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Orthogonal matching pursuit (OMP) is a widely used greedy algorithm for recovering the support of a sparse signal x from the underdetermined model y = Ax. In practice, we should analyze the performance of OMP under general perturbations, which means that both y and A are perturbed. In this paper, under general perturbations, we present necessary and sufficient conditions for the exact support recovery with the OMP. We also discuss the performance of OMP for recovering &#x03B1; strongly decaying sparse signals. Typically, in the noise-free case, we show that the upper bound of our sufficient condition is unrelated with K and is a sharp bound. Furthermore, we establish sufficient conditions for the recovery of OMP, which can guarantee that the recovery is in the order of the signal entries' magnitude.

An Improved Analysis for Support Recovery With Orthogonal Matching Pursuit Under General Perturbations