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	2007
形態種別	研究論文（学術雑誌）
査読	査読あり
標題	Clifford Algebra Cl(3,0)-valued Wavelet Transformation, Clifford Wavelet Uncertainty Inequality and Clifford Gabor Wavelets
執筆形態	共著
掲載誌名	International Journal of Wavelets, Multiresolution and Information Processing
掲載区分	国外
出版社・発行元	World Scientific Singapore
巻・号・頁	5(6),pp.997-1019
著者・共著者	HITZER Eckhard, B. Mawardi
概要	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.
DOI	10.1142/S0219691307002166