Restoration of Time-Varying Graph Signals using Deep Algorithm Unrolling

In this paper, we propose a restoration method of time-varying graph signals, i.e., signals on a graph whose signal values change over time, using deep algorithm unrolling. Deep algorithm unrolling is a method that learns parameters in an iterative optimization algorithm with deep learning techniques. It is expected to improve convergence speed and accuracy while the iterative steps are still interpretable. In the proposed method, the minimization problem is formulated so that the time-varying graph signal is smooth both in time and spatial domains. The internal parameters, i.e., time domain FIR filters and regularization parameters, are learned from training data. Experimental results using synthetic data and real sea surface temperature data show that the proposed method improves signal reconstruction accuracy compared to several existing time-varying graph signal re- construction methods.

1. INTRODUCTION

Graph signal processing (GSP) is a signal processing field to build theory and applications for analyzing signals on a graph (i.e., graph signals) [1]–[3]. A graph is a data structure consisting of nodes and edges, and is used as a mathematical representation of various networks. GSP makes it possible to construct theories and techniques for signals on a wide variety of networks, such as signals on sensor networks and EEG, as well as three-dimensional point clouds and other signals whose relationships among samples are assumed to be given by networks. This has attracted the attention of researchers in various fields of science, engineering, and industry [4][5]–[8].