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Noise-Shaping Quantization Methods for Frame-Based and Compressive Sampling Systems

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Sampling Theory, a Renaissance

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

Abstract

Noise shaping refers to an analog-to-digital conversion methodology in which quantization error is arranged to lie mostly outside the signal spectrum by means of oversampling and feedback. Recently it has been successfully applied to more general redundant linear sampling and reconstruction systems associated with frames as well as non-linear systems associated with compressive sampling. This chapter reviews some of the recent progress in this subject.

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Acknowledgements

FK and RS acknowledge support by the German Science Foundation (DFG) in the context of the Emmy-Noether Junior Research Group KR 4512/1-1 “RaSenQuaSI”. ÖY was funded in part by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant (22R82411), an NSERC Accelerator Award (22R68054) and an NSERC Collaborative Research and Development Grant DNOISE II (22R07504).

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Authors and Affiliations

  1. Courant Institute, 251 Mercer Street, New York, NY, 10012, USA

    Evan Chou & C. Sinan Güntürk

  2. Google, New York, NY, 10011, USA

    Evan Chou

  3. Department of Mathematics, Technische Universität München, Boltzmannstr. 3, 85748, Garching/Munich, Germany

    Felix Krahmer

  4. University of California, San Diego, 9500 Gilman Drive, Dept. 0112, La Jolla, CA, 92093, USA

    Rayan Saab

  5. University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada, V6T 1Z2

    Özgür Yılmaz

Authors
  1. Evan Chou
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  2. C. Sinan Güntürk
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  3. Felix Krahmer
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  4. Rayan Saab
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  5. Özgür Yılmaz
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Corresponding author

Correspondence to Evan Chou .

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Editors and Affiliations

  1. School of Engineering and Science, Jacobs University Bremen, Bremen, Bremen, Germany

    Götz E. Pfander

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Chou, E., Güntürk, C.S., Krahmer, F., Saab, R., Yılmaz, Ö. (2015). Noise-Shaping Quantization Methods for Frame-Based and Compressive Sampling Systems. In: Pfander, G. (eds) Sampling Theory, a Renaissance. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-19749-4_4

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