Non-convex approach to binary compressed sensing

TL;DR

This paper introduces a non-convex method for binary compressed sensing that improves signal recovery by focusing on local minimization of a specially designed cost functional, outperforming traditional convex methods like Lasso.

Contribution

The paper presents a novel non-convex optimization approach for binary signal recovery in compressed sensing, including theoretical guarantees and a practical procedure for local minimization.

Findings

The proposed method successfully recovers binary signals under mild conditions.

Numerical experiments demonstrate improved performance over Lasso.

The approach offers a new perspective on non-convex optimization in compressed sensing.

Abstract

We propose a new approach to the recovery of binary signals in compressed sensing, based on the local minimization of a non-convex cost functional. The desired signal is proved to be a local minimum of the functional under mild conditions on the sensing matrix and on the number of measurements. We develop a procedure to achieve the desired local minimum, and, finally, we propose numerical experiments that show the improvement obtained by the proposed approach with respect to the classical convex approach, i.e., Lasso.