期刊
INVERSE PROBLEMS
卷 36, 期 12, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1361-6420/abc531
关键词
imperfect forward models; f-divergences; Kullback– Leibler divergence; Wasserstein distances; Bregman distances; discrepancy principle; Banach lattices
资金
- European Union's Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant [777826]
- Bundesministerium fur Bildung und Forschung [05M16PMB]
- Royal Society (Newton International Fellowship) [NF170045]
- EPSRC [EP/S026045/1, EP/T003553/1, EP/V003615/1]
- Cantab Capital Institute for the Mathematics of Information
- National Physical Laboratory
- Leverhulme Trust project on 'Breaking the non-convexity barrier'
- Philip Leverhulme Prize
- Wellcome Innovator Award [RG98755]
- European Union Horizon 2020 research and innovation programmes under the Marie Skodowska-Curie grant [777826 NoMADS, 691070 CHiPS]
- Alan Turing Institute
- EPSRC Centre [EP/N014588/1]
- EPSRC [EP/T003553/1, EP/N014588/1, EP/M00483X/1, EP/S026045/1] Funding Source: UKRI
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, phi-divergences, norms, as well as sums and infimal convolutions of those.
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