Viscosity Stabilized Plug-and-Play Reconstruction

Abstract: The plug-and-play (PnP) method uses a deep denoiser within a proximal algorithm for model-based image reconstruction (IR). Unlike end-to-end IR, PnP allows the same pretrained denoiser to be used across different imaging tasks, without the need for retraining. However, black-box networks can make the iterative process in PnP unstable. A common issue observed across architectures like CNNs, diffusion models, and transformers is that the visual quality and PSNR often improve initially but then degrade in later iterations. Previous attempts to ensure stability usually impose restrictive constraints on the denoiser. However, standard denoisers, which are freely trained for single-step noise removal, need not satisfy such constraints. We propose a simple data-driven stabilization mechanism that adaptively averages the potentially unstable PnP operator with a contractive IR operator. This acts as a form of viscosity regularization, where the contractive component progressively dampens updates in later iterations, helping to suppress oscillations and prevent divergence. We validate the effectiveness of our stabilization mechanism across different proximal algorithms, denoising architectures, and imaging tasks.