Continuous quaternion fourier and wavelet transforms

被引：25

作者：

Bahri, Mawardi ^{[1
]}

Ashino, Ryuichi ^{[2
]}

Vaillancourt, Remi ^{[3
]}

机构：

[1] Univ Hasanuddin, Dept Math, Makassar 90245, Indonesia

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

[3] Univ Ottawa, Dept Math & Stat, Ottawa, ON K1N 6N5, Canada

来源：

INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING | 2014年 / 12卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Quaternion-valued function; quaternion algebra; quaternion Fourier transform; FIELDS;

D O I：

10.1142/S0219691314600030

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

A two-dimensional (2D) quaternion Fourier transform (QFT) defined with the kernel e(-i+j+k/root 3w.x) is proposed. Some fundamental properties, such as convolution, Plancherel and vector differential theorems, are established. The heat equation in quaternion algebra is presented as an example of the application of the QFT to partial differential equations. The wavelet transform is extended to quaternion algebra using the kernel of the QFT.

引用

页数：21

共 26 条

[1]

[Anonymous], 2001, J NAT GEOM

[2]

[Anonymous], PARTIAL DIFFERENTIAL

[3] Local quaternion Fourier transform and color image texture analysis [J].