ヒッツェル，エクハルト   HITZER, Eckhard   ヒッツェル, エクハルト    所属   国際基督教大学教養学部 アーツ・サイエンス学科    職種   上級准教授
言語種別	英語
発行・発表の年月	2009
形態種別	研究論文（国際会議プロシーディングス）
査読	査読あり
標題	Clifford (Geometric) Algebra Wavelet Transform
執筆形態	単著
掲載誌名	Proc. of GraVisMa 2009, 02-04 Sep. 2009, Plzen, Czech Republic
掲載区分	国外
巻・号・頁	pp.94-101
著者・共著者	HITZER Eckhard
概要	While the Clifford (geometric) algebra Fourier Transform (CFT) is global, we introduce here the local Clifford (geometric) algebra (GA) wavelet concept. We show how for n = 2,3(mod 4) continuous 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 element of C (complex numbers) 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 CFT and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the CliRord wavelet transform. As an explicit example, we introduce Clifford Gabor wavelets. We further invent a generalized Clifford wavelet uncertainty principle. Extensions of CFTs and Clifford wavelets to Cl(0,n') ; n' = 1,2(mod 4) appear straight forward.