Robust sensing matrix design for the Orthogonal Matching Pursuit algorithm in compressive sensing

Abstract

In compressive sensing, Orthogonal Matching Pursuit (OMP) is a greedy algorithm used for recovering sparse signals from their incomplete linear measurements. Conventionally, the OMP algorithm relies on both the measurement matrix and the measurement signal to reconstruct sparse signals. A sensing matrix can be designed to have a small mutual coherence with respect to (w.r.t.) the measurement matrix, which is used to boost the performance of the OMP algorithm in sparse signal reconstruction. Nevertheless, sensing matrices designed by current methods are vulnerable to measurement noises. In this paper, we begin by examining the underlying cause of the non-robustness to measurement noises exhibited by these sensing matrices. Subsequently, we propose a novel approach to design a robust sensing matrix capable of withstanding the influence of measurement noises. Finally, we conduct numerical simulations to demonstrate the effectiveness and robustness of the sensing matrix designed by the proposed method.