The performance of orthogonal multi-matching pursuit under RIP

The orthogonal multi-matching pursuit (OMMP) is a natural extension of 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 (OMMP) under RIP. In particular, we show that, when the measurement matrix A satisfies (9s, 1/10)-RIP, there exists an absolutely constant M0 ≤ 8 so that OMMP(M0) can recover s-sparse signal within s iterations. We furthermore prove that, for slowly-decaying s-sparse signal, OMMP(M) can recover s-sparse signal within O( s M ) iterations for a large class of M . In particular, for M = s a with a ∈ [0, 1/2], OMMP(M) can recover slowly-decaying s-sparse signal within O(s1−a) iterations. The result implies that OMMP can reduce the computational complexity heavily.