Graph-Time Trend Filtering and Unrolling Network

Reconstructing missing values and removing noise from network-based multivariate time series requires developing graph-time regularizers capable of capturing their spatiotemporal behavior. However, current approaches based on joint spatiotemporal smoothness, diffusion, or variations thereof may not be effective for time series with discontinuities across the graph or time. To address this challenge, we propose a joint graph-time trend filter operating over a product graph representing spatiotemporal relations. Additionally, we develop a graph-time unrolled neural network to learn the prior from the data, which is based on the alternating direction method of multipliers iterations of the graph-time trend filter and on graph-time convolutional filters. Numerical tests with two synthetic and four real datasets corroborate the effectiveness of both approaches, highlight their inherent trade-offs, and show they compare well with state-of-the-art alternatives.