Decentralized Bayesian learning of jointly sparse signals

In this work, we consider the estimation of multiple jointly sparse vectors (or signals) from noisy, undetermined, linear measurements acquired by multiple nodes connected in a network. We propose a decentralized Bayesian algorithm, which is able to exploit the joint sparsity structure across the nodes. In the proposed algorithm, each node seeks the maximum a posterior probability (MAP) estimate of a local sparse signal vector by learning the parameters of a sparsity inducing signal prior, which is assumed to be common to the nodes, in a distributed fashion. Through simulations, we show that our algorithm significantly outperforms DCS-SOMP, an existing algorithm, in terms of number of measurements required per node for exact recovery of the common support. We also propose a tuning procedure to accelerate the convergence of our algorithm.