stopping rule is proposed for orthogonal multi-matching
pursuit (OMMP). We show that, for ℓ2 bounded noise case, OMMP with the new
stopping rule can recover the true support of any K-sparse signal x from noisy
measurements y = Φx + e in at most K iterations, provided that all the nonzero
components of x and the elements of the matrix Φ 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.