Distributed soft thresholding for sparse signal recovery

In this paper, we address the problem of distributed sparse recovery of signals acquired via compressed measurements in a sensor network. We propose a new class of distributed algorithms to solve Lasso regression problems, when the communication to a gateway node is not possible, e.g., due to communication cost or privacy reasons. More precisely, we introduce a distributed iterative soft thresholding algorithm (DISTA) that consists of three steps: an averaging step, a subgradient step, and a soft thresholding operation. We prove the convergence of DISTA in a network represented by a complete graph, and we show that it outperforms existing algorithms in terms of performance and complexity.