An Interplay of Ridgelet and Linear Canonical Transforms

Hari M. Srivastava, Azhar Y. Tantary, Firdous A. Shah and Ahmed I. Zayed
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Hari M. Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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

Mathematics, 2022, vol. 10, issue 12, 1-17

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.

Keywords: linear canonical transform; radon transform; ridgelet transform; wavelet transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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