Abstract-We consider the orthogonal matching pursuit (OMP) algorithm for the recovery of a high-dimensional sparse signal based on a small number of noisy linear measurements. OMP is an iterative greedy algorithm that selects at each step the column, which is most correlated with the current residuals. In this paper, we present a fully data driven OMP algorithm with explicit stopping rules. It is shown that under conditions on the mutual incoherence and the minimum magnitude of the nonzero components of the signal, the support of the signal can be recovered exactly by the OMP algorithm with high probability. In addition, we also consider the problem of identifying significant components in the case where some of the nonzero components are possibly small. It is shown that in this case the OMP algorithm will still select all the significant components before possibly selecting incorrect ones. Moreover, with modified stopping rules, the OMP algorithm can ensure that no zero components are selected.
Meanwhile, it has been proved that, under the conditions of the minimum magnitude of the nonzero elements in x and the mutual coherence or RIP, OMP can exactly reconstruct the support of the sparse signal from noisy measurements with high probability REF [15].
Orthogonal Matching Pursuit for Sparse Signal Recovery With Noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Computer Science