The construction of wavelets is a key problem in wavelet analysis. In the background of the one-dimensional double wavelet theory and the one dimensional biorthogonal bidirectional wavelet construction theory, this paper extends the one-dimensional bidirectional wavelet to the two-scale three-dimensional eight-direction biorthogonal wavelet. By using the method of tensor products to construct higher dimensional wavelets, the two-scale three-dimensional eight-direction multi-resolution analysis, two-scale three-dimensional eight-direction scale function and wavelet function are obtained. In addition, the conditions satisfied of the orthogonal and biorthogonal properties of the two-scale three-dimensional eight-direction wavelet are studied.
| Published in | American Journal of Applied Mathematics (Volume 9, Issue 4) |
| DOI | 10.11648/j.ajam.20210904.15 |
| Page(s) | 141-155 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Two-scale Three-dimensional Eight-direction Wavelet, Two-scale Three-dimensional Eight-direction Multiresolution Analysis, Orthogonal Wavelet
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APA Style
Jing Zhang, Gang Wang, Chuanyan Hou, Xiaoying Yang. (2021). The Orthogonality of Two-scale Three-dimensional Eight-direction Wavelet. American Journal of Applied Mathematics, 9(4), 141-155. https://doi.org/10.11648/j.ajam.20210904.15
ACS Style
Jing Zhang; Gang Wang; Chuanyan Hou; Xiaoying Yang. The Orthogonality of Two-scale Three-dimensional Eight-direction Wavelet. Am. J. Appl. Math. 2021, 9(4), 141-155. doi: 10.11648/j.ajam.20210904.15
AMA Style
Jing Zhang, Gang Wang, Chuanyan Hou, Xiaoying Yang. The Orthogonality of Two-scale Three-dimensional Eight-direction Wavelet. Am J Appl Math. 2021;9(4):141-155. doi: 10.11648/j.ajam.20210904.15
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Download@article{10.11648/j.ajam.20210904.15,
author = {Jing Zhang and Gang Wang and Chuanyan Hou and Xiaoying Yang},
title = {The Orthogonality of Two-scale Three-dimensional Eight-direction Wavelet},
journal = {American Journal of Applied Mathematics},
volume = {9},
number = {4},
pages = {141-155},
doi = {10.11648/j.ajam.20210904.15},
url = {https://doi.org/10.11648/j.ajam.20210904.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210904.15},
abstract = {The construction of wavelets is a key problem in wavelet analysis. In the background of the one-dimensional double wavelet theory and the one dimensional biorthogonal bidirectional wavelet construction theory, this paper extends the one-dimensional bidirectional wavelet to the two-scale three-dimensional eight-direction biorthogonal wavelet. By using the method of tensor products to construct higher dimensional wavelets, the two-scale three-dimensional eight-direction multi-resolution analysis, two-scale three-dimensional eight-direction scale function and wavelet function are obtained. In addition, the conditions satisfied of the orthogonal and biorthogonal properties of the two-scale three-dimensional eight-direction wavelet are studied.},
year = {2021}
}
TY - JOUR T1 - The Orthogonality of Two-scale Three-dimensional Eight-direction Wavelet AU - Jing Zhang AU - Gang Wang AU - Chuanyan Hou AU - Xiaoying Yang Y1 - 2021/08/31 PY - 2021 N1 - https://doi.org/10.11648/j.ajam.20210904.15 DO - 10.11648/j.ajam.20210904.15 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 141 EP - 155 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20210904.15 AB - The construction of wavelets is a key problem in wavelet analysis. In the background of the one-dimensional double wavelet theory and the one dimensional biorthogonal bidirectional wavelet construction theory, this paper extends the one-dimensional bidirectional wavelet to the two-scale three-dimensional eight-direction biorthogonal wavelet. By using the method of tensor products to construct higher dimensional wavelets, the two-scale three-dimensional eight-direction multi-resolution analysis, two-scale three-dimensional eight-direction scale function and wavelet function are obtained. In addition, the conditions satisfied of the orthogonal and biorthogonal properties of the two-scale three-dimensional eight-direction wavelet are studied. VL - 9 IS - 4 ER -
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