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arXiv · 1612.02702

Discretization of quaternionic continuous wavelet transforms

A. Askari Hemmat·K. Thirulogasanthar·A. Krzyzak
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Abstract

A scheme to form a basis and a frame for a Hilbert space of quaternion valued square integrable function from a basis and a frame, respectively, of a Hilbert space of complex valued square integrable functions is introduced. Using the discretization techniques for 2D-continuous wavelet transform of the $SIM(2)$ group, the quaternionic continuous wavelet transform, living in a complex valued Hilbert space of square integrable functions, of the quaternion wavelet group is discretized, and thereby, a discrete frame for quaternion valued Hilbert space of square integrable functions is obtained.

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A. Askari Hemmat, K. Thirulogasanthar, A. Krzyzak. 2016-12-08. Discretization of quaternionic continuous wavelet transforms. https://doi.org/10.1016/j.geomphys.2017.02.013.

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