🤖 AI Summary
This study addresses the disconnect between theory and practice in plug-and-play (PnP) image restoration, where existing convergence analyses typically assume fixed noise levels, contradicting practical annealing strategies. To bridge this gap, we establish rigorous convergence guarantees for PnP algorithms employing decreasing noise levels. Our core contribution is the first proof of asymptotic stationarity with respect to a terminal denoising objective for a broad class of PnP frameworks—including RED, PGD, and SNORE—without requiring predefined decay rates, thereby unifying theoretical analysis across deterministic and stochastic optimization settings. Experiments demonstrate that this annealing strategy achieves the theoretically predicted convergence behavior and significantly improves restoration performance across various inverse problems, including image inpainting and super-resolution.
📝 Abstract
Plug-and-Play (PnP) methods solve imaging inverse problems by incorporating deep denoisers into iterative optimization algorithms. Although practical implementations often decrease the denoiser noise level $\sigma$ along iterations, most existing convergence analyses assume a fixed denoiser. In this work, we establish convergence guarantees for a broad family of Plug-and-Play algorithms with annealed noise level, spanning deterministic methods (RED--GD and PnP--PGD) and stochastic methods (SNORE, equivariant RED, and a variant of PnP--Flow). For each method, we identify an explicit, nonconvex objective associated with the terminal denoising level and prove asymptotic stationarity of the iterates with respect to this objective. Our analysis does not prescribe any decay rate for the noise schedule, and our assumptions cover both learned gradient-step denoisers and exact MMSE denoisers. Overall, our theoretical results bridge the gap between existing PnP convergence theory and the decreasing-denoising practices used by state-of-the-art image restoration methods. We empirically demonstrate the benefits of such schedules and illustrate the predicted convergence behavior on several imaging inverse problems, including inpainting, super-resolution, demosaicing and tomography.