带退火噪声水平的收敛即插即用图像恢复

中文摘要 AI 辅助

即插即用（PnP）方法通过将深度去噪器融入迭代优化算法来解决成像逆问题。尽管实际实现中通常沿迭代降低去噪器噪声水平$\sigma$，但大多数现有收敛性分析假设去噪器固定不变。在本工作中，我们为一大类具有退火噪声水平的即插即用算法建立了收敛性保证，涵盖确定性方法（RED--GD和PnP--PGD）和随机方法（SNORE、等变RED以及PnP--Flow的一种变体）。对于每种方法，我们确定了与终端去噪水平相关的显式非凸目标函数，并证明了迭代序列关于该目标的渐近平稳性。我们的分析不规定噪声调度的任何衰减率，且我们的假设同时涵盖学习型梯度步去噪器和精确MMSE去噪器。总体而言，我们的理论结果弥合了现有PnP收敛理论与最先进图像恢复方法所采用的递减去噪实践之间的差距。我们通过实验证明了此类调度的优势，并在多个成像逆问题（包括修复、超分辨率、去马赛克和断层扫描）上展示了预测的收敛行为。

英文摘要

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 $σ$ 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.

发表机构

• ENS Paris（巴黎高等师范学院）
• PSL（巴黎文理研究大学）
• CNRS（法国国家科学研究中心）

机构由 AI 辅助整理，请以论文原文为准。