Distributed algorithms for in-network recovery of jointly sparse signals

We propose a new class of distributed algorithms for the in-network reconstruction of jointly sparse signals. We consider a network in which each node has to reconstruct a different signal, but all the signals share the same support. The problem is formulated as follows: each node iteratively solves a lasso, in which the weight of the l1-norm is tuned based on information on the support gathered from the other nodes. This promotes consensus on the support, and allows the single nodes to recover their signals, even when the number of measurements is not sufficient for individual reconstruction. Numerical simulations prove that our method outperforms the state-of-the-art greedy algorithms.