Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization. (11th June 2022)

• Record Type: Journal Article
• Authors: Hintermüller, Michael; Papafitsoros, Kostas; Rautenberg, Carlos N.; Sun, Hongpeng
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 8(2022)
• Page Start: 887
• Page End: 932
• Publication Date: 2022-06-11
• Subjects: Image denoising -- regularization parameter selection -- bilevel optimization -- total generalized variation; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2069812
• Languages: English
• ISSNs: 0163-0563

Abstract

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.