Plug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications
Plug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications
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DOI：
10.1109/tci.2016.2629286
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发表时间：
2017-03-01
影响因子：
5.4
通讯作者：
Elgendy, Omar A.
中科院分区：
文献类型：
--
作者：
Chan, Stanley H.;Wang, Xiran;Elgendy, Omar A.
乘子交替方向法（ADMM）是一种广泛用于解决图像恢复中约束优化问题的算法。在许多有用的功能中，ADMM 算法的一个关键功能是其模块化结构，它允许插入任何现成的图像去噪算法来解决 ADMM 算法中的子问题。由于插件性质，这种类型的 ADMM 算法被称为“即插即用 ADMM”。即插即用 ADMM 在最近的许多论文中展示了有希望的实证结果。然而，目前尚不清楚在什么条件下以及使用什么去噪算法可以保证收敛。此外，由于即插即用 ADMM 使用特定的方式来分割变量，因此尚不清楚是否可以快速实现常见的高斯和泊松图像恢复问题。在本文中，我们提出了一种具有可证明定点收敛性的即插即用 ADMM 算法。我们证明，对于任何满足渐近标准的去噪算法（称为有界去噪器），即插即用 ADMM 在连续方案下收敛到固定点。我们还提出了超分辨率和单光子成像的两个图像恢复问题的快速实现。我们将即插即用 ADMM 与每种问题类型中最先进的算法进行比较，并展示该算法有希望的实验结果。
Alternating direction method of multiplier (ADMM) is a widely used algorithm for solving constrained optimization problems in image restoration. Among many useful features, one critical feature of the ADMM algorithm is its modular structure, which allows one to plug in any off-the-shelf image denoising algorithm for a subproblem in the ADMM algorithm. Because of the plug-in nature, this type of ADMM algorithms is coined the name "Plug-and-Play ADMM." Plug-and-Play ADMM has demonstrated promising empirical results in a number of recent papers. However, it is unclear under what conditions and by using what denoising algorithms would it guarantee convergence. Also, since Plug-and-Play ADMM uses a specific way to split the variables, it is unclear if fast implementation can be made for common Gaussian and Poissonian image restoration problems. In this paper, we propose a Plug-and-Play ADMM algorithm with provable fixed-point convergence. We show that for any denoising algorithm satisfying an asymptotic criteria, called bounded denoisers, Plug-and-Play ADMM converges to a fixed point under a continuation scheme. We also present fast implementations for two image restoration problems on superresolution and single-photon imaging. We compare Plug-and-Play ADMM with state-of-the-art algorithms in each problem type and demonstrate promising experimental results of the algorithm.