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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Bibliographic Details
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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Summary: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2021/2140189