证明了随机近端去噪算法在非凸条件下的收敛性，为图像修复提供理论支撑。
Convergence Analysis of a Proximal Stochastic Denoising Regularization Algorithm
- 提出基于随机近端梯度的去噪修复算法，结合迭代优化与深度去噪器
- 在非凸假设下证明算法收敛，适用于图像补全等复杂任务
- 适合关注图像恢复理论保障的研究者与工程开发者
图像修复中的插件式方法是通过求解变分问题从退化观测中恢复清晰图像的迭代算法，具有对退化类型灵活适应且性能达到前沿水平的特点。近年来，研究者们基于插件式或去噪正则化（RED）框架探索新型随机算法，如SNORE——一种收敛的随机梯度下降算法。其变体SNORE Prox在图像补全任务中表现优异，达到了当前最优性能。然而，作为随机近端梯度下降的SNORE Prox尚未有收敛性分析。本文首次在非凸假设条件下证明了SNORE Prox的收敛性，为该类算法提供了理论依据。
原文摘要 · Abstract (English)
Plug-and-Play methods for image restoration are iterative algorithms that solve a variational problem to recover a clean image from a degraded observation. These algorithms are known to be flexible to changes of degradation and to perform state-of-the-art restoration. Recently, significant efforts have been made to explore new stochastic algorithms based on the Plug-and-Play or REgularization by Denoising (RED) frameworks, such as SNORE, which is a convergent stochastic gradient descent algorithm. A variant of this algorithm, named SNORE Prox, reaches state-of-the-art performances, especially for inpainting tasks. However, the convergence of SNORE Prox, that can be seen as a stochastic proximal gradient descent, has not been analyzed so far. In this paper, we prove the convergence of SNORE Prox under non convex assumptions.
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