ipINPEEYInverse ProblemsIPInverse Problems0266-56111361-6420IOP Publishingipabc53110.1088/1361-6420/abc531abc531IP-102748.R2PaperVariational regularisation for inverse problems with imperfect forward operators and general noise models0000-0002-6554-9892BungertLeon1leon.bungert;martin.burger@fau.de0000-0003-2619-2912BurgerMartin10000-0002-6339-652XKorolevYury2*yk362@cam.ac.ukSchönliebCarola-Bibiane2 Department Mathematik, University of Erlangen-Nürnberg, Cauerstrasse 11, 91058 Erlangen, Germany Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

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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.

imperfect forward models f-divergencesKullback–Leibler divergenceWasserstein distancesBregman distancesdiscrepancy principleBanach latticesCantab Capital Institute for the Mathematics of InformationBundesministerium für Bildung und Forschunghttps://doi.org/10.13039/501100002347 05M16PMB (MED4D)H2020 Marie Skłodowska-Curie Actionshttps://doi.org/10.13039/100010665 691070 CHiPS 777826 (NoMADS)Engineering and Physical Sciences Research Councilhttps://doi.org/10.13039/501100000266 EP/N014588/1 EP/S026045/1 EP/T003553/1 EP/V003615/1Leverhulme Trusthttps://doi.org/10.13039/501100000275 Breaking the non-convexity barrier Philip Leverhulme PrizeWellcome Trusthttps://doi.org/10.13039/100004440 Wellcome Innovator Award RG98755National Physical Laboratoryhttps://doi.org/10.13039/501100007851 Royal Societyhttps://doi.org/10.13039/501100000288 NF170045Alan Turing Institutehttps://doi.org/10.13039/100012338 ccc1361-6420/20/125014+32$33.00printedPrinted in the UKcrossmarkyes