On sparse recovery with Structured Noise under sensing constraints

摘要

This paper considers sparse signal recovery under sensing constraints originating from the limitations of practical data acquisition systems. Such limitations introduce non-linearities in the underlying measurement model. We first develop a more accurate measurement model with structured noise representing a known non-linear function of the sparse signal obtained by leveraging side information about the physical sampling structure. Then, we devise two iterative denoising algorithms, namely, Orthogonal Matching Pursuit with Structured Noise (OMPSN), and Subspace Pursuit with Structured Noise (SPSN) that are shown to enhance the quality of sparse recovery in presence of physical constraints by iteratively estimating and eliminating the non-linear term from the measurements. Numerical and simulation results demonstrate that the proposed algorithms outperform standard algorithms in detecting the support and estimating the sparse vector.