Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Models

Many imaging problems can be formulated as inverse problems seeking to recover high-quality images from their low-quality observations. Such problems arise across the fields of biomedical imaging (McCann et al., 2017a), computer vision (Pizlo, 2001), and computational imaging (Ongie et al., 2020). Since imaging inverse problems are generally ill-posed, it is common to apply prior models on the desired images. There has been significant progress in developing Deep Learning (DL) based image priors, where a deep model is trained to directly map degraded observations to images (McCann et al., 2017b; Jin et al., 2017; Li et al., 2020). Model-based DL (MBDL) is an alternative to traditional DL that explicitly uses knowledge of the forward model by integrating DL denoisers as implicit priors into model-based optimization algorithms (Venkatakrishnan et al., 2013; Romano et al., 2017). It has been generally observed that learned denoisers are essential for achieving the state-of-the-art results in many imaging contexts (Metzler et al., 2018; Ulondu-Mendes et al., 2023; Ryu et al., 2019; Hurault et al., 2022; Wu et al., 2020). However, most prior work in the area has focused on methods that can only produce point estimates without any quantification of the reconstruction uncertainty (Belhasin et al., 2023), which can be essential in critical applications such as healthcare or security (Liu et al., 2023). In recent years, the exploration of strategies for sampling from the posterior probability has emerged as a focal point in the field of inverse problem in imaging (Pereyra et al., 2015; Bouman & Buzzard, 2023; Chung et al., 2023; Song et al., 2022). This pursuit has given rise to a plethora of techniques, encompassing wellestablished methods such as Gibbs sampling (Coeurdoux et al., 2023), the Unadjusted Langevin Algorithm