Graph Signal Restoration Using Nested Deep Algorithm Unrolling
Graph Signal Restoration Using Nested Deep Algorithm Unrolling
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DOI：
10.1109/tsp.2022.3180546
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发表时间：
2021-06
影响因子：
5.4
通讯作者：
Masatoshi Nagahama;Koki Yamada;Yuichi Tanaka;Stanley H. Chan;Yonina C. Eldar
中科院分区：
文献类型：
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作者：
Masatoshi Nagahama;Koki Yamada;Yuichi Tanaka;Stanley H. Chan;Yonina C. Eldar
图形信号处理在许多应用中是一项普遍存在的任务，例如传感器，社交，交通和大脑网络，点云处理和图形神经网络。通常，图形信号在感测过程中被破坏，因此需要恢复。本文提出了两种基于深度算法展开（DAU）的图信号恢复方法。首先，我们提出了一个图形信号去噪器的交替方向乘法（ADMM）的展开迭代。然后，我们提出了一个通用的线性退化恢复方法，即插即用ADMM（PnP-ADMM）的展开迭代。在第二种方法中，展开的基于ADMM的去噪器被合并为一个子模块，导致嵌套的DAU结构。所提出的去噪/恢复方法中的参数可以以端到端的方式训练。我们的方法是可解释的，并且保持参数的数量很小，因为我们只调整图独立的正则化参数。我们克服了现有图信号恢复方法中的两个主要挑战：1）由于经常手动确定的固定参数，凸优化算法的性能有限。2)图神经网络的参数多，训练困难。几个实验的图形信号去噪和插值进行合成和真实世界的数据。所提出的方法在这两项任务的均方根误差方面表现出比现有的几种技术的性能改进。
Graph signal processing is a ubiquitous task in many applications such as sensor, social, transportation and brain networks, point cloud processing, and graph neural networks. Often, graph signals are corrupted in the sensing process, thus requiring restoration. In this paper, we propose two graph signal restoration methods based on deep algorithm unrolling (DAU). First, we present a graph signal denoiser by unrolling iterations of the alternating direction method of multiplier (ADMM). We then suggest a general restoration method for linear degradation by unrolling iterations of Plug-and-Play ADMM (PnP-ADMM). In the second approach, the unrolled ADMM-based denoiser is incorporated as a submodule, leading to a nested DAU structure. The parameters in the proposed denoising/restoration methods are trainable in an end-to-end manner. Our approach is interpretable and keeps the number of parameters small since we only tune graph-independent regularization parameters. We overcome two main challenges in existing graph signal restoration methods: 1) limited performance of convex optimization algorithms due to fixed parameters which are often determined manually. 2) large number of parameters of graph neural networks that result in difficulty of training. Several experiments for graph signal denoising and interpolation are performed on synthetic and real-world data. The proposed methods show performance improvements over several existing techniques in terms of root mean squared error in both tasks.