An improved RIP-based performance guarantee for sparse signal reconstruction with noise via orthogonal matching pursuit

Stability of sparse signal reconstruction in the noisy case via orthogonal matching pursuit has been widely studied in the literature of compressive sensing. To guarantee exact support identification under l₂ / l_∞-norm bounded noise, sufficient conditions, characterized in terms of the restricted isometry constant and the minimum magnitude of the signal components, were reported in [2]. In this paper, we derive a less conservative set of sufficient conditions of the same kind. Our analyses exploit a newly developed “near-orthogonality” condition, which specifies the achievable angles between two compressed orthogonal sparse vectors. Thus, our improved performance guarantee benefits from more explicit knowledge about the geometry of the compressed space.