Time-Varying Graph Signal Inpainting Via Unrolling Networks

Abstract

We propose an interpretable graph neural network based on algorithm unrolling to reconstruct a time-varying graph signal from partial measurements. The proposed graph unrolling networks expand algorithm unrolling to the graph-time domain and provide an interpretation of the architecture design from a signal processing perspective. We unroll an iterative inpainting algorithm by mapping each iteration to a single network layer. The feed-forward process is thus equivalent to iteratively reconstructing a time-varying graph signal. We train this network through unsupervised learning, where the input time-varying graph signal is used to supervise the training. By leveraging the learning ability of neural networks, we adaptively capture appropriate priors from input data, instead of manually choosing signal priors. To validate the proposed methods, we conduct experiments on three real-world datasets and demonstrate that our networks achieve smaller reconstruction errors than conventional inpainting algorithms and state-of-the-art graph neural networks.

Time-Varying Signals Recovery Via Graph Neural Networks

“…Sampling and reconstructing (or imputing) graph signals have become crucial tasks that have attracted considerable interest from both the signal processing and machine learning fields in recent times [1], [20]- [26]. However, there is a lack of research on the reconstruction of time-varying graph signals 1 despite its numerous applications in sensor networks, time-series forecasting, and infectious disease prediction [23], [27]- [29]. Prior research has primarily concentrated on expanding the concept of smoothness from static graph signals to those that evolve over time, as evidenced by Qiu et al [30].…”