Orthogonal Matching Pursuit for Sparse Signal Recovery with Noise
Orthogonal Matching Pursuit for Sparse Signal Recovery with Noise
- 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 measurements. The OMP is an iterative greedy algorithm that selects at each step the variable which is most correlated with the current residuals. Stopping rules are given and the algorithm is fully data driven. 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 variables 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 variables before possibly selecting incorrect ones. Moreover, with modified stopping rules, the OMP algorithm can ensure that no incorrect variables are selected.
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