Performance of Orthogonal Matching Pursuit for Multiple Measurement Vectors

Abstract

In this paper, we consider orthogonal matching pursuit (OMP) algorithm for multiple measurement vectors (MMV) problem. The robustness of OMPMMV is studied under general perturbations---when the measurement vectors as well as the sensing matrix are incorporated with additive noise. The main result shows that although exact recovery of the sparse solutions is unrealistic in noisy scenario, recovery of the support set of the solutions is guaranteed under suitable conditions. Specifically, a sufficient condition is derived that guarantees exact recovery of the sparse solutions in noiseless scenario.