TGV-based restoration of Poissonian images with automatic estimation of the regularization parameter

TL;DR

This paper presents a method for restoring Poisson-noisy images using TGV regularization with an automatic parameter estimation, solved via a 3-block ADMM, showing promising preliminary results.

Contribution

It introduces an automatic strategy for selecting the regularization parameter in TGV-based Poisson image restoration, enhancing existing methods.

Findings

Effective automatic parameter estimation for TGV regularization.

Improved preservation of image features in Poisson noise restoration.

Preliminary numerical experiments demonstrate the approach's potential.

Abstract

The problem of restoring images corrupted by Poisson noise is common in many application fields and, because of its intrinsic ill posedness, it requires regularization techniques for its solution. The effectiveness of such techniques depends on the value of the regularization parameter balancing data fidelity and regularity of the solution. Here we consider the Total Generalized Variation regularization introduced in [SIAM J. Imag. Sci, 3(3), 492-526, 2010], which has demonstrated its ability of preserving sharp features as well as smooth transition variations, and introduce an automatic strategy for defining the value of the regularization parameter. We solve the corresponding optimization problem by using a 3-block version of ADMM. Preliminary numerical experiments support the proposed approach.