Lunz, S;
Hauptmann, A;
Tarvainen, T;
Schönlieb, C-B;
Arridge, S;
(2021)
On Learned Operator Correction in Inverse Problems.
SIAM Journal on Imaging Sciences
, 14
(1)
pp. 92-127.
10.1137/20m1338460.
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Abstract
We discuss the possibility of learning a data-driven explicit model correction for inverse problems and whether such a model correction can be used within a variational framework to obtain regularized reconstructions. This paper discusses the conceptual difficulty of learning such a forward model correction and proceeds to present a possible solution as a forward-adjoint correction that explicitly corrects in both data and solution spaces. We then derive conditions under which solutions to the variational problem with a learned correction converge to solutions obtained with the correct operator. The proposed approach is evaluated on an application to limited view photoacoustic tomography and compared to the established framework of the Bayesian approximation error method.
| Type: | Article |
|---|---|
| Title: | On Learned Operator Correction in Inverse Problems |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/20m1338460 |
| Publisher version: | http://dx.doi.org/10.1137/20m1338460 |
| Language: | English |
| Additional information: | © 2021, Society for Industrial and Applied Mathematics. Published by SIAM under the terms of the Creative Commons 4.0 license |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10122533 |
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