Variational regularisation for inverse problems with imperfect forward operators and general noise models
Numerical Analysis
2020-12-25 v4 Numerical Analysis
Optimization and Control
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 regularized solutions in terms of Bregman distances. Our results apply to fidelity terms such as Wasserstein distances, f-divergences, norms, as well as sums and infimal convolutions of those.
Cite
@article{arxiv.2005.14131,
title = {Variational regularisation for inverse problems with imperfect forward operators and general noise models},
author = {Leon Bungert and Martin Burger and Yury Korolev and Carola-Bibiane Schoenlieb},
journal= {arXiv preprint arXiv:2005.14131},
year = {2020}
}