Quantization and compressive sensing

Petros T. Boufounos, Laurent Jacques, Felix Krahmer, Rayan Saab

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

54 Scopus citations

Abstract

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance bounds applicable to any quantization approach. Next, we consider several forms of scalar quantizers, namely uniform, non-uniform, and 1-bit. We provide performance bounds and fundamental analysis, as well as practical quantizer designs and reconstruction algorithms that account for quantization. Furthermore, we provide an overview of Sigma-Delta (Σ Δ) quantization in the compressed sensing context, and also discuss implementation issues, recovery algorithms, and performance bounds. As we demonstrate, proper accounting for quantization and careful quantizer design has significant impact in the performance of a compressive acquisition system.

Original languageEnglish
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Pages193-237
Number of pages45
Edition9783319160412
DOIs
StatePublished - 2015

Publication series

NameApplied and Numerical Harmonic Analysis
Number9783319160412
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Keywords

  • Compressive sensing
  • Dual frame
  • Reconstruction error
  • Scalar quantization
  • Sparse signal

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