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), 2021. Published by Science Publishing Group |
Two-scale Three-dimensional Eight-direction Wavelet, Two-scale Three-dimensional Eight-direction Multiresolution Analysis, Orthogonal Wavelet
| [1] | Wang Shupeng; Zhao Weigang; Zhang Guangyuan; Xu, Hongbin; Du, Yanliang. Identification of structural parameters from free vibration data using Gabor wavelet transform [J]. Mechanical Systems and Signal Processing, 2021, 147: 107122. |
| [2] | L. Shen; H. H. Tan; J. Y. Tham; Symmetric-antisymmetric orthonarmal multiwavelets and related scalar wavelets [J]. Appl. Comp. Harm. Anal, 2000, 8: 258-279. |
| [3] | Lebrun J, Vetterli M. High order balanced multiwavelets [J]. In: Proc IEEE Int Conf Acoustics, Speech and Signal Processing, 1998, 3: 1529-1532. |
| [4] | Yang Shouzhi; Zhang Kecun. Fast algorithm for multiwavelet function values [J]. Numerical calculation and computer applications, 2002, 6: 18-23. |
| [5] | Leng Jingsong; Cheng Zhengxing; Yang Shouzhi; Huang Tingzhu. Construction of orthogonal conjugate filter [J]. Numerical mathematics, 2004, 10:151-160. |
| [6] | Li Youfa; Yang Shouzhi. The construction algorithm of Armlet multiwavele [J]. Numerical calculation and computer applications, 2007, 8: 290-297. |
| [7] | Lebrun J; Vetterli M. Balanced multiwavelets theory and design, IEEE Trans Signal Process, 1998, 46(4): 1119-1125. |
| [8] | Yang Shouzhi; Peng Lizhong. An orthogonal multi-scale function with high order equilibrium is constructed based on PTST method [J]. Science in China Series E Information Science. 2006, 36(6): 644-656. |
| [9] | Lian J A. Analysis-ready multiwavelets (Armlet) for processing scalar-valude Signal [J]. IEEE Processing letters, 2004, 11: 205-208. |
| [10] | Lian J A. Armlet and balanced multiwavelets: flipping filter construction [J]. IEEE Transaction on Signal Processing, 2005, 53:1754-1767. |
| [11] | Cui C. K; Lian J A. A study on orthonormal multiwavelets [J]. J. Appl. Numer. Math, 1996, 20: 273-298. |
| [12] | Han B.; Mo Q. Multiwavelet frames from refinement function vectors [J]. Adv. Comp. Math. 2003, 18(2): 211-245. |
| [13] | Yang shouzhi; Li Youfa. Two-direction refinable functions and two-direction wavelets with dilation factor m [J]. Appiled Mathematics and Computation, 2007, 188: 1905-1920. |
| [14] | Yang Shouzhi; Li Youfa. Bidirectional fine-grained functions and bidirectional wavelets with high approximation order and regularity [J]. Science in China Series A: Mathematics, 2007, 37 (7): 770-795. |
| [15] | Zhang Jing; Huang Yunhu; Guan Huihui, et. al. An algorithm for constructing the scale function of a-scale three-dimensional eight-dimensional plus fine waves [J]. university mathematics, 2017, 33(005): 12-23. |
| [16] | Zhang Jing; Zhou Shihang. Biorthogonal a-scale three-dimensional eight-dimensional scale function and wavelet function construction algorithm [J]. Journal of Hubei University (Natural Science), 2018, 40(03): 36-46. |
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
Share This Article
Twitter
Linked In
Facebook
Copy
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 -
Email: