Domain Adaptation of Mismatched Proximal Denoiser for Plug-and-Play Image Reconstruction

2026-07-16

AI Summary

This work addresses the degraded convergence in plug-and-play (PnP) image reconstruction caused by mismatch between the denoiser and the target domain. It introduces the concept of “proximal mismatch,” formally characterizing its impact on the convergence of PnP proximal gradient descent (PnP-PGD) and establishing a stationarity bound that incorporates mismatch-induced errors. Building on this analysis, the authors propose a domain adaptation mechanism explicitly designed to achieve proximal alignment, replacing conventional mean squared error–based adaptation strategies. By integrating proximal gradient descent, proximal mapping theory, and learned denoisers, the method is theoretically grounded and empirically validated through few-shot experiments. It achieves substantial improvements over existing approaches in Gaussian deblurring and super-resolution tasks, particularly excelling in low-data regimes where reconstruction quality is significantly enhanced.

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.

Problem

• domain adaptation
• plug-and-play
• proximal mismatch
• image reconstruction
• denoiser

Innovation

• proximal mismatch
• plug-and-play image reconstruction
• domain adaptation
• proximal matching
• inexact proximal gradient