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Construction of Orthogonal Vector-valued Wavelets and Characteristics of Vector-valued Wavelet Packets 被引量:1
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作者 CHEN Qing-jiang LIU Hong-yun 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第3期360-367,共8页
The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vec... The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2(R, C^n) from these wavelet packets. 展开更多
关键词 ORTHOGONAL Hermitian matrix vector-valued multiresolution analysis vector-valued scaling functions vector-valued wavelets vector-valued wavelet packets
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Characterizations of Orthogonal Vector-valued Multivariate Wavelet Packets
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作者 HUA De-lin FENG Jin-shun 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第4期606-614,共9页
In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 (R^s, C^n) is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties ar... In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 (R^s, C^n) is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2(R^s,C^n) are extracted from these wavelet packets. 展开更多
关键词 ORTHOGONALITY refinement equation vector-valued multiresolution analysis vector-valued scaling function vector-valued wavelet packets
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The Biorthogonality of Multiple Vector-valued Bivariate Wavelet Packets
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作者 CHEN Shao-dong HUANG Na 《Chinese Quarterly Journal of Mathematics》 CSCD 2010年第2期208-213,共6页
The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavel... The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained. 展开更多
关键词 BIVARIATE multiple vector-valued multiresolution analysis multiple vectorvalued scaling function multiple vector-valued wavelet packets biorthogonality
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Orthogonal Multiple Vector-Valued Wavelet Packets 被引量:3
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作者 陈清江 程正兴 李学志 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2007年第2期289-297,共9页
The multiple vector-valued wavelet packets are defined and investigated. A procedure for constructing the multiple vector-valued wavelet packets is presented. The properties of multiple vector-valued wavelet packets a... The multiple vector-valued wavelet packets are defined and investigated. A procedure for constructing the multiple vector-valued wavelet packets is presented. The properties of multiple vector-valued wavelet packets are discussed by using integral transformation and operator theory. Finally, new orthogonal bases of L^2(R, C^s×s) is constructed from the orthogonal multiple vector-valued wavelet packets. 展开更多
关键词 vector-valued multiresolution analysis multiple vector-valued scaling functions multiple vector-valued wavelet packets refinement equation.
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一类任意矩阵伸缩双向向量值小波包
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作者 苏宇 王刚 库福立 《山西师范大学学报(自然科学版)》 2014年第1期11-17,共7页
本文给出了双向向量值多分辩分析和具有矩阵伸缩的高维双向向量值小波包,研究了高维双向向量值小波包的性质,得到了矩阵伸缩的双向向量值正交小波基.
关键词 整数伸缩 正交 多分辨分析 双向尺度函数 加细面具 向量值小波
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