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Quantized Compressed Sensing: A Survey

  • Sjoerd DirksenEmail author
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (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.

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Utrecht University, Mathematical InstituteUtrechtThe Netherlands

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