On Quaternion Shearlet Transforms

TL;DR

This paper introduces the quaternion shearlet transform, extending shearlet analysis to quaternion-valued functions, and establishes its fundamental properties, inversion, and uncertainty principles.

Contribution

It presents the first comprehensive study of quaternion shearlet transforms, including their properties, inversion formulae, and uncertainty inequalities.

Findings

Established fundamental properties of quaternion shearlet transforms

Derived Moyal's and inversion formulae for the transform

Proved Heisenberg's uncertainty inequality and logarithmic version

Abstract

In this paper, we introduce the notion of quaternion shearlet transform- which is an extension of the ordinary shearlet transform. Firstly, we study the fundamental properties of quaternion shearlet transforms and then establish some basic results including Moyal's and inversion formulae. Finally, we derive the associated Heisenberg's uncertainty inequality and the corresponding logarithmic version for quaternion shearlet transforms.