Domain Adaptation of Mismatched Proximal Denoiser for Plug-and-Play Image Reconstruction
Machine Learning
Summary
The authors study how a popular image reconstruction technique, called PnP-PGD, works when the denoiser used isn’t perfectly suited for the image type (a situation called proximal mismatch). They show that this mismatch affects how well the method converges to good solutions. To fix this, they suggest adapting the denoiser by aligning it with a theoretical ideal step (proximal matching) rather than just minimizing average errors (MSE). Their experiments demonstrate that this adaptation strategy improves image reconstruction quality, especially when only a few examples are available.
Authors
Guixian Xu, Jinglai Li, Junqi Tang
Abstract
Plug-and-play proximal gradient descent (PnP-PGD) enables flexible image reconstruction by using denoisers as implicit priors. In practice, these denoisers are often deployed outside their training domains. Existing analyses establish convergence under structural assumptions on the deployed denoiser, such as requiring it to be a proximal map or a contraction. However, they do not measure how domain mismatch affects convergence of PnP-PGD. We define this effect as \emph{proximal mismatch}: the discrepancy between a deployed denoiser $\widehat{\mathsf D}$ and a target-domain reference map $\mathsf D_\star=\operatorname{prox}_{R_\star}$ associated with the underlying regularizer $R_\star$. Under this mismatch, each denoising update becomes an inexact proximal step for the target objective. We further derive a stationarity bound that decays at a rate of $\mathcal{O}(1/K)$, with an additive term proportional to the average squared proximal mismatch. This result motivates adaptation via proximal matching rather than MSE-based adaptation alone. We study this approach with two established denoiser families: learned proximal networks and gradient-step denoisers. Experiments on Gaussian deblurring and super-resolution under substantial domain shift show that proximal matching adaptation improves reconstruction quality significantly over MSE-based adaptation, yielding the largest numerical gains in the few-shot regime.