Joint Sparsity Pattern Recovery with 1-bit Compressive Sensing in Sensor Networks

TL;DR

This paper introduces a method for accurately recovering the common sparse support in sensor networks using 1-bit compressive measurements, even under noisy conditions, by employing a likelihood-based optimization with an $l_{1, infty}$ norm.

Contribution

It proposes a novel support recovery algorithm tailored for 1-bit measurements in sensor networks, combining likelihood maximization with joint sparsity regularization.

Findings

Support can be recovered accurately with few measurements per sensor.

The method is robust to measurement noise.

Supports are recovered effectively in a distributed sensor setting.

Abstract

We study the problem of jointly sparse support recovery with 1-bit compressive measurements in a sensor network. Sensors are assumed to observe sparse signals having the same but unknown sparse support. Each sensor quantizes its measurement vector element-wise to 1-bit and transmits the quantized observations to a fusion center. We develop a computationally tractable support recovery algorithm which minimizes a cost function defined in terms of the likelihood function and the $l_{1,\infty}$ norm. We observe that even with noisy 1-bit measurements, jointly sparse support can be recovered accurately with multiple sensors each collecting only a small number of measurements.