Convergent Plug-and-Play Image Restoration with Annealed Noise Levels

Plug-and-Play methods solve imaging inverse problems by incorporating deep denoisers into iterative optimization algorithms. We establish convergence guarantees for deterministic and stochastic Plug-and-Play schemes with an annealed denoiser noise level, including RED-GD, PnP-PGD, SNORE, equivariant RED, SNOPnP, and PnP-Flow. For each method, we identify an explicit nonconvex objective associated with the terminal denoising level and prove asymptotic stationarity of the iterates.