Statistics > Machine Learning
[Submitted on 15 Aug 2023 (v1), last revised 25 Oct 2023 (this version, v2)]
Title:Monte Carlo guided Diffusion for Bayesian linear inverse problems
View PDFAbstract:Ill-posed linear inverse problems arise frequently in various applications, from computational photography to medical imaging. A recent line of research exploits Bayesian inference with informative priors to handle the ill-posedness of such problems. Amongst such priors, score-based generative models (SGM) have recently been successfully applied to several different inverse problems. In this study, we exploit the particular structure of the prior defined by the SGM to define a sequence of intermediate linear inverse problems. As the noise level decreases, the posteriors of these inverse problems get closer to the target posterior of the original inverse problem. To sample from this sequence of posteriors, we propose the use of Sequential Monte Carlo (SMC) methods. The proposed algorithm, MCGDiff, is shown to be theoretically grounded and we provide numerical simulations showing that it outperforms competing baselines when dealing with ill-posed inverse problems in a Bayesian setting.
Submission history
From: Yazid Janati El Idrissi [view email][v1] Tue, 15 Aug 2023 18:32:00 UTC (42,450 KB)
[v2] Wed, 25 Oct 2023 22:35:20 UTC (24,290 KB)
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