Decentralized Joint-Sparse Signal Recovery: A Sparse Bayesian Learning Approach

This work proposes a decentralized, iterative, sparse Bayesian learning algorithm for in-network estimation of multiple joint-sparse vectors by a network of nodes, using noisy and underdetermined linear measurements. The proposed algorithm, called consensus-based distributed sparse Bayesian learning, exploits the network wide joint sparsity of the unknown sparse vectors to recover them from significantly fewer number of local measurements compared to standalone sparse signal recovery schemes. To reduce the amount of internode communication and the associated overheads, the nodes exchange messages with only a small set of bridge nodes. Under this communication scheme, we separately analyze the convergence of the underlying bridge node-based alternating direction method of multiplier (ADMM) iterations used in our proposed algorithm and establish its linear convergence rate. The findings from the convergence analysis of decentralized ADMM are used to accelerate the convergence of the proposed algorithm. Using Monte Carlo simulations as well as real-world-data-based experiments, we demonstrate the superior performance of our proposed algorithm compared to existing decentralized algorithms: DRL-1, DCOMP, and DCSP.