Convergence rates for regularization functionals with polyconvex integrands. (28th July 2017)

• Record Type: Journal Article
• Authors: Kirisits, Clemens; Scherzer, Otmar
• Is Part Of: Inverse problems. Volume 33:Number 8(2017:Aug.)
• Publication Date: 2017-07-28
• Subjects: inverse problems -- regularization theory -- convergence rates -- polyconvex functions -- Bregman distance -- image registration; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa7a1e
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Convergence rates results for variational regularization methods typically assume the regularization functional to be convex. While this assumption is natural for scalar-valued functions, it can be unnecessarily strong for vector-valued ones. In this paper we focus on regularization functionals with polyconvex integrands. Even though such functionals are nonconvex in general, it is possible to derive linear convergence rates with respect to a generalized Bregman distance, an idea introduced by Grasmair in 2010. As a case example we consider the image registration problem.