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Electrical Engineering and Systems Science > Image and Video Processing

arXiv:2406.16658 (eess)
[Submitted on 24 Jun 2024 (v1), last revised 5 Nov 2024 (this version, v3)]

Title:Sampling Strategies in Bayesian Inversion: A Study of RTO and Langevin Methods

Authors:Remi Laumont, Yiqiu Dong, Martin Skovgaard Andersen
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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 quality of the reconstruction and that the RTO method is more robust to the choice of the parameters.
Subjects: Image and Video Processing (eess.IV); Computer Vision and Pattern Recognition (cs.CV); Statistics Theory (math.ST)
MSC classes: 65K10, 65K05, 65D18, 62F15, 62C10, 68Q25, 68U10, 90C25, 65C05
Cite as: arXiv:2406.16658 [eess.IV]
  (or arXiv:2406.16658v3 [eess.IV] for this version)
  https://doi.org/10.48550/arXiv.2406.16658

Submission history

From: Remi Laumont [view email]
[v1] Mon, 24 Jun 2024 14:08:27 UTC (10,134 KB)
[v2] Tue, 25 Jun 2024 09:36:21 UTC (10,134 KB)
[v3] Tue, 5 Nov 2024 11:53:56 UTC (11,458 KB)
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