Simultaneous Orthogonal Matching Pursuit With Noise Stabilization: Theoretical Analysis

Abstract: This paper studies the joint support recovery of similar sparse vectors on the basis of a limited number of noisy linear measurements, i.e., in a multiple measurement vector (MMV) model. The additive noise signals on each measurement vector are assumed to be Gaussian and to exhibit different variances. The simultaneous orthogonal matching pursuit (SOMP) algorithm is generalized to weight the impact of each measurement vector on the choice of the atoms to be picked according to their noise levels. The new algorithm is referred to as SOMP-NS where NS stands for noise stabilization. To begin with, a theoretical framework to analyze the performance of the proposed algorithm is developed. This framework is then used to build conservative lower bounds on the probability of partial or full joint support recovery. Numerical simulations show that the proposed algorithm outperforms SOMP and that the theoretical lower bound provides a great insight into how SOMP-NS behaves when the weighting strategy is modified.