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

TL;DR

This paper introduces CB-DSBL, a decentralized Bayesian algorithm that efficiently recovers multiple jointly sparse signals with fewer measurements and communication, demonstrating superior performance over existing methods.

Contribution

It presents a novel decentralized Bayesian algorithm for joint sparse signal recovery that reduces communication overhead and accelerates convergence using ADMM analysis.

Findings

CB-DSBL outperforms existing decentralized algorithms in signal reconstruction.

The algorithm achieves linear convergence rate under the proposed communication scheme.

Simulation results confirm improved support recovery accuracy.

Abstract

This work proposes a decentralized, iterative, Bayesian algorithm called CB-DSBL for in-network estimation of multiple jointly sparse vectors by a network of nodes, using noisy and underdetermined linear measurements. The proposed algorithm exploits the network wide joint sparsity of the un- known sparse vectors to recover them from significantly fewer number of local measurements compared to standalone sparse signal recovery schemes. To reduce the amount of inter-node communication and the associated overheads, the nodes exchange messages with only a small subset of their single hop neighbors. Under this communication scheme, we separately analyze the convergence of the underlying Alternating Directions Method of Multipliers (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 CB-DSBL algorithm. Using Monte Carlo simulations, we demonstrate the superior signal reconstruction as well as support recovery performance of our proposed algorithm compared to existing decentralized algorithms: DRL-1, DCOMP and DCSP.