Automated Parameter Selection for Total Variation Minimization in Image Restoration

TL;DR

This paper introduces automated methods for selecting regularization parameters in total variation models for image restoration, using discrepancy principles and multi-scale optimization, with demonstrated efficiency in denoising and deblurring tasks.

Contribution

It presents novel automated parameter selection algorithms for total variation models, including locally varying parameters, with convergence analysis and practical numerical validation.

Findings

Algorithms are efficient and competitive in image denoising.

Methods successfully handle both scalar and locally varying parameters.

Numerical experiments confirm the effectiveness of the proposed approaches.

Abstract

Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an $L^{\tau}$-data fidelity term, $\tau\in \{1,2\}$, are presented. The automated selection of the regularization parameter is based on the discrepancy principle, whereby in each iteration a total variation model has to be minimized. In the case of a locally varying parameter this amounts to solve a multi-scale total variation minimization problem. For solving the constituted multi-scale total variation model convergent first and second order methods are introduced and analyzed. Numerical experiments for image denoising and image deblurring show the efficiency, the competitiveness, and the performance of the proposed fully automated scalar and locally varying parameter selection algorithms.