Quantized Compressive Sensing

TL;DR

This paper investigates the effects of various quantization methods on compressive sensing measurements, providing theoretical bounds and demonstrating improved reconstruction accuracy through adapted algorithms.

Contribution

It introduces a detailed analysis of quantization-induced distortion in CS and adapts reconstruction algorithms to mitigate these effects, enhancing performance.

Findings

Quantization schemes' asymptotic behavior is characterized with bounds.

Modified algorithms significantly reduce reconstruction distortion.

Theoretical insights guide improved CS measurement quantization.

Abstract

We study the average distortion introduced by scalar, vector, and entropy coded quantization of compressive sensing (CS) measurements. The asymptotic behavior of the underlying quantization schemes is either quantified exactly or characterized via bounds. We adapt two benchmark CS reconstruction algorithms to accommodate quantization errors, and empirically demonstrate that these methods significantly reduce the reconstruction distortion when compared to standard CS techniques.