A blind stopping condition for orthogonal matching pursuit with applications to compressive sensing radar

Abstract

Orthogonal matching pursuit (OMP) is a popular greedy algorithm because of its simplicity and low computational cost. In the application of OMP, one of the most important issue is to design a stopping condition according to some prior information, such as sparsity and noise level. In this paper, we provide a blind stopping condition for OMP in the presence of Gaussian noise. We theoretically analyze the stopping condition in terms of the mutual incoherence and the minimum component signal-to-noise ratio (SNR), with which OMP can stop with correct support recovery. Different from other alternatives, the proposed stopping condition can be explicitly determined regardless of prior information. So it is much suitable for practical applications. In the application of compressive sensing pulse-Doppler radar, we further analyze the support recovery performance of the proposed condition. By separately recovering the targets belonging to different Doppler frequencies, we remarkably reduce the requirement on the minimum component SNR of all targets, and thus our stopping condition is applicable to low SNR scenes. Numerical results illustrate that the proposed condition has comparable performance to the alternative with a priori information.