One-Bit Compressive Sensing with Partial Support

TL;DR

This paper introduces new methods for one-bit compressive sensing that incorporate partial support information, significantly improving signal recovery accuracy by leveraging prior knowledge in extreme quantization scenarios.

Contribution

It presents the first efficient recovery mechanisms that utilize partial support information in one-bit compressed sensing, enhancing reconstruction performance.

Findings

Improved signal recovery with partial support knowledge.

Methods effective across varying prior information accuracy.

First to incorporate prior support info in one-bit setting.

Abstract

The Compressive Sensing framework maintains relevance even when the available measurements are subject to extreme quantization, as is exemplified by the so-called one-bit compressed sensing framework which aims to recover a signal from measurements reduced to only their sign-bit. In applications, it is often the case that we have some knowledge of the structure of the signal beforehand, and thus would like to leverage it to attain more accurate and efficient recovery. This work explores avenues for incorporating such partial-support information into the one-bit setting. Experimental results demonstrate that newly proposed methods of this work yield improved signal recovery even for varying levels of accuracy in the prior information. This work is thus the first to provide recovery mechanisms that efficiently use prior signal information in the one-bit reconstruction setting.