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Volume 9 , Issue 4 , August 2021 , Pages: 141 - 155
The Orthogonality of Two-scale Three-dimensional Eight-direction Wavelet
Jing Zhang, School of Mathematical Sciences, Xinjiang Normal University, Urumqi, China
Gang Wang, School of Mathematical Sciences, Xinjiang Normal University, Urumqi, China
Chuanyan Hou, School of Mathematical Sciences, Xinjiang Normal University, Urumqi, China
Xiaoying Yang, School of Mathematical Sciences, Xinjiang Normal University, Urumqi, China
Received: Aug. 14, 2021;       Accepted: Aug. 26, 2021;       Published: Aug. 31, 2021
DOI: 10.11648/j.ajam.20210904.15        View        Downloads  
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.
Two-scale Three-dimensional Eight-direction Wavelet, Two-scale Three-dimensional Eight-direction Multiresolution Analysis, Orthogonal Wavelet
To cite this article
Jing Zhang, Gang Wang, Chuanyan Hou, Xiaoying Yang, The Orthogonality of Two-scale Three-dimensional Eight-direction Wavelet, American Journal of Applied Mathematics. Vol. 9, No. 4, 2021, pp. 141-155. doi: 10.11648/j.ajam.20210904.15
Copyright © 2021 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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