Cooperative Sparsity Pattern Recovery in Distributed Networks Via Distributed-OMP

TL;DR

This paper introduces a distributed greedy algorithm based on Orthogonal Matching Pursuit for collaboratively recovering the sparsity pattern of signals in networks, achieving significant performance improvements with fewer measurements per node.

Contribution

The paper proposes a novel distributed OMP-based algorithm that estimates sparse support collaboratively, reducing iterations and measurement requirements compared to independent estimation methods.

Findings

Significant support recovery performance gain in distributed networks.

Effective binary hypothesis testing for sparse signal detection.

Reduced number of iterations needed per node for accurate support estimation.

Abstract

In this paper, we consider the problem of collaboratively estimating the sparsity pattern of a sparse signal with multiple measurement data in distributed networks. We assume that each node makes Compressive Sensing (CS) based measurements via random projections regarding the same sparse signal. We propose a distributed greedy algorithm based on Orthogonal Matching Pursuit (OMP), in which the sparse support is estimated iteratively while fusing indices estimated at distributed nodes. In the proposed distributed framework, each node has to perform less number of iterations of OMP compared to the sparsity index of the sparse signal. Thus, with each node having a very small number of compressive measurements, a significant performance gain in support recovery is achieved via the proposed collaborative scheme compared to the case where each node estimates the sparsity pattern independently and then fusion is performed to get a global estimate. We further extend the algorithm to estimate the sparsity pattern in a binary hypothesis testing framework, where the algorithm first detects the presence of a sparse signal collaborating among nodes with a fewer number of iterations of OMP and then increases the number of iterations to estimate the sparsity pattern only if the signal is detected.