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Quantized Compressed Sensing: A Survey

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Compressed Sensing and Its Applications

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

The field of quantized compressed sensing investigates how to jointly design a measurement matrix, quantizer, and reconstruction algorithm in order to accurately reconstruct low-complexity signals from a minimal number of measurements that are quantized to a finite number of bits. In this short survey, we give an overview of the state-of-the-art rigorous reconstruction results that have been obtained for three popular quantization models: one-bit quantization, uniform scalar quantization, and noise-shaping methods.

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Acknowledgements

It is a pleasure to thank the anonymous reviewer, Rayan Saab, and especially Laurent Jacques for many comments that improved this book chapter. This work was supported by the DFG through the project Quantized Compressive Spectrum Sensing (QuaCoSS), which is part of the Priority Program SPP 1798 Compressive Sensing in Information Processing (COSIP).

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Authors and Affiliations

  1. Utrecht University, Mathematical Institute, P.O. Box 80010, 3508, Utrecht, TA, The Netherlands

    Sjoerd Dirksen

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  1. Sjoerd Dirksen
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Correspondence to Sjoerd Dirksen .

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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Munich Center for Quantum Science and Technology (MCQST), Technical University of Munich, Munich, Germany

    Holger Boche

  2. Institute of Telecommunications Systems, Technical University of Berlin, Berlin, Germany

    Giuseppe Caire

  3. Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA

    Robert Calderbank

  4. Department of Mathematics, Technical University of Berlin, Berlin, Germany

    Gitta Kutyniok

  5. Faculty of Electrical Engineering and Information Technology, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Rudolf Mathar

  6. Mathematical Institute, University of Oxford, Oxford, UK

    Philipp Petersen

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Dirksen, S. (2019). Quantized Compressed Sensing: A Survey. In: Boche, H., Caire, G., Calderbank, R., Kutyniok, G., Mathar, R., Petersen, P. (eds) Compressed Sensing and Its Applications. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-73074-5_2

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