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A Convolution-Based Shearlet Transform in Free Metaplectic Domains

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

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.

Suggested Citation

  • Tarun K. Garg & Waseem Z. Lone & Firdous A. Shah & Hatem Mejjaoli & Ram Jiwari, 2021. "A Convolution-Based Shearlet Transform in Free Metaplectic Domains," Journal of Mathematics, Hindawi, vol. 2021, pages 1-23, October.
    • Handle: RePEc:hin:jjmath:2140189
    DOI: 10.1155/2021/2140189
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