Learning Parametric Time-Vertex Graph Processes from Incomplete Realizations

We consider the problem of estimating time-varying graph signals with missing observations, which is of interest in many applications involving data acquisition on irregular topologies. We model time-varying graph signals as jointly stationary time-vertex ARMA graph processes. We formulate the learning of ARMA process parameters as an optimization problem where the joint power spectral density of the model is fit to a rough empirical estimate of the process covariance matrix. We propose a convex relaxation of this problem, which results in an algorithm more flexible than existing methods regarding the pattern of available and missing observations of the process. Experimental results on meteorological signals show that the proposed method compares favorably to reference state-of-the-art algorithms.