Block Coordinate Plug-and-Play Methods for Blind Inverse Problems
This addresses a gap in plug-and-play methods for imaging inverse problems, offering a principled framework for joint estimation, though it appears incremental as it extends existing plug-and-play techniques to blind settings.
The paper tackles blind inverse problems, where both the image and measurement operator are unknown, by proposing a block-coordinate plug-and-play method that uses learned denoisers as priors for both, and demonstrates its efficiency on tasks like MRI coil sensitivity estimation and blind image deblurring.
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.