Convergence rates and structure of solutions of inverse problems with imperfect forward models

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autor(en): Burger M, Korolev Y, Rasch J
Zeitschrift: Inverse Problems
Jahr der Veröffentlichung: 2019
Band: 35
Heftnummer: 2
ISSN: 0266-5611


Abstract

The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the regularised solutions and allow us to obtain convergence rates in terms of Bregman distances-as usual in inverse problems, under an additional assumption on the exact solution called the source condition. These results are obtained for general absolutely one-homogeneous functionals. In the special case of TV-based regularisation we also study the structure of regularised solutions and prove convergence of their level sets to those of an exact solution. Finally, using the developed theory, we adapt the concept of debiasing to inverse problems with imperfect operators and propose an approach to pointwise error estimation in TV-based regularisation.


FAU-Autoren / FAU-Herausgeber

Burger, Martin Prof. Dr.
Lehrstuhl für Angewandte Mathematik


Autor(en) der externen Einrichtung(en)
University of Cambridge
Westfälische Wilhelms-Universität (WWU) Münster


Zitierweisen

APA:
Burger, M., Korolev, Y., & Rasch, J. (2019). Convergence rates and structure of solutions of inverse problems with imperfect forward models. Inverse Problems, 35(2). https://dx.doi.org/10.1088/1361-6420/aaf6f5

MLA:
Burger, Martin, Yury Korolev, and Julian Rasch. "Convergence rates and structure of solutions of inverse problems with imperfect forward models." Inverse Problems 35.2 (2019).

BibTeX: 

Zuletzt aktualisiert 2019-25-02 um 08:28