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An Interplay of Ridgelet and Linear Canonical Transforms

Author

Listed:
  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan
    Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy)

  • Azhar Y. Tantary

    (Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India)

  • Firdous A. Shah

    (Department of Mathematics, University of Kashmir, South Campus, Anantnag 192101, Jammu and Kashmir, India)

  • Ahmed I. Zayed

    (Department of Mathematical Sciences, DEPAUL College of Science and Health, Chicago, IL 60614, USA)

Abstract

The present study is the first of its kind, aiming to explore the interface between the ridgelet and linear canonical transforms. To begin with, we formulate a family of linear canonical ridgelet waveforms by suitably chirping a one-dimensional wavelet along a specific direction. The construction of novel ridgelet waveforms is demonstrated via a suitable example supported by vivid graphics. Subsequently, we introduce the notion of linear canonical ridgelet transform, which not only embodies the classical ridgelet transform but also yields another new variant of the ridgelet transform based on the fractional Fourier transform. Besides studying all the fundamental properties, we also present an illustrative example on the implementation of the linear canonical ridgelet transform on a bivariate function.

Suggested Citation

  • Hari M. Srivastava & Azhar Y. Tantary & Firdous A. Shah & Ahmed I. Zayed, 2022. "An Interplay of Ridgelet and Linear Canonical Transforms," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:1986-:d:834437
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    References listed on IDEAS

    as
    1. Azhar Y. Tantary & Firdous A. Shah & Georgios Psihoyios, 2020. "An Intertwining of Curvelet and Linear Canonical Transforms," Journal of Mathematics, Hindawi, vol. 2020, pages 1-14, November.
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