Regularization by denoising: Bayesian model and Langevin-within-split Gibbs sampling

• URL: http://arxiv.org/abs/2402.12292v1
• Date: Mon, 19 Feb 2024 17:12:16 GMT
• Title: Regularization by denoising: Bayesian model and Langevin-within-split Gibbs sampling
• Authors: Elhadji C. Faye, Mame Diarra Fall and Nicolas Dobigeon
• Abstract summary: This paper introduces a Bayesian framework for image inversion by deriving a probabilistic counterpart to the regularization-by-denoising (RED) paradigm. It implements a Monte Carlo algorithm specifically tailored for sampling from the resulting posterior distribution, based on anally exact data augmentation (AXDA) The proposed algorithm is an approximate instance of split Gibbs sampling (SGS) which embeds one Langevin Monte Carlo step.
• Score: 6.453497703172228
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper introduces a Bayesian framework for image inversion by deriving a probabilistic counterpart to the regularization-by-denoising (RED) paradigm. It additionally implements a Monte Carlo algorithm specifically tailored for sampling from the resulting posterior distribution, based on an asymptotically exact data augmentation (AXDA). The proposed algorithm is an approximate instance of split Gibbs sampling (SGS) which embeds one Langevin Monte Carlo step. The proposed method is applied to common imaging tasks such as deblurring, inpainting and super-resolution, demonstrating its efficacy through extensive numerical experiments. These contributions advance Bayesian inference in imaging by leveraging data-driven regularization strategies within a probabilistic framework.

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