Image reconstruction with imperfect forward models and applications in deblurring

Yury Korolev, Jan Lellmann

Research output: Contribution to journalArticlepeer-review

7 Citations (SciVal)


We present and analyze an approach to image reconstruction problems with imperfect forward models based on partially ordered spaces—Banach lattices. In this approach, errors in the data and in the forward models are described using order intervals. The method can be characterized as the lattice analogue of the residual method, where the feasible set is defined by linear inequality constraints. The study of this feasible set is the main contribution of this paper. Convexity of this feasible set is examined in several settings, and modifications for introducing additional information about the forward operator are considered. Numerical examples demonstrate the performance of the method in deblurring with errors in the blurring kernel.

Original languageEnglish
Pages (from-to)197-218
Number of pages22
JournalSIAM Journal on Imaging Sciences
Issue number1
Publication statusPublished - 24 Jan 2018

Bibliographical note

Publisher Copyright:
© 2018 Yury Korolev and Jan Lellmann.


  • Blind deblurring
  • Blind deconvolution
  • Deblurring
  • Deconvolution
  • Imperfect forward models
  • Inverse problems
  • Residual method
  • Uncertainty quantification

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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