Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization

12Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

This article is free to access.

Abstract

Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This helps to avoid the staircasing effect of Total Variation (TV) regularization, while still preserving sharp contrasts in images. The associated regularization effect crucially hinges on two parameters whose proper adjustment represents a challenging task. In this work, a bilevel optimization framework with a suitable statistics-based upper level objective is proposed in order to automatically select these parameters. The framework allows for spatially varying parameters, thus enabling better recovery in high-detail image areas. A rigorous dualization framework is established, and for the numerical solution, a Newton type method for the solution of the lower level problem, i.e. the image reconstruction problem, and a bilevel TGV algorithm are introduced. Denoising tests confirm that automatically selected distributed regularization parameters lead in general to improved reconstructions when compared to results for scalar parameters.

Cite

CITATION STYLE

APA

Hintermüller, M., Papafitsoros, K., Rautenberg, C. N., & Sun, H. (2022). Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization. Numerical Functional Analysis and Optimization, 43(8), 887–932. https://doi.org/10.1080/01630563.2022.2069812

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free