A Convolution-Based Shearlet Transform in Free Metaplectic Domains

The free metaplectic transformation (FMT) is a multidimensional integral transform that encompasses a broader range of integral transforms, from the classical Fourier to the more recent linear canonical transforms. The aim of this study is to introduce a novel shearlet transform by employing the fre...

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Published inJournal of mathematics (Hidawi) Vol. 2021; pp. 1 - 23
Main Authors Garg, Tarun K., Lone, Waseem Z., Shah, Firdous A., Mejjaoli, Hatem
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2021
Hindawi Limited
Subjects
Approximation
Convolution
Fourier transforms
Integral transforms
Mathematics
Orthogonality
Uncertainty principles
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Abstract The free metaplectic transformation (FMT) is a multidimensional integral transform that encompasses a broader range of integral transforms, from the classical Fourier to the more recent linear canonical transforms. The aim of this study is to introduce a novel shearlet transform by employing the free metaplectic convolution structures. Besides obtaining the orthogonality relation, inversion formula, and range theorem, we also study the homogeneous approximation property for the proposed transform. Towards the culmination, we formulate the Heisenberg and logarithmic-type uncertainty principles associated with the free metaplectic shearlet transform.
AbstractList The free metaplectic transformation (FMT) is a multidimensional integral transform that encompasses a broader range of integral transforms, from the classical Fourier to the more recent linear canonical transforms. The aim of this study is to introduce a novel shearlet transform by employing the free metaplectic convolution structures. Besides obtaining the orthogonality relation, inversion formula, and range theorem, we also study the homogeneous approximation property for the proposed transform. Towards the culmination, we formulate the Heisenberg and logarithmic-type uncertainty principles associated with the free metaplectic shearlet transform.
Author Garg, Tarun K.
Lone, Waseem Z.
Mejjaoli, Hatem
Shah, Firdous A.
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  givenname: Waseem Z.
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  organization: Department of MathematicsUniversity of KashmirSouth CampusAnantnag-192101Jammu and KashmirIndiakashmiruniversity.net
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  givenname: Hatem
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  surname: Mejjaoli
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  organization: Department of MathematicsCollege of SciencesTaibah UniversityP.O. Box 30002Al MadinahAl MunawarahSaudi Arabiataibahu.edu.sa
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10.1016/j.ijleo.2021.167689
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10.1007/s00041-011-9209-y
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Copyright Copyright © 2021 Tarun K. Garg et al.
Copyright © 2021 Tarun K. Garg et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0
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SubjectTerms Approximation
Convolution
Fourier transforms
Integral transforms
Mathematics
Orthogonality
Uncertainty principles
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Title A Convolution-Based Shearlet Transform in Free Metaplectic Domains
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