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Splitting of Framelets and Framelet Packets

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  • Zhihua Zhang

    (School of Mathematics, Shandong University, Jinan 250100, China)

Abstract

Due to resilience to background noise, stability of sparse reconstruction, and ability to capture local time-frequency information, the frame theory is becoming a dynamic forefront topic in data science. In this study, we overcome the disadvantages in the construction of traditional framelet packets derived by frame multiresolution analysis and square iterative matrices. We propose two novel approaches: One is to directly split known framelets again and again; the other approach is based on a generalized scaling function whose shifts are not a frame of some space. In these two approaches, the iterative matrices used are not square and the number of rows in the iterative matrix can be any integer number.

Suggested Citation

  • Zhihua Zhang, 2021. "Splitting of Framelets and Framelet Packets," Mathematics, MDPI, vol. 9(7), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:697-:d:522999
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    References listed on IDEAS

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    1. San Antolín, A. & Zalik, R.A., 2018. "Compactly supported Parseval framelets with symmetry associated to Ed(2)(Z) matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 179-190.
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    Cited by:

    1. Zhihua Zhang, 2021. "Characterization of Frequency Domains of Bandlimited Frame Multiresolution Analysis," Mathematics, MDPI, vol. 9(9), pages 1-9, May.

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