The Research of the Orthogonality Property of Matrix Univariate Wavelet Packets with an Integer Dilation Factor

Author

Du, Shude ; Wu, Hong-E

Author_Institution

Dept. of Appl. Math., Nanyang Inst. of Technol., Nanyang, China

Volume

3

fYear

2009

fDate

21-22 Nov. 2009

Firstpage

628

Lastpage

631

Abstract

The notion of matrix-valued multiresolution analysis. A procedure for designing orthogonal matrix-valued univariate wavelet packets is presented and their orthogonality 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 basis of L²(R, C^{u Ã— u}) are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

Keywords

functional analysis; image resolution; matrix algebra; time-frequency analysis; video signal processing; functional analysis method; integer dilation factor; matrix theory; matrix univariate wavelet packets; matrix-valued multiresolution analysis; orthogonality property; orthonormal basis; time-frequency analysis; Biomedical signal processing; Discrete transforms; Functional analysis; Image coding; Information technology; Mathematics; Multiresolution analysis; Time frequency analysis; Wavelet analysis; Wavelet packets; matrix-valued multiresolution analysis; matrix-valued wavelet packets; orthogonal; orthonormal basis; univariate;

fLanguage

English

Publisher

ieee

Conference_Titel

Intelligent Information Technology Application, 2009. IITA 2009. Third International Symposium on

Conference_Location

Nanchang

Print_ISBN

978-0-7695-3859-4

Type

conf

DOI

10.1109/IITA.2009.246

Filename

5370191