Graph Signal Restoration Using Nested Deep Algorithm Unrolling.

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. Graph signals are often corrupted through sensing processes, and need to be restored for the above applications. 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 propose a general restoration method for linear degradation by unrolling iterations of Plug-and-Play ADMM (PnP-ADMM). In the second method, the unrolled ADMM-based denoiser is incorporated as a submodule. Therefore, our restoration method has a nested DAU structure. Thanks to DAU, parameters in the proposed denoising/restoration methods are trainable in an end-to-end manner. Since the proposed restoration methods are based on iterations of a (convex) optimization algorithm, the method is interpretable and keeps the number of parameters small because we only need to tune graph-independent regularization parameters. We solve two main problems 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 to several existing methods in terms of root mean squared error in both tasks.