A Distributed Sparse Signal Reconstruction Algorithm in Wireless Sensor Network

We address the sparse signal reconstruction problem over networked sensing system. Signal acquisition is performed as in compressive sensing (CS), hence the number of measurements is reduced. Majority of existing algorithms are developed based on p minimization in the framework of distributed convex optimization and thus whose performance is sensitive to the tuning of additional parameters. In this paper, we propose a distributed sparse signal reconstruction algorithm in the full Bayesian framework by using Variational Bayesian (VB) with embedded consensus filter. Specifically, each node executes one-step average-consensus with its neighbors per VB step and thus reaches a consensus on estimate of sparse signal finally. The proposed approach is ease of implementation and scalability to large networks. In addition, due to the observability of nodes can be enhanced by average-consensus, the number of measurements for each node can be further reduced and not necessary to satisfy lower bound required by CS. Simulation results demonstrate that the proposed distributed approach have good recovery performance and converge to their centralized counterpart. Keyword Compressive Sensing; Sparse Signal; Variational Bayesian; Consensus Filter; Wireless Sensor Networks