Sparse linear regression with compressed and low-precision data via concave quadratic programming

TL;DR

This paper introduces a non-convex quadratic programming approach for recovering sparse signals from compressed, low-precision data, improving support recovery when classical methods struggle due to quantization noise.

Contribution

It proposes a novel non-convex quadratic programming method that leverages prior information to enhance sparse support recovery under quantization noise.

Findings

The method outperforms classical l1 approaches in certain conditions.

Sufficient conditions for successful recovery are established.

Numerical simulations demonstrate practical effectiveness.

Abstract

We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may be present in the feasible set, and the classical l1 approach may be unsuccessful. For this motivation, we propose a non-convex quadratic programming method, which exploits prior information on the magnitude of the non-zero parameters. This results in a more efficient support recovery. We provide sufficient conditions for successful recovery and numerical simulations to illustrate the practical feasibility of the proposed method.