Decentralized Joint-Sparse Signal Recovery: A Sparse Bayesian Learning Approach
This addresses efficient signal processing in distributed networks, such as sensor arrays, by improving recovery with less data and communication, though it is incremental as it builds on existing sparse Bayesian and ADMM methods.
The paper tackles decentralized recovery of jointly sparse signals from underdetermined measurements, proposing CB-DSBL, which reduces local measurement needs and inter-node communication while achieving linear convergence via ADMM. Simulation results show superior reconstruction and support recovery compared to existing decentralized algorithms like DRL-1, DCOMP, and DCSP.
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.