  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.
