Variational regularisation for inverse problems with imperfect forward operators and general noise models

Bungert L, Burger M, Korolev Y, Schönlieb CB (2020)

Publication Status: Submitted

Publication Type: Journal article

Future Publication Type: Journal article

Publication year: 2020

Journal

Inverse Problems Institute of Physics: Hybrid Open Access

Book Volume: 36

Journal Issue: 12

URI: https://iopscience.iop.org/article/10.1088/1361-6420/abc531

DOI: 10.1088/1361-6420/abc531

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, phiv-divergences, norms, as well as sums and infimal convolutions of those.

Authors with CRIS profile

Leon Bungert
Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

University of Cambridge GB United Kingdom (GB)

How to cite

APA:

Bungert, L., Burger, M., Korolev, Y., & Schönlieb, C.B. (2020). Variational regularisation for inverse problems with imperfect forward operators and general noise models. Inverse Problems, 36(12). https://dx.doi.org/10.1088/1361-6420/abc531

MLA:

Bungert, Leon, et al. "Variational regularisation for inverse problems with imperfect forward operators and general noise models." Inverse Problems 36.12 (2020).

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