Binary Compressive Sensing via Smoothed $\ell_0$ Gradient Descent

TL;DR

This paper introduces a novel compressive sensing algorithm tailored for binary signals, utilizing a smoothed $ ext{l}_0$ gradient descent approach that improves recovery accuracy and speed over existing methods.

Contribution

It proposes a new non-convex optimization algorithm specifically designed for binary signal reconstruction using smoothed $ ext{l}_0$ norms.

Findings

Outperforms existing algorithms in recovery rate

Requires shorter run time

Effective for binary signal reconstruction

Abstract

We present a Compressive Sensing algorithm for reconstructing binary signals from its linear measurements. The proposed algorithm minimizes a non-convex cost function expressed as a weighted sum of smoothed $\ell_0$ norms which takes into account the binariness of signals. We show that for binary signals the proposed algorithm outperforms other existing algorithms in recovery rate while requiring a short run time.