A proximal approach for signal recovery based on information measures

Recently, methods based on Non-Local Total Variation (NLTV) minimization have become popular in image processing. They play a prominent role in a variety of applications such as denoising, compressive sensing, and inverse problems in general. In this work, we extend the NLTV framework by using some information divergences to build new sparsity measures for signal recovery. This leads to a general convex formulation of optimization problems involving information divergences. We address these problems by means of fast parallel proximal algorithms. In denoising and deconvolution examples, our approach is compared with ℓ₂-NLTV based approaches. The proposed approach applies to a variety of other inverse problems.