Dual-Domain-Based Plug-and-Play Image Restoration

Abstract

Plug-and-play (PnP) methods, which embed powerful image denoisers into classical optimization algorithms, have achieved remarkable performance on a variety of imaging inverse problems. However, most existing PnP frameworks impose regularization only in the spatial domain. In many practical settings, measurement noise is added in the transform (degradation) domain, i.e., after the action of the blur or downsampling operator. As a result, spatial-only regularization can generate artifacts that are inconsistent with the true noise statistics when evaluating the data-fidelity proximal operator, making them harder for denoisers to recognize and remove. In this paper, we propose a dual-domain regularization model for PnP image restoration that simultaneously exploits priors in the spatial and transform domains. The transform-domain regularizer explicitly suppresses measurement noise, while the spatial-domain regularizer promotes sharp and visually plausible reconstructions. Building on this paradigm, we develop DuDoPIR, an ADMM-based algorithm with a simple parameter selection strategy, and establish a conditional fixed-point convergence result for the associated multivariable operator under explicit residual-Lipschitz and parameter assumptions. Numerical results on image deblurring and single-image super-resolution show that, when identical denoisers are used, DuDoPIR consistently outperforms its spatial-only ADMM counterpart, i.e., PnP-ADMM. Compared with current state-of-the-art PnP and all-in-one methods, DuDoPIR achieves competitive reconstruction performance in most cases and superior performance in some cases on standard benchmarks. The source code will be made publicly available at https://github.com/Wenjian-Du/DuDoPIR