Variational regularisation for inverse problems with imperfect forward operators and general noise models.
Publication Date
2020-12Journal Title
Inverse Probl
ISSN
0266-5611
Publisher
IOP Publishing
Volume
36
Issue
12
Language
en
Type
Article
This Version
VoR
Metadata
Show full item recordCitation
Bungert, L., Burger, M., Korolev, Y., & Schönlieb, C. (2020). Variational regularisation for inverse problems with imperfect forward operators and general noise models.. Inverse Probl, 36 (12) https://doi.org/10.1088/1361-6420/abc531
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
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.
Keywords
Paper, imperfect forward models, f-divergences, Kullback–Leibler divergence, Wasserstein distances, Bregman distances, discrepancy principle, Banach lattices
Sponsorship
Engineering and Physical Sciences Research Council (EP/M00483X/1)
Engineering and Physical Sciences Research Council (EP/N014588/1)
European Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (777826)
Leverhulme Trust (PLP-2017-275)
National Physical Laboratory (NPL) (Unknown)
Alan Turing Institute (Unknown)
EPSRC (EP/S026045/1)
EPSRC (EP/T003553/1)
European Commission Horizon 2020 (H2020) Marie Sk?odowska-Curie actions (691070)
EPSRC (EP/V003615/1)
Identifiers
ipabc531, abc531, ip-102748.r2
External DOI: https://doi.org/10.1088/1361-6420/abc531
This record's URL: https://www.repository.cam.ac.uk/handle/1810/332490
Rights
Licence:
https://creativecommons.org/licenses/by/4.0/
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