B. Mawardi, E.M.S. Hitzer

*International Journal of Wavelets, Multiresolution and Information Processing*,
**5**(6), pp. 997-1019 (2007).

**Abstract:**
In this paper, it is shown how continuous Clifford Cl3,0-valued admissible wavelets can
be constructed using the similitude group SIM(3), a subgroup of the affine group of R3.
We express the admissibility condition in terms of a Cl3,0 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
of multivector functions. We invent a generalized Clifford wavelet uncertainty principle.
For scalar admissibility constant, it sets bounds of accuracy in multivector wavelet
signal and image processing. As concrete example, we introduce multivector Clifford
Gabor wavelets, and describe important properties such as the Clifford Gabor transform
isometry, a reconstruction formula, and an uncertainty principle for Clifford Gabor
wavelets.

The original publication is available
here
from Wolrd Scientific Singapore

Preprint [ PDF ] 302K

[Geometric Calculus Japan index]