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The Orthogonality of Two-scale Three-dimensional Eight-direction Wavelet

Received: 14 August 2021     Accepted: 26 August 2021     Published: 31 August 2021
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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.

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

Keywords

Two-scale Three-dimensional Eight-direction Wavelet, Two-scale Three-dimensional Eight-direction Multiresolution Analysis, Orthogonal Wavelet

References
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Cite This Article
  • 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

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    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

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    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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  • @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}
    }
    

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  • 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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Author Information
  • School of Mathematical Sciences, Xinjiang Normal University, Urumqi, China

  • School of Mathematical Sciences, Xinjiang Normal University, Urumqi, China

  • School of Mathematical Sciences, Xinjiang Normal University, Urumqi, China

  • School of Mathematical Sciences, Xinjiang Normal University, Urumqi, China

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