Real Clifford Algebra Cl(n,0), n = 2,3(mod 4) Wavelet Transform
We show how for n = 2,3(mod 4) continuous Clifford (geometric) algebra (GA) Cl_n-valued admissible wavelets can be constructed using the similitude group SIM(n). We strictly aim for real geometric interpretation, and replace the imaginary unit i of C therefore with a GA blade squaring to -1. Consequences due to non-commutativity arise. We express the admissibility condition in terms of a Cl_n 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.
Clifford geometric algebra, Clifford wavelet transform, multidimensional wavelets, continuous wavelets, similitude group
AMS Subj. Class.
15A66, 42C40, 94A12
Source: E. Hitzer, hitzer_at_mech.fukui-u.ac.jp