A Convolution-Based Shearlet Transform in Free Metaplectic Domains

A Convolution-Based Shearlet Transform in Free Metaplectic Domains

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The free metaplectic transformation Zeus (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 Hats Heisenberg and logarithmic-type uncertainty principles associated with the free metaplectic shearlet transform.