Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence
  Analysis
Shirin Shoushtari Jiaming Liu Edward P. Chandler M. Salman Asif Ulugbek S. Kamilov
Plug-and-Play (PnP) priors is a widely-used family of methods for solving
imaging inverse problems by integrating physical measurement models with image
priors specified using image denoisers. PnP methods have been shown to achieve
state-of-the-art performance when the prior is obtained using powerful deep
denoisers. Despite extensive work on PnP, the topic of distribution mismatch
between the training and testing data has often been overlooked in the PnP
literature. This paper presents a set of new theoretical and numerical results
on the topic of prior distribution mismatch and domain adaptation for
alternating direction method of multipliers (ADMM) variant of PnP. Our
theoretical result provides an explicit error bound for PnP-ADMM due to the
mismatch between the desired denoiser and the one used for inference. Our
analysis contributes to the work in the area by considering the mismatch under
nonconvex data-fidelity terms and expansive denoisers. Our first set of
numerical results quantifies the impact of the prior distribution mismatch on
the performance of PnP-ADMM on the problem of image super-resolution. Our
second set of numerical results considers a simple and effective domain
adaption strategy that closes the performance gap due to the use of mismatched
denoisers. Our results suggest the relative robustness of PnP-ADMM to prior
distribution mismatch, while also showing that the performance gap can be
significantly reduced with few training samples from the desired distribution.