Distributed recovery of jointly sparse signals under communication constraints

TL;DR

This paper introduces a reweighted  soft thresholding algorithm for distributed joint sparse signal recovery that is communication-efficient, converges reliably, and outperforms existing greedy methods in accuracy and communication load.

Contribution

It proposes a novel reweighted  thresholding method that adapts to network constraints and requires only local communication, with proven convergence and improved performance.

Findings

Outperforms state-of-the-art greedy algorithms in accuracy and communication efficiency.

Requires only local communication with finite set messages.

Proven convergence of the proposed algorithm.

Abstract

The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed measurements, and exploiting network communication, each node aims at reconstructing the support and the non-zero values of its observed signal. In the literature, distributed greedy algorithms have been proposed to tackle this problem, among which the most reliable ones require a large amount of transmitted data, which barely adapts to realistic network communication constraints. In this work, we address the problem through a reweighted $\ell_1$ soft thresholding technique, in which the threshold is iteratively tuned based on the current estimate of the support. The proposed method adapts to constrained networks, as it requires only local communication among neighbors, and the transmitted messages are indices from a finite set. We analytically prove the convergence of the proposed algorithm and we show that it outperforms the state-of-the-art greedy methods in terms of balance between recovery accuracy and communication load.