Variational regularisation for inverse problems with imperfect forward operators and general noise models. (30th November 2020)

• Record Type: Journal Article
• Authors: Bungert, Leon; Burger, Martin; Korolev, Yury; Schönlieb, Carola-Bibiane
• Is Part Of: Inverse problems. Volume 36:Number 12(2020)
• Publication Date: 2020-11-30
• Subjects: imperfect forward models -- f-divergences -- Kullback–Leibler divergence -- Wasserstein distances -- Bregman distances -- discrepancy principle -- Banach lattices; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abc531
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and convex duality for general data fidelity terms and regularisation functionals. Both for a priori and a posteriori parameter choice rules, we obtain convergence rates of the regularised solutions in terms of Bregman distances. Our results apply to fidelity terms such as Wasserstein distances, φ -divergences, norms, as well as sums and infimal convolutions of those.