Estimating high-quality images while also quantifying their uncertainty are two desired features in an image reconstruction algorithm for solving ill-posed inverse problems. In this paper, we propose plug-and-play Monte Carlo (PMC) as a principled framework for characterizing the space of possible solutions to a general inverse problem. PMC is able to incorporate expressive score-based generative priors for high-quality image reconstruction while also performing uncertainty quantification via posterior sampling. In particular, we introduce two PMC algorithms which can be viewed as the sampling analogues of the traditional plug-and-play priors (PnP) and regularization by denoising (RED) algorithms. We also establish a theoretical analysis for characterizing the convergence of the PMC algorithms. Our analysis provides non-asymptotic stationarity guarantees for both algorithms, even in the presence of non-log-concave likelihoods and imperfect score networks. We demonstrate the performance of the PMC algorithms on multiple representative inverse problems with both linear and nonlinear forward models. Experimental results show that PMC significantly improves reconstruction quality and enables high-fidelity uncertainty quantification.

本文提出了一种基于蒙特卡洛方法的插拔算法，用于解决不适定问题中的图像重建及不确定性量化，并通过后验抽样结合生成先验实现高质量图像重建和不确定性量化。在理论分析中，证明了该算法的收敛性，即使在存在非对数凹似然函数和非完美评分网络的情况下，也能提供非渐进稳定性保证。实验结果表明，该算法显著提高了重建质量并实现了高保真度的不确定性量化。

可证明的基于得分的生成先验的概率成像