Stationary time-vertex signal processing

• Main Authors: Andreas Loukas, Nathanaël Perraudin
• Format: Article
• Language: English
• Published: SpringerOpen 2019-08-01
• Series: EURASIP Journal on Advances in Signal Processing
• Subjects: Stationarity; Multivariate time-vertex processes; Harmonic analysis; Graph signal processing; PSD estimation
• Online Access: http://link.springer.com/article/10.1186/s13634-019-0631-7

Abstract This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some known graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity for short, that goes beyond product graphs. Joint stationarity helps by reducing the estimation variance and recovery complexity. In particular, for any jointly stationary process (a) one reliably learns the covariance structure from as little as a single realization of the process and (b) solves MMSE recovery problems, such as interpolation and denoising, in computational time nearly linear on the number of edges and timesteps. Experiments with three datasets suggest that joint stationarity can yield accuracy improvements in the recovery of high-dimensional processes evolving over a graph, even when the latter is only approximately known, or the process is not strictly stationary.