Decentralized recovery of sparse signals for sensor network applications

In this paper, we consider the problem of distributed ℓ₁ regularized quadratic optimization in a large-scale sensor network setting. Specifically, we consider sensor nodes which can measure only a part of the entire measurement vector and whose communication capabilities are limited to only their neighboring nodes. We formulate the ℓ₁-optimization problem as bound constrained quadratic optimization and develop a distributed, gossip-based algorithm using the projected-gradient approach. The sensor nodes reach a consensus on the gradient to be used for vector update at each step of the optimization algorithm. Finally we analyze the performance of the proposed algorithm using synthetic data and compare it with a standard ℓ₁ solver.