Distributed Jointly Sparse Bayesian Learning With Quantized Communication

We consider the problem of the distributed recovery of jointly sparse signals by a number of nodes in a sensor network, using multiple noisy linear measurements. In the literature, distributed Bayesian algorithms have been proposed to tackle this problem, most of which assume that nodes can transmit real data with infinite precision. However, in many practical applications, sensor networks have a limited communication bandwidth and finite capacity channels, and digital quantization of the transmitted data is inevitable. In this paper, we consider the case that the transmitted quantities/messages between nodes (instead of the measurement data) are quantized with discrete value and finite precision. We formulate a fully hierarchical jointly sparse Bayesian model and propose a novel distributed variational Bayesian (VB) algorithm, which uses only the quantized transmitted messages. In the proposed VB algorithm, an inexact alternating direction method of multipliers is developed for achieving quantized consensus. We theoretically analyze the convergence of the proposed algorithm and study the effect of digital quantization. Through numerical simulations, we find a counterintuitive result that the proposed quantized algorithm can even perform better than the corresponding unquantized algorithm and the centralized counterpart.