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Performance Analysis of Plug-and-Play ADMM: A Graph Signal Processing Perspective

2018-08-31 18:45:02
Stanley H. Chan

Abstract

The Plug-and-Play (PnP) ADMM algorithm is a powerful image restoration framework that allows advanced image denoising priors to be integrated into physical forward models to yield a provably convergent algorithm. However, despite the enormous applications and promising results, very little is known about why the PnP ADMM performs so well. This paper presents a formal analysis of the performance of PnP ADMM. By restricting the denoisers to the class of graph filters, or more specifically the symmetric smoothing filters, we offer three contributions: (1) We rigorously show conditions under which an equivalent maximum-a-posteriori (MAP) optimization exists, (2) we derive the mean squared error of the PnP solution, and provide a simple geometric interpretation which can explain the performance, (3) we introduce a new analysis technique via the concept of consensus equilibrium, and provide interpretations to general linear inverse problems and problems with multiple priors.

Abstract (translated)

即插即用(PnP)ADMM算法是一个功能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前向模型中,以产生可证明的收敛算法。然而,尽管有巨大的应用和有希望的结果,但很少有人知道为什么PnP ADMM表现如此之好。本文对PnP ADMM的性能进行了正式分析。通过将降噪器限制为图形滤波器类,或者更具体地说是对称平滑滤波器,我们提供了三个贡献:(1)我们严格地显示了存在等效最大后验(MAP)优化的条件,(2)我们导出PnP解的均方误差,并提供可以解释性能的简单几何解释。(3)我们通过共识平衡的概念引入一种新的分析技术,并提供对一般线性逆问题和多重问题的解释。先验。

URL

https://arxiv.org/abs/1809.00020

PDF

https://arxiv.org/pdf/1809.00020.pdf


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