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Orthogonal matching pursuit (OMP) is a greedy algorithm widely used for therecovery of sparse signals from compressed measurements. In this paper, weanalyze the number of iterations required for the OMP algorithm to performexact recovery of sparse signals. Our analysis shows that OMP can accuratelyrecover all $K$-sparse signals within $\lceil 2.8 K \rceil$ iterations when themeasurement matrix satisfies a restricted isometry property (RIP). Our resultimproves upon the recent result of Zhang and also bridges the gap betweenZhang's result and the fundamental limit of OMP at which exact recovery of$K$-sparse signals cannot be uniformly guaranteed.

Exact Recovery of Sparse Signals via Orthogonal Matching Pursuit: How Many Iterations Do We Need?