Time-varying graph signal inpainting via unrolling networks

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.