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

Martin Burger, Yury Korolev, Julian Rasch

Research output: Contribution to journalArticlepeer-review

8 Citations (SciVal)

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.

Original languageEnglish
Article number024006
JournalInverse Problems
Volume35
Issue number2
DOIs
Publication statusPublished - 3 Jan 2019

Keywords

  • Bregman distances
  • debiasing
  • error estimation
  • extended support
  • operator uncertainty
  • source condition
  • total variation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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