arXiv：cs.LG（机器学习，全量分类）· Samuel Hurault·· 1 天前AI 评分29
退火噪声水平的收敛式 Plug-and-Play 图像恢复
Convergent Plug-and-Play Image Restoration with Annealed Noise Levels
AI 导读
该研究为采用退火噪声水平的 Plug-and-Play 算法建立了收敛保证，覆盖 RED-GD、PnP-PGD 等确定性方法和 SNORE、等变 RED 及 PnP-Flow 变体等随机方法。
正文
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.
| Subjects: | Optimization and Control (math.OC); Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.32393 [math.OC] |
| (or arXiv:2609.32393v2 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2609.32393 arXiv-issued DOI via DataCite |
Submission history
From: Samuel Hurault [view email]
[v1]
Sat, 26 Sep 2026 09:12:06 UTC (1,867 KB)
[v2]
Thu, 1 Oct 2026 17:00:14 UTC (1,867 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org