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.

该论文介绍了一种贝叶斯框架图像反演方法，通过导出一种与正则化去噪（RED）范式相对应的概率模型实现。同时，还实现了一种针对得到的后验分布进行采样的蒙特卡罗算法，其基于渐近精确的数据增广（AXDA）。该算法是分裂吉布斯采样（SGS）的近似实例，嵌入了一个 Langevin 蒙特卡罗步骤。该方法被应用于常见的图像处理任务，如去模糊、修复和超分辨，通过广泛的数值实验证明了其有效性。这些贡献通过在概率框架内利用数据驱动的正则化策略推进了图像处理中的贝叶斯推断。