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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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/2140189 |
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| _version_ | 1832546070179086336 |
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| author | Tarun K. Garg Waseem Z. Lone Firdous A. Shah Hatem Mejjaoli |
| author_facet | Tarun K. Garg Waseem Z. Lone Firdous A. Shah Hatem Mejjaoli |
| author_sort | Tarun K. Garg |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8c57a0b266184e51815fd433c4095318 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-8c57a0b266184e51815fd433c40953182025-02-03T07:24:00ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/21401892140189A Convolution-Based Shearlet Transform in Free Metaplectic DomainsTarun K. Garg0Waseem Z. Lone1Firdous A. Shah2Hatem Mejjaoli3Department of Mathematics, Satyawati College, University of Delhi, Delhi-110052, IndiaDepartment of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, IndiaDepartment of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, IndiaDepartment of Mathematics, College of Sciences, Taibah University, P.O. Box 30002, Al Madinah, Al Munawarah, Saudi ArabiaThe 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.http://dx.doi.org/10.1155/2021/2140189 |
| spellingShingle | Tarun K. Garg Waseem Z. Lone Firdous A. Shah Hatem Mejjaoli A Convolution-Based Shearlet Transform in Free Metaplectic Domains Journal of Mathematics |
| title | A Convolution-Based Shearlet Transform in Free Metaplectic Domains |
| title_full | A Convolution-Based Shearlet Transform in Free Metaplectic Domains |
| title_fullStr | A Convolution-Based Shearlet Transform in Free Metaplectic Domains |
| title_full_unstemmed | A Convolution-Based Shearlet Transform in Free Metaplectic Domains |
| title_short | A Convolution-Based Shearlet Transform in Free Metaplectic Domains |
| title_sort | convolution based shearlet transform in free metaplectic domains |
| url | http://dx.doi.org/10.1155/2021/2140189 |
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