On Characteristics of Biorthogonal Vector-Valued Multivariate Wavelet Packets Associated with a Quantity Dilation Matrix

Wavelet analysis has been a widely applied one method for analyzing signal. In this work, the notion of vector-valued wavelet packets for space L 2 (R n ) s is proposed, which are generalizations of univariate wavelet packets. A constructive method for a class of biorthogonal vector-valued multivari...

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Bibliographic Details
Main Authors: Shude Du, Deyou Yuan
Format: Conference Proceeding
Language:English
Subjects:
Aggregates
biorthogonality formulas
Discrete transforms
Information analysis
Mathematics
Pixel
scaling functions
Signal analysis
Space technology
Time frequency analysis
vector-valued
Wavelet analysis
Wavelet packets
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Summary:Wavelet analysis has been a widely applied one method for analyzing signal. In this work, the notion of vector-valued wavelet packets for space L 2 (R n ) s is proposed, which are generalizations of univariate wavelet packets. A constructive method for a class of biorthogonal vector-valued multivariate wavelet packets is formulated and their biorthogonality properties are discussed by virtue of matrix theory, and operator theory. Three biorthogonality formulas concerning these wavelet packets are provided. Furthermore, new Riesz bases of space L 2 (R n ) s from these wavelet packets are obtained.
DOI:10.1109/ESIAT.2009.399