q-ary Compressive Sensing

TL;DR

This paper extends 1-bit compressive sensing to q-ary compressive sensing, introducing a new sensing mechanism and recovery method, analyzing their properties theoretically and empirically, and exploring the tradeoffs involved.

Contribution

It proposes a novel q-ary sensing mechanism and recovery procedure, generalizing 1-bit compressive sensing and analyzing the impact of quantization levels on recovery accuracy.

Findings

Theoretical analysis shows a tradeoff between quantization parameter q and measurement number m.

Empirical results validate the recovery performance and robustness to noise.

Special case of 1-bit compressive sensing is recovered within the framework.

Abstract

We introduce q-ary compressive sensing, an extension of 1-bit compressive sensing. We propose a novel sensing mechanism and a corresponding recovery procedure. The recovery properties of the proposed approach are analyzed both theoretically and empirically. Results in 1-bit compressive sensing are recovered as a special case. Our theoretical results suggest a tradeoff between the quantization parameter q, and the number of measurements m in the control of the error of the resulting recovery algorithm, as well its robustness to noise.