Graph signal recovery using variational Bayes in Fourier pairs with Cramér–Rao bounds

Abstract

In this paper, the graph signal recovery problem is addressed by employing an aggregation of samples in the vertex domain and the Fourier graph transform domain. The statistical graph signal is modeled using a Gaussian Markov Random Field (GMRF). The reconstruction process involves employing a variational Bayes (VB) algorithm, which is a fully Bayesian method that iteratively estimates all unknown parameters by computing the posteriors in a closed-form. Furthermore, the closed-form of the Cramér–Rao lower bound (CRLB) for graph signal estimation is also derived. Simulation results demonstrate the superiority of the proposed algorithm over some of state-of-the-art algorithms in the literature.