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.

翻译：在解决病态逆问题的图像重建算法中，估计高质量图像同时量化其不确定性是两项理想特性。本文提出即插即用蒙特卡洛（PMC）方法，将其作为表征一般逆问题可能解空间的理论框架。PMC能够整合具有高表达能力的基于分数的生成先验，实现高质量图像重建的同时，通过后验采样完成不确定性量化。具体而言，我们提出了两种PMC算法，可视为传统即插即用先验（PnP）与去噪正则化（RED）算法的采样对应物。同时建立了PMC算法收敛性的理论分析框架，该分析在非对数凹似然函数与不完美评分网络存在的条件下，为两种算法提供了非渐近平稳性保证。我们通过多个具有线性与非线性前向模型的代表性逆问题验证了PMC算法的性能。实验结果表明，PMC显著提升了重建质量，并实现了高保真度的不确定性量化。