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Non-Separable Meyer-like Wavelet Frames

Author

Listed:
  • Zhihua Zhang

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

Abstract

In the theory of wavelet frames, the known Daubechies wavelet bases have been generalized to compactly supported (Daubechies-like) wavelet frames, while the known bandlimited Meyer wavelet bases have not been generalized to date. In this study, we will generalize known Meyer wavelet basis into non-separable Meyer-like wavelet frames. By using a characteristic function to mask the Fourier transform of the one-dimensional Meyer scaling function with a width parameter, we can produce a family of Meyer-like frame scaling functions and associated Meyer-like wavelet frames. After that, by inserting a real-valued function into the width parameter of a one-dimensional Meyer-like frame scaling function, we propose a novel approach to construct non-separable Meyer-like frame scaling functions with unique circular symmetry. Finally, we construct the corresponding non-separable Meyer-like wavelet frames.

Suggested Citation

  • Zhihua Zhang, 2022. "Non-Separable Meyer-like Wavelet Frames," Mathematics, MDPI, vol. 10(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2296-:d:852852
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    References listed on IDEAS

    as
    1. Zhihua Zhang, 2021. "Characterization of Frequency Domains of Bandlimited Frame Multiresolution Analysis," Mathematics, MDPI, vol. 9(9), pages 1-9, May.
    2. 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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