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Plug-and-play (PnP) prior is a well-known class of methods for solving imaging inverse problems by computing fixed-points of operators combining physical measurement models and learned image denoisers. While PnP methods have been extensively used for image recovery with known measurement operators, there is little work on PnP for solving blind inverse problems. We address this gap by presenting a new block-coordinate PnP (BC-PnP) method that efficiently solves this joint estimation problem by introducing learned denoisers as priors on both the unknown image and the unknown measurement operator. We present a new convergence theory for BC-PnP compatible with blind inverse problems by considering nonconvex data-fidelity terms and expansive denoisers. Our theory analyzes the convergence of BC-PnP to a stationary point of an implicit function associated with an approximate minimum mean-squared error (MMSE) denoiser. We numerically validate our method on two blind inverse problems: automatic coil sensitivity estimation in magnetic resonance imaging (MRI) and blind image deblurring. Our results show that BC-PnP provides an efficient and principled framework for using denoisers as PnP priors for jointly estimating measurement operators and images. 

Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image de-noisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications using pre-trained deep neural nets as denoisers. Despite the recent progress, the stable convergence of RED algorithms remains an open problem. The existing RED theory only guarantees stability for convex data-fidelity terms and nonexpansive denoisers. This work addresses this issue by developing a new monotone RED (MRED) algorithm, whose convergence does not require nonexpansiveness of the deep denoising prior. Simulations on image deblurring and compressive sensing recovery from random matrices show the stability of MRED even when the traditional RED diverges. 

Parallel magnetic resonance imaging (MRI) is a widely-used technique that accelerates data collection by making use of the spatial encoding provided by multiple receiver coils. A key issue in parallel MRI is the estimation of coil sensitivity maps (CSMs) that are used for reconstructing a single high-quality image. This paper addresses this issue by developing SS-JIRCS, a new self-supervised model-based deep-learning (DL) method for image reconstruction that is equipped with automated CSM calibration. Our deep network consists of three types of modules: data-consistency, regularization, and CSM calibration. Unlike traditional supervised DL methods, these modules are directly trained on undersampled and noisy k-space data rather than on fully sampled high-quality ground truth. We present empirical results on simulated data that show the potential of the proposed method for achieving better performance than several baseline methods.