Regularization by denoising: Bayesian model and Langevin-within-split Gibbs sampling
This work advances Bayesian inference in imaging by integrating data-driven regularization, though it appears incremental as it builds on existing RED paradigms.
The paper tackled image inversion problems by developing a Bayesian framework for regularization-by-denoising and implementing a Monte Carlo sampling algorithm, showing efficacy in tasks like deblurring and super-resolution through numerical experiments.
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.