Compressive sensing using the modified entropy functional

In most compressive sensing problems, ℓ1ℓ1 norm is used during the signal reconstruction process. In this article, a modified version of the entropy functional is proposed to approximate the ℓ1ℓ1 norm. The proposed modified version of the entropy functional is continuous, differentiable and convex. Therefore, it is possible to construct globally convergent iterative algorithms using Bregmanʼs row-action method for compressive sensing applications. Simulation examples with both 1D signals and images are presented.