Sampling Strategies in Bayesian Inversion: A Study of RTO and Langevin Methods
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917828505894912 |
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| author | Laumont, Remi Dong, Yiqiu Andersen, Martin Skovgaard |
| author_facet | Laumont, Remi Dong, Yiqiu Andersen, Martin Skovgaard |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_16658 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sampling Strategies in Bayesian Inversion: A Study of RTO and Langevin Methods Laumont, Remi Dong, Yiqiu Andersen, Martin Skovgaard Image and Video Processing Computer Vision and Pattern Recognition Statistics Theory 65K10, 65K05, 65D18, 62F15, 62C10, 68Q25, 68U10, 90C25, 65C05 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. |
| title | Sampling Strategies in Bayesian Inversion: A Study of RTO and Langevin Methods |
| topic | Image and Video Processing Computer Vision and Pattern Recognition Statistics Theory 65K10, 65K05, 65D18, 62F15, 62C10, 68Q25, 68U10, 90C25, 65C05 |
| url | https://arxiv.org/abs/2406.16658 |