Analysis of orthogonal multi-matching pursuit under restricted isometry property

Abstract

Orthogonal multi-matching pursuit (OMMP) is a natural extension of orthogonal matching pursuit (OMP) in the sense that N (N ⩾ 1) indices are selected per iteration instead of 1. In this paper, the theoretical performance of OMMP under the restricted isometry property (RIP) is presented. We demonstrate that OMMP can exactly recover any K-sparse signal from fewer observations y = Φx, provided that the sampling matrix Φ satisfies $$\delta _{KN - N + 1} + \sqrt {\frac{K} {N}} \theta _{KN - N + 1} ,N < 1.$$ Moreover, the performance of OMMP for support recovery from noisy observations is also discussed. It is shown that, for l2 bounded and l∞ bounded noisy cases, OMMP can recover the true support of any K-sparse signal under conditions on the restricted isometry property of the sampling matrix Φ and the minimum magnitude of the nonzero components of the signal.