Sampling Matrix Perturbation Analysis of Subspace Pursuit for Compressive Sensing

Abstract

In this paper, the Subspace Pursuit (SP) recovery of signals with sensing matrix perturbations is analyzed. Previous studies have only considered the robustness of Basis pursuit and greedy algorithms to recover the signal in the presence of additive noise with measurement and/or signal. Since it is impractical to exactly implement the sampling matrix A in a physical sensor, precision errors must be considered. Recently, work has been done to analyze the methods with noise in the sampling matrix, which generates a multiplicative noise term. This new perturbed framework (both additive and multiplicative noise) extends the prior work of Basis pursuit and greedy algorithms on stable signal recovery from incomplete and inaccurate measurements. Our works show that, under reasonable conditions, the stability of the SP solution of the completely perturbed scenario was limited by the total noise in the observation.