Quantization and Compressive Sensing

  • Petros T. BoufounosEmail author
  • Laurent Jacques
  • Felix Krahmer
  • Rayan Saab
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


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.


Compressive Sensing Reconstruction Error Sparse Signal Dual Frame Scalar Quantization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Petros T. Boufounos is exclusively supported by Mitsubishi Electric Research Laboratories. Laurent Jacques is a Research Associate funded by the Belgian F.R.S.-FNRS. Felix Krahmer and Rayan Saab acknowledge support by the German Science Foundation (DFG) in the context of the Emmy-Noether Junior Research Group KR 4512/1-1 “RaSenQuaSI.”


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Petros T. Boufounos
    • 1
    Email author
  • Laurent Jacques
    • 2
  • Felix Krahmer
    • 3
  • Rayan Saab
    • 4
  1. 1.Mitsubishi Electric Research LaboratoriesCambridgeUSA
  2. 2.ISPGroup, ICTEAM/ELENUniversité catholique de LouvainLouvain-la-NeuveBelgium
  3. 3.Technische Universität MünchenGarching bei MünchenGermany
  4. 4.University of CaliforniaLa JollaUSA

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