Distributed soft thresholding for sparse signal recovery

TL;DR

This paper introduces a distributed iterative soft thresholding algorithm (DISTA) for sparse signal recovery in sensor networks, enabling efficient Lasso regression without centralized communication, with proven convergence and performance advantages.

Contribution

The paper presents a novel distributed algorithm for sparse recovery that operates without a fusion center and proves its convergence in regular graph networks.

Findings

DISTA converges in regular graph networks.

DISTA outperforms existing methods in performance, memory, and complexity.

The algorithm effectively solves Lasso regression in distributed settings.

Abstract

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 fusion center 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 gradient step, and a soft thresholding operation. We prove the convergence of DISTA in networks represented by regular graphs, and we compare it with existing methods in terms of performance, memory, and complexity.