Compressive Sensing Using the Entropy Functional

TL;DR

This paper introduces a novel entropy-based functional as an alternative to the l1 norm for compressive sensing, enabling globally convergent iterative algorithms with improved mathematical properties.

Contribution

It proposes a modified entropy functional that is continuous, differentiable, and convex, facilitating new algorithms for compressive sensing.

Findings

The entropy functional approximates the l1 norm effectively.

The proposed method ensures global convergence of the reconstruction algorithm.

Simulation results demonstrate the method's viability.

Abstract

In most compressive sensing problems l1 norm is used during the signal reconstruction process. In this article the use of entropy functional is proposed to approximate the l1 norm. A modified version of the entropy functional is continuous, differentiable and convex. Therefore, it is possible to construct globally convergent iterative algorithms using Bregman's row action D-projection method for compressive sensing applications. Simulation examples are presented.