The Exact Recovery of Sparse Signals via Orthogonal Matching Pursuit

Abstract

This paper aims to investigate sufficient conditions for the recovery of sparse signals via the orthogonal matching pursuit (OMP) algorithm. In the noiseless case, we present a novel sufficient condition for the exact recovery of all $k$-sparse signals by the OMP algorithm, and demonstrate that this condition is sharp. In the noisy case, a sufficient condition for recovering the support of $k$-sparse signal is also presented. Generally, the computation for the restricted isometry constant (RIC) in these sufficient conditions is typically difficult, therefore we provide a new condition which is not only computable but also sufficient for the exact recovery of all $k$-sparse signals.