Performance Analysis of Plug-and-Play ADMM: A Graph Signal Processing Perspective
Performance Analysis of Plug-and-Play ADMM: A Graph Signal Processing Perspective
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DOI：
10.1109/tci.2019.2892123
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发表时间：
2019-06-01
影响因子：
5.4
通讯作者：
Chan, Stanley H.
中科院分区：
文献类型：
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作者：
Chan, Stanley H.
即插即用（PnP）交替方向乘法器（ADMM）算法是一个强大的图像恢复框架，它允许将高级图像去噪先验集成到物理正演模型中，以生成高质量的图像恢复结果。然而，尽管有大量的应用程序和一些理论研究试图通过利用凸分析中的工具来证明收敛性，但人们对该算法为什么做得这么好知之甚少。本文的目标是通过讨论PnP ADMM的性能来填补这一空白。通过将去噪器限制为线性假设下的图滤波器类，或者更具体地说是对称平滑滤波器，我们提供了三个贡献：首先，我们展示了存在等效最大后验优化的条件；其次，我们提出了一个几何解释，并表明性能增益是由于PnP先验的固有预噪声特性；第三，我们通过共识均衡的概念引入了一种新的分析技术，并对涉及多先验的问题提供了解释。
The Plug-and-Play (PnP) alternating direction method of multiplier (ADMM) algorithm is a powerful image restoration framework that allows advanced image denoising priors to be integrated into physical forward models to generate high-quality image restoration results. However, despite the enormous number of applications and several theoretical studies trying to prove convergence by leveraging tools in convex analysis, very little is known about why the algorithm is doing so well. The goal of this paper is to fill the gap by discussing the performance of PnP ADMM. By restricting the denoisers to the class of graph filters under a linearity assumption, or more specifically the symmetric smoothing filters, we offer three contributions: First, we show conditions under which an equivalent maximum-a-posteriori optimization exists; second, we present a geometric interpretation and show that the performance gain is due to an intrinsic prede-noising characteristic of the PnP prior; and third, we introduce a new analysis technique via the concept of consensus equilibrium, and provide interpretations to problems involving multiple priors.