In-network reconstruction of jointly sparse signals with ADMM

In this paper, we tackle the problem of in-network recovery of sparse signals. We assume that the nodes of the network measure a signal composed by a common component and an innovation, both sparse and unknown, according to the Joint Sparsity Model 1 (JSM-1). We present a distributed algorithm based on the alternating direction method of multipliers (ADMM to recover such signals, along with a second version requiring only binary messaging. Then we assess the impact of the compression level at the acquisition stage and measurement noise on such schemes