  Graph-based methods for signal processing have shown promise for the analysis
of data exhibiting irregular structure, such as those found in social,
transportation, and sensor networks. Yet, though these systems are often
dynamic, state-of-the-art methods for signal processing on graphs ignore the
dimension of time, treating successive graph signals independently or taking a
global average. To address this shortcoming, this paper considers the
statistical analysis of time-varying graph signals. We introduce a novel
definition of joint (time-vertex) stationarity, which generalizes the classical
definition of time stationarity and the more recent definition appropriate for
graphs. Joint stationarity gives rise to a scalable Wiener optimization
framework for joint denoising, semi-supervised learning, or more generally
inversing a linear operator, that is provably optimal. Experimental results on
real weather data demonstrate that taking into account graph and time
dimensions jointly can yield significant accuracy improvements in the
reconstruction effort.
