The properties of orthogonal vector-valued wavelet packets in higher dimensions

2006 ◽  
Author(s):  
QING-JIANG CHEN ◽  
TONG-QI ZHANG
Keyword(s):  
Higher Dimensions ◽  
Wavelet Packets ◽  
Orthogonal Vector ◽  
Vector Valued

The Biorthogonality Property of the Multidimensional Wavelet Packets with Multi-Scale Factor

2010 ◽  
Vol 439-440 ◽  
pp. 1093-1098
Author(s):  
Jian Feng Zhou ◽  
Ping An Wang
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Multi Scale ◽  
Vector Valued

In this article, we introduce a sort of vector-valued wavelet packets with multi-scale dilation of space , which are generalizations of multivariaale wavelet packets. A method for designing a sort of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality property is characterized by virtue of time-frequency analysis method, matrix theory, and operator theory. Three biorthogonality formulas regarding these wavelet packets are established. Furtherore, it is shown how to obtain new Riesz bases of space from these wavelet packets.

An Optimization Algorithm for Orthogonal Trivariate Wavelets with Short Support

2012 ◽  
Vol 461 ◽  
pp. 835-839
Author(s):  
Ke Zhong Han
Keyword(s):  
Filter Bank ◽  
Scaling Function ◽  
Wavelet Packets ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Orthogonal Vector ◽  
Multi Scale ◽  
Dilation Factor ◽  
Necessary And Sufficient ◽  
Vector Valued

Wavelet analysis is nowadays a widely used tool in applied mathe-matics. The advantages of wavelet packets and their promising features in various application have attracted a lot of interest and effort in recent years.. The notion of vector-valued binary wavelets with two-scale dilation factor associated with an orthogonal vector-valued scaling function is introduced. The existence of orthogonal vector-valued wavelets with multi-scale is discussed. A necessary and sufficient condition is presented by means of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a sort of orthogonal vector-valued wave-lets with compact support is proposed, and their properties are investigated.

Construction and characterizations of orthogonal vector-valued multivariate wavelet packets

2009 ◽  
Vol 40 (4) ◽  
pp. 1835-1844 ◽  
Author(s):  
Qingjiang Chen ◽  
Huaixin Cao ◽  
Zhi Shi
Keyword(s):  
Wavelet Packets ◽  
Orthogonal Vector ◽  
Vector Valued

Generation and Characteristics of a Class of Four-Dimensional Multiwavelet Packets with Six-Scale Dilation Factor

2011 ◽  
Vol 460-461 ◽  
pp. 317-322
Author(s):  
Qing Jiang Chen ◽  
Zong Tian Wei
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Dilation Factor ◽  
Vector Valued

In this paper, we introduce a class of vector-valued wavelet packets of space , which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are derived. Moreover, it is shown how to gain new Riesz bases of space from these wavelet packets.

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