Joint Topology Learning and Graph Signal Recovery Using Variational Bayes in Non-Gaussian Noise

This brief proposes a joint graph signal recovery and topology learning algorithm using a Variational Bayes (VB) framework in the case of non-Gaussian measurement noise. It is assumed that the graph signal is Gaussian Markov Random Field (GMRF) and the graph weights are considered statistical with the Gaussian prior. Moreover, the non-Gaussian noise is modeled using two distributions: Mixture of Gaussian (MoG), and Laplace. All the unknowns of the problem which are graph signal, Laplacian matrix, and the (Hyper)parameters are estimated by a VB framework. All the posteriors are calculated in closed forms and the iterative VB algorithm is devised to solve the problem. The efficiency of the proposed algorithm in comparison to some state-of-the-art algorithms in the literature is shown in the simulation results.