Controlled Total Variation regularization for inverse problems

TL;DR

This paper introduces a novel algorithm for inverse problems that relaxes traditional Total Variation minimization, leading to improved approximations as demonstrated in deconvolution tasks.

Contribution

It proposes a new controlled Total Variation regularization method that enhances inverse problem solutions beyond classical approaches.

Findings

Outperforms previous methods in deconvolution tasks

Provides better approximation to inverse problems

Demonstrates effectiveness through numerical experiments

Abstract

This paper provides a new algorithm for solving inverse problems, based on the minimization of the $L^2$ norm and on the control of the Total Variation. It consists in relaxing the role of the Total Variation in the classical Total Variation minimization approach, which permits us to get better approximation to the inverse problems. The numerical results on the deconvolution problem show that our method outperforms some previous ones.