A Convolution-Based Shearlet Transform in Free Metaplectic Domains

Tarun K. Garg, Waseem Z. Lone, Firdous A. Shah, Hatem Mejjaoli and Ram Jiwari

Journal of Mathematics, 2021, vol. 2021, 1-23

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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2140189

DOI: 10.1155/2021/2140189

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