Recovery of sparse signals using OMP and its variants: convergence analysis based on RIP

Abstract

Orthogonal matching pursuit (OMP) is a commonly used algorithm for recovery sparse signals due to its low complexity and simple implementation. We analyze the convergence property of OMP based on the restricted isometry property (RIP), and show that the OMP algorithm can exactly recover an arbitrary K-sparse signal using K steps provided that the sampling matrix Φ satisfies the RIP with parameter . In addition, we also give the convergence analysis of OMP for the case of inaccurate measurements. Moreover, a variant of OMP, referred to as multi-candidate OMP (MOMP) algorithm, is proposed to recover sparse signals, which can further reduce the computational complexity of OMP. The key point of MOMP is that at each step it selects multi-candidates adding to the optimal atom set, whilst OMP only selects one atom. We also present the convergence analysis of MOMP using the RIP. Finally, we testify the performance of the proposed algorithm using several numerical experiments.