  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.
