Unrolled Time-Varying Graph Signal Restoration under Spatiotemporal Smoothness Priors

Abstract: In this paper, we propose restoration methods for time-varying graph signals using deep algorithm unrolling (DAU). Time-varying graph signals, such as signals obtained from sensor networks, are nonuniformly distributed in space and observed as time series. Since these observed signals often contain noise and missing values, their restoration needs to consider both spatial and temporal relationships. Our approach is based on an optimization problem that models signal properties using a spatiotemporal regularizer that combines a Sobolev operator for spatial smoothness and a multi-tap FIR filter for temporal smoothness. We then unroll the iterative conjugate gradient method to solve this problem and learn the regularization parameters and filter coefficients in each iteration. Our method can be applied to supervised batch, supervised online, and unsupervised batch settings to learn these parameters. Experiments on several synthetic and real-world datasets show that the supervised batch method achieves the lowest RMSEs in almost all cases. The supervised online and the unsupervised batch methods outperform the existing methods of their own settings, and are often competitive with the existing batch methods.