One-bit compressed sensing with non-Gaussian measurements

TL;DR

This paper demonstrates that approximately sparse signals can be accurately reconstructed from one-bit measurements sampled from sub-Gaussian distributions using convex optimization, extending compressed sensing capabilities beyond Gaussian measurements.

Contribution

It introduces a method for robustly recovering approximately sparse signals from one-bit measurements with non-Gaussian, sub-Gaussian distributions, broadening the scope of compressed sensing.

Findings

Successful reconstruction of approximately sparse signals from sub-Gaussian measurements.

Convex programming effectively recovers signals in the one-bit compressed sensing setting.

Extension of theoretical guarantees to non-Gaussian measurement distributions.

Abstract

In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable to natural non-Gaussian distributions without further assumptions, as can be demonstrated by simple counter-examples. We show that approximately sparse signals that are not extremely sparse can be accurately reconstructed from single-bit measurements sampled according to a sub-gaussian distribution, and the reconstruction comes as the solution to a convex program.