Robust GNC approach for quantised compressed sensing

Abstract

Practical acquisition of compressed sensing measurements involves a finite-range finite-precision quantisation step. To solve the sparse recovery problem and handle the quantisation distortion, this Letter proposes a non-smooth graduated-non-convexity approach that follows a path of gradually improved solutions along a sequence of non-smooth non-convex optimisation problems that progressively promote quantisation consistency (QC) and sparsity. We consider two classes of multi-scale continuous approximation functions to depict intermediate QC degrees and sparsity-inducing strengths, respectively, and apply recent proximal splitting methods to solve the resulting subproblem at each refinement scale. The simulations demonstrate the convergence of intermediate solutions to a nearly optimal estimation, in terms of accuracy and support recovery.