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Orthogonal Matching Pursuit (OMP) is a simple, yet empirically competitivealgorithm for sparse recovery. Recent developments have shown that OMPguarantees exact recovery of K-sparse signals with K or more than K iterationsif the observation matrix satisfies the restricted isometry property (RIP) withsome conditions. We develop RIP-based online guarantees for recovery of aK-sparse signal with more than K OMP iterations. Though these guarantees cannotbe generalized to all sparse signals a priori, we show that they can still holdonline when the state-of-the-art K-step recovery guarantees fail. In addition,we present bounds on the number of correct and false indices in the supportestimate for the derived condition to be less restrictive than the K-stepguarantees. Under these bounds, this condition guarantees exact recovery of aK-sparse signal within 3K/2 iterations, which is much less than the number ofsteps required for the state-of-the-art exact recovery guarantees with morethan K steps. Moreover, we present phase transitions of OMP in comparison tobasis pursuit and subspace pursuit, which are obtained after extensive recoverysimulations involving different sparse signal types. Finally, we empiricallyanalyse the number of false indices in the support estimate, which indicatesthat these do not violate the developed upper bound in practice.

Online Recovery Guarantees and Analytical Results for OMP