A general construction of nonseparable multivariate orthonormal wavelet bases

Abderrazek Karoui

Open Mathematics (2008)

  • Volume: 6, Issue: 4, page 504-525
  • ISSN: 2391-5455

Abstract

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The construction of nonseparable and compactly supported orthonormal wavelet bases of L 2(R n); n ≥ 2, is still a challenging and an open research problem. In this paper, we provide a special method for the construction of such wavelet bases. The wavelets constructed by this method are dyadic wavelets. Also, we show that our proposed method can be adapted for an eventual construction of multidimensional orthogonal multiwavelet matrix masks, candidates for generating multidimensional multiwavelet bases.

How to cite

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Abderrazek Karoui. "A general construction of nonseparable multivariate orthonormal wavelet bases." Open Mathematics 6.4 (2008): 504-525. <http://eudml.org/doc/269350>.

@article{AbderrazekKaroui2008,
abstract = {The construction of nonseparable and compactly supported orthonormal wavelet bases of L 2(R n); n ≥ 2, is still a challenging and an open research problem. In this paper, we provide a special method for the construction of such wavelet bases. The wavelets constructed by this method are dyadic wavelets. Also, we show that our proposed method can be adapted for an eventual construction of multidimensional orthogonal multiwavelet matrix masks, candidates for generating multidimensional multiwavelet bases.},
author = {Abderrazek Karoui},
journal = {Open Mathematics},
keywords = {multidimensional wavelets; non-separable orthogonal wavelet bases; stability; transition operator; multidimensional multiwavelet masks},
language = {eng},
number = {4},
pages = {504-525},
title = {A general construction of nonseparable multivariate orthonormal wavelet bases},
url = {http://eudml.org/doc/269350},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Abderrazek Karoui
TI - A general construction of nonseparable multivariate orthonormal wavelet bases
JO - Open Mathematics
PY - 2008
VL - 6
IS - 4
SP - 504
EP - 525
AB - The construction of nonseparable and compactly supported orthonormal wavelet bases of L 2(R n); n ≥ 2, is still a challenging and an open research problem. In this paper, we provide a special method for the construction of such wavelet bases. The wavelets constructed by this method are dyadic wavelets. Also, we show that our proposed method can be adapted for an eventual construction of multidimensional orthogonal multiwavelet matrix masks, candidates for generating multidimensional multiwavelet bases.
LA - eng
KW - multidimensional wavelets; non-separable orthogonal wavelet bases; stability; transition operator; multidimensional multiwavelet masks
UR - http://eudml.org/doc/269350
ER -

References

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  5. [5] Karoui A., A note on the construction of nonseparable wavelet bases and multiwavelet matrix filters of L 2(R n); where n ≥ 2, Electron. Res. Announc. Amer. Math. Soc., 2003, 9, 32-39 Zbl1020.65110
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  8. [8] Lawton W., Lee S.L., Shen Z., Stability and orthonormality of multivariate refinable functions, SIAM J. Math. Anal., 1997, 28, 999–1014 http://dx.doi.org/10.1137/S003614109528815X Zbl0872.41003
  9. [9] Lin E.B., Ling Y., Image compression and denoising via nonseparable wavelet approximation, J. Comput. Appl. Math., 2003, 155, 131–152 http://dx.doi.org/10.1016/S0377-0427(02)00896-8 Zbl1022.65147
  10. [10] Maass P., Families of orthogonal two-dimensional wavelets, SIAM J. Math. Anal., 1996, 27, 1454–1481 http://dx.doi.org/10.1137/S003614109324649X Zbl0881.42022
  11. [11] Shen Z., Refinable function vectors, SIAM J. Math. Anal., 1998, 29, 235–250 http://dx.doi.org/10.1137/S0036141096302688 Zbl0913.42028
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