The Characterization of Orthogonal Matrix-valued Multivariable Wavelet Packets Associated with an Integer-valued Dilation Matrix

The notion of matrix-valued multiresolution analysis of space of matrix-valued higher-dimensional functions is introduced. An approach for constructing orthogonal matrix-valued higher-dimensional wavelet packets is presented and their properties are discussed by means of time-frequency analysis meth...

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Bibliographic Details
Main Author: Deyou Yuan
Format: Conference Proceeding
Language:English
Subjects:
Discrete wavelet transforms
Functional analysis
higher-dimensional
Intelligent systems
Mathematics
matrix-valued
Multidimensional systems
Multiresolution analysis
orthogonal
Space technology
Time frequency analysis
Wavelet analysis
Wavelet packets
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Description
Summary:The notion of matrix-valued multiresolution analysis of space of matrix-valued higher-dimensional functions is introduced. An approach for constructing orthogonal matrix-valued higher-dimensional wavelet packets is presented and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal bases of L 2 (R d ,C rtimesr ) are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.
ISSN:2155-6083
2155-6091
DOI:10.1109/GCIS.2009.403