The Exact Recovery of Sparse Signals Via Orthogonal Matching Pursuit

Abstract

This paper aims to investigate sufficient conditions for the r 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 allk-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.