Generalized residual ratio thresholding

Abstract

Recovering sparse high dimensional vectors from low dimensional linear measurements is an important compressive sensing (CS) problem. Many CS algorithms assume a priori knowledge of parameters like signal sparsity or noise variance which are unavailable in most real-life problems. It is also difficult to efficiently estimate these parameters with finite sample guarantees. This article proposes a support recovery technique called generalized residual ratio thresholding (GRRT) that can operate many popular sparsity or noise variance dependent sparse recovery algorithms in a sparsity and noise variance oblivious fashion with finite sample guarantees when the noise is composed of independent and identically distributed (i.i.d) Gaussian random variables and design matrix satisfies certain regularity conditions. Numerical simulations and theoretical results in sparse estimation scenarios like single measurement vector, multiple measurement vectors, block sparsity etc. indicate that the performance of algorithms operated using GRRT is comparable to the performance of same algorithms when operated with a priori knowledge of sparsity and noise variance.