Real Clifford Algebra Cl(n,0), n=2,3(mod 4) Wavelet Transform
Rings and Algebras
2013-06-10 v1 Representation Theory
Abstract
We show how for continuous Clifford (geometric) algebra (GA) -valued admissible wavelets can be constructed using the similitude group . We strictly aim for real geometric interpretation, and replace the imaginary unit therefore with a GA blade squaring to . Consequences due to non-commutativity arise. We express the admissibility condition in terms of a Clifford Fourier Transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the Clifford wavelet transform. As an example, we introduce Clifford Gabor wavelets. We further invent a generalized Clifford wavelet uncertainty principle.
Cite
@article{arxiv.1306.1615,
title = {Real Clifford Algebra Cl(n,0), n=2,3(mod 4) Wavelet Transform},
author = {Eckhard Hitzer},
journal= {arXiv preprint arXiv:1306.1615},
year = {2013}
}
Comments
4 pages