Two-dimensional quaternion wavelet transform

被引：41

作者：

Bahri, Mawardi ^{[2
]}

Ashino, Ryuichi ^{[1
]}

Vaillancourt, Remi ^{[3
]}

机构：

[1] Osaka Kyoiku Univ, Div Math Sci, Osaka 5828582, Japan

[2] Hasanuddin Univ, Dept Math, Makassar, Indonesia

[3] Univ Ottawa, Dept Math & Stat, Ottawa, ON KIN 6N5, Canada

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 218卷 / 01期

关键词：

Quaternion Fourier transform; Admissible quaternion wavelets; FOURIER-TRANSFORM; DIRECTIONAL WAVELETS; FIELDS;

D O I：

10.1016/j.amc.2011.05.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several examples of the CQWT. As an application we derive a Heisenberg type uncertainty principle for these extended wavelets. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：10 / 21

页数：12

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