The Performance of Orthogonal Multi-Matching Pursuit under the Restricted Isometry Property

Abstract

The orthogonal multi-matching pursuit (OMMP) is a natural extension of the orthogonal matching pursuit (OMP). We denote the OMMP with the parameter M as OMMP(M) where M ≥ 1 is an integer. The main difference between OMP and OMMP(M) is that OMMP(M) selects M atoms per iteration, while OMP only adds one atom to the optimal atom set. In this paper, we study the performance of orthogonal multi-matching pursuit under RIP. In particular, we show that, when the measurement matrix A satisfies (25s, 1/10)-RIP, OMMP(M0) with M0 = 12 can recover s-sparse signals within s iterations. We furthermore prove that OMMP(M) can recover s-sparse signals within O(s/M) iterations for a large class of M . Mathematics subject classification: 94A12, 65H99, 65D15.