Robust Recovery of Joint Sparse Signals via Simultaneous Orthogonal Matching Pursuit

Abstract

Simultaneous orthogonal matching pursuit (SOMP) is a classical algorithm for solving multiple measurement vectors (MMV) problems. In this paper, we analyze the theoretical performance of the SOMP algorithm using the restricted isometry property (RIP). In particular, we show that SOMP can robustly recover any joint K-sparse signal from its noisy measurements if the sensing matrix satisfies the RIP with isometry constant upper bounded by an absolute constant. Our result significantly improves upon some exiting results that require the isometry constant to be at least inversely proportional to $\sqrt K$.