On Probability of Support Recovery for Orthogonal Matching Pursuit Using Mutual Coherence

In this letter, we present a new coherence-based performance guarantee for the orthogonal matching pursuit (OMP) algorithm. A lower bound for the probability of correctly identifying the support of a sparse signal with additive white Gaussian noise is derived. Compared to previous research work, the new bound takes into account the signal parameters, such as dynamic range, noise variance, and sparsity. Numerical simulations show significant improvements over previous research work and a closer match to empirically obtained results of the OMP algorithm.