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.

中文翻译：

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使用嵌套深度算法展开图信号恢复


图信号处理是传感器、社交、交通和脑网络、点云处理和图神经网络等许多应用中普遍存在的任务。通常，图形信号在传感过程中会被损坏，因此需要恢复。在本文中，我们提出了两种基于深度算法展开（DAU）的图信号恢复方法。首先，我们通过展开乘法器交替方向法（ADMM）的迭代来提出图形信号降噪器。然后，我们提出了一种通过展开即插即用 ADMM (PnP-ADMM) 迭代来恢复线性退化的通用方法。在第二种方法中，展开的基于 ADMM 的降噪器被合并为子模块，从而形成嵌套的 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进行训练。我们的方法是可解释的，并且参数数量保持较少，因为我们只调整与图无关的正则化参数。我们克服了现有图信号恢复方法中的两个主要挑战：1）由于通常手动确定的固定参数，凸优化算法的性能有限。 2）图神经网络参数较多，导致训练困难。对合成数据和真实数据进行了图形信号去噪和插值的多项实验。所提出的方法在这两项任务中均方根误差方面显示了比几种现有技术的性能改进。