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Use of Quillen-Suslin Theorem for Laurent Polynomials in Wavelet Filter Bank Design

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Excursions in Harmonic Analysis, Volume 5

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

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Abstract

In this chapter we give an overview of a method recently developed for designing wavelet filter banks via the Quillen-Suslin Theorem for Laurent polynomials. In this method, the Quillen-Suslin Theorem is used to transform vectors with Laurent polynomial entries to other vectors with Laurent polynomial entries so that the matrix analysis tools that were not readily available for the vectors before the transformation can now be employed. As a result, a powerful and general method for designing non-redundant wavelet filter banks is obtained. In particular, the vanishing moments of the resulting wavelet filter banks can be controlled in a very simple way, which is especially advantageous compared to other existing methods for the multi-dimensional cases.

This chapter is mainly based on the work with Hyungju Park and Fang Zheng presented in [15]. This research was partially supported by National Research Foundation of Korea (NRF) Grants 20151003262 and 20151009350.

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Notes

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Author information

Authors and Affiliations

  1. Department of Mathematics, Yonsei University, Seoul, 03722, Korea

    Youngmi Hur

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  1. Youngmi Hur
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Correspondence to Youngmi Hur .

Editor information

Editors and Affiliations

  1. Norbert Wiener Center, University of Maryland, College Park, Maryland, USA

    Radu Balan

  2. Norbert Wiener Center, University of Maryland, College Park, Maryland, USA

    John J. Benedetto

  3. Norbert Wiener Center, University of Maryland, College Park, Maryland, USA

    Wojciech Czaja

  4. Norbert Wiener Center, University of Maryland, College Park, Maryland, USA

    Matthew Dellatorre

  5. Norbert Wiener Center, University of Maryland, College Park, Maryland, USA

    Kasso A. Okoudjou

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Hur, Y. (2017). Use of Quillen-Suslin Theorem for Laurent Polynomials in Wavelet Filter Bank Design. In: Balan, R., Benedetto, J., Czaja, W., Dellatorre, M., Okoudjou, K. (eds) Excursions in Harmonic Analysis, Volume 5. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-54711-4_12

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