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 | |
| Publication status | Published - 2017 Jan 1 |
Publication series
| Name | Applied and Numerical Harmonic Analysis |
|---|---|
| Number | 9783319547107 |
| ISSN (Print) | 2296-5009 |
| ISSN (Electronic) | 2296-5017 |
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All Science Journal Classification (ASJC) codes
- Applied Mathematics
Cite this
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Use of Quillen-Suslin theorem for laurent polynomials in wavelet filter bank design. / Hur, Youngmi.
Applied and Numerical Harmonic Analysis. 9783319547107. ed. Springer International Publishing, 2017. p. 303-313 (Applied and Numerical Harmonic Analysis; No. 9783319547107).Research output: Chapter in Book/Report/Conference proceeding › Chapter
TY - CHAP
T1 - Use of Quillen-Suslin theorem for laurent polynomials in wavelet filter bank design
AU - Hur, Youngmi
PY - 2017/1/1
Y1 - 2017/1/1
N2 - 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.
AB - 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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UR - http://www.scopus.com/inward/citedby.url?scp=85047267927&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-54711-4_12
DO - 10.1007/978-3-319-54711-4_12
M3 - Chapter
T3 - Applied and Numerical Harmonic Analysis
SP - 303
EP - 313
BT - Applied and Numerical Harmonic Analysis
PB - Springer International Publishing
ER -