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Variational regularisation for inverse problems with imperfect forward operators and general noise models

Published version
Peer-reviewed

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Authors

martin.burger@fau.de 
Schönlieb, Carola-Bibiane 

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.

Description

Funder: Cantab Capital Institute for the Mathematics of Information


Funder: National Physical Laboratory; doi: https://doi.org/10.13039/501100007851


Funder: Alan Turing Institute; doi: https://doi.org/10.13039/100012338

Keywords

Paper, imperfect forward models, f-divergences, Kullback–Leibler divergence, Wasserstein distances, Bregman distances, discrepancy principle, Banach lattices

Journal Title

Inverse Problems

Conference Name

Journal ISSN

0266-5611
1361-6420

Volume Title

36

Publisher

IOP Publishing
Sponsorship
Bundesministerium für Bildung und Forschung (05M16PMB (MED4D))
H2020 Marie Skłodowska-Curie Actions (691070 CHiPS 777826 (NoMADS))
Engineering and Physical Sciences Research Council (EP/N014588/1 EP/S026045/1 EP/T003553/1 EP/V003615/1)
Leverhulme Trust (Breaking the non-convexity barrier Philip Leverhulme Prize)
Wellcome Trust (Wellcome Innovator Award RG98755)
Royal Society (NF170045)