An improved RIP-based performance guarantee for sparse signal recovery via orthogonal matching pursuit

A sufficient condition reported very recently for perfect recovery of a K-sparse vector via orthogonal matching pursuit in K iterations is that the restricted isometry constant of the sensing matrix satisfies δ_K+1 <; 1/(√K + 1). By exploiting a “near orthogonality” condition specified in terms of the achievable angles between two orthogonal sparse vectors upon compression, this paper shows that the requirement on δ_K+1 can be further relaxed to δ_k+1 <; √4k+1 - 12K. This result thus narrows the gap between the so far best known bound and the ultimate performance guarantee δ_K+1 <; 1/√K that is conjectured by Dai and Milenkovic in 2009.