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

Leon Bungert, Martin Burger, Yury Korolev, Carola Bibiane Schönlieb

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3 Citations (SciVal)

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

Original languageEnglish
Article number125014
JournalInverse Problems
Volume36
Issue number12
DOIs
Publication statusPublished - Dec 2020

Keywords

  • Banach lattices
  • Bregman distances
  • Discrepancy principle
  • F -divergences
  • Imperfect forward models
  • Kullback-Leibler divergence
  • Wasserstein distances

ASJC Scopus subject areas

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

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