Edward P. Chandler

Shirin Shoushtari, Jiaming Liu, Edward P. Chandler et al.

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.

Edward P. Chandler, Shirin Shoushtari, Jiaming Liu et al.

Plug-and-Play Priors (PnP) is a well-known class of methods for solving inverse problems in computational imaging. PnP methods combine physical forward models with learned prior models specified as image denoisers. A common issue with the learned models is that of a performance drop when there is a distribution shift between the training and testing data. Test-time training (TTT) was recently proposed as a general strategy for improving the performance of learned models when training and testing data come from different distributions. In this paper, we propose PnP-TTT as a new method for overcoming distribution shifts in PnP. PnP-TTT uses deep equilibrium learning (DEQ) for optimizing a self-supervised loss at the fixed points of PnP iterations. PnP-TTT can be directly applied on a single test sample to improve the generalization of PnP. We show through simulations that given a sufficient number of measurements, PnP-TTT enables the use of image priors trained on natural images for image reconstruction in magnetic resonance imaging (MRI).