  This paper investigates the problem of graph signal recovery (GSR) when the
topology of the graph is not known in advance. In this paper, the elements of
the weighted adjacency matrix is statistically related to normal distribution
and the graph signal is assumed to be Gaussian Markov Random Field (GMRF).
Then, the problem of GSR is solved by a Variational Bayes (VB) algorithm in a
Bayesian manner by computing the posteriors in a closed form. The posteriors of
the elements of weighted adjacency matrix are proved to have a new distribution
which we call it generalized compound confluent hypergeometric (GCCH)
distribution. Moreover, the variance of the noise is estimated by calculating
its posterior via VB. The simulation results on synthetic and real-world data
shows the superiority of the proposed Bayesian algorithm over some
state-of-the-art algorithms in recovering the graph signal.
