Distributed Compressed Sensing For Static and Time-Varying Networks

TL;DR

This paper develops distributed algorithms based on IHT for compressed sensing in static and dynamic networks, achieving efficient signal recovery with minimal communication and robustness to network changes.

Contribution

It introduces a novel distributed IHT algorithm for static and time-varying networks, extending centralized IHT to handle inexact computations with proven guarantees.

Findings

Outperforms previous solutions in time and bandwidth efficiency

Provides theoretical guarantees for inexact distributed IHT in dynamic networks

Demonstrates effective signal recovery in both static and time-varying network settings

Abstract

We consider the problem of in-network compressed sensing from distributed measurements. Every agent has a set of measurements of a signal $x$, and the objective is for the agents to recover $x$ from their collective measurements using only communication with neighbors in the network. Our distributed approach to this problem is based on the centralized Iterative Hard Thresholding algorithm (IHT). We first present a distributed IHT algorithm for static networks that leverages standard tools from distributed computing to execute in-network computations with minimized bandwidth consumption. Next, we address distributed signal recovery in networks with time-varying topologies. The network dynamics necessarily introduce inaccuracies to our in-network computations. To accommodate these inaccuracies, we show how centralized IHT can be extended to include inexact computations while still providing the same recovery guarantees as the original IHT algorithm. We then leverage these new theoretical results to develop a distributed version of IHT for time-varying networks. Evaluations show that our distributed algorithms for both static and time-varying networks outperform previously proposed solutions in time and bandwidth by several orders of magnitude.