Title :
The Characterization of a Sort of Biorthogonal Multivariate Wavelet Packets According to an Integer-valued Dilation Matrix
Author :
Ma, Jinshuan ; Tian, Xinxian
Author_Institution :
Sch. of Educ., Nanyang Inst. of Technol., Nanyang, China
Abstract :
The notion of matrix-valued multiresolution analysis of space of matrix-valued multivariate functions is proposed. An approach for constructing orthogonal matrix-valued multivariate wavelet packets is developed 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 L2(Rs, Cr×r) are obtained by constructing a series of subspaces of biorthogonal matrix-valued wavelet packets.
Keywords :
functional analysis; matrix algebra; time-frequency analysis; wavelet transforms; biorthogonal multivariate wavelet packets; functional analysis method; integer valued dilation matrix; matrix theory; matrix valued multiresolution analysis; matrix valued wavelet packets; orthogonality formulas; orthonormal bases; time frequency analysis method; Discrete transforms; Educational technology; Functional analysis; Information technology; Multiresolution analysis; Space technology; Time frequency analysis; Variable speed drives; Wavelet analysis; Wavelet packets; biorthogonal; matrix theory; matrix-valued wavelet packets; multivariate; orthonormal bases;
Conference_Titel :
Intelligent Information Technology Application, 2009. IITA 2009. Third International Symposium on
Conference_Location :
Nanchang
Print_ISBN :
978-0-7695-3859-4
DOI :
10.1109/IITA.2009.247
