Sampling strategies in Bayesian inversion: A study of RTO and Langevin methods

Rémi Laumont*, Yiqiu Dong, Martin Skovgaard Andersen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

This paper studies two classes of sampling methods for the solution of inverse problems, namely Randomize-Then-Optimize (RTO), which is rooted in sensitivity analysis, and Langevin methods, which are rooted in the Bayesian framework. The two classes of methods correspond to different assumptions and yield samples from different target distributions. We highlight the main conceptual and theoretical differences between the two approaches and compare them from a practical point of view by tackling two classical inverse problems in imaging: deblurring and inpainting. We show that the choice of the sampling method has a significant impact on the reconstruction and the proposed uncertainty.
Original languageEnglish
JournalInverse Problems and Imaging
Number of pages21
ISSN1930-8337
DOIs
Publication statusAccepted/In press - 2025

Keywords

  • Inverse problem
  • Sampling
  • RTO
  • Langevin methods
  • Deblurring
  • Inpainting
  • Parameter selection

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