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 (25$s$, 1/10)-RIP, OMMP($M_0$) with $M_0$ = 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 $M$.