Use of Quillen-Suslin theorem for laurent polynomials in wavelet filter bank design

Youngmi Hur

doi:10.1007/978-3-319-54711-4_12

Use of Quillen-Suslin theorem for laurent polynomials in wavelet filter bank design

Youngmi Hur

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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.

Original language	English
Title of host publication	Applied and Numerical Harmonic Analysis
Publisher	Springer International Publishing
Pages	303-313
Number of pages	11
Edition	9783319547107
DOIs	https://doi.org/10.1007/978-3-319-54711-4_12
Publication status	Published - 2017

Publication series

Name	Applied and Numerical Harmonic Analysis
Number	9783319547107
ISSN (Print)	2296-5009
ISSN (Electronic)	2296-5017

Bibliographical note

Funding Information:
*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.

All Science Journal Classification (ASJC) codes

Applied Mathematics

Access to Document

10.1007/978-3-319-54711-4_12

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Cite this

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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.",

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