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

Author

Yuan, Deyou

Author_Institution

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

Volume

2

fYear

2009

fDate

19-21 May 2009

Firstpage

577

Lastpage

580

Abstract

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 L²(R^d,C^rtimesr) are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

Keywords

matrix algebra; time-frequency analysis; wavelet transforms; functional analysis; integer-valued dilation matrix; matrix theory; matrix-valued higher-dimensional function; matrix-valued multiresolution analysis; orthogonal matrix-valued higher-dimensional wavelet packet; orthogonal matrix-valued multivariable wavelet packet; orthogonality formula; orthonormal bases; time-frequency analysis; Discrete wavelet transforms; Functional analysis; Intelligent systems; Mathematics; Multidimensional systems; Multiresolution analysis; Space technology; Time frequency analysis; Wavelet analysis; Wavelet packets; higher-dimensional; matrix-valued; multiresolution analysis; orthogonal; wavelet packets;

fLanguage

English

Publisher

ieee

Conference_Titel

Intelligent Systems, 2009. GCIS '09. WRI Global Congress on

Conference_Location

Xiamen

Print_ISBN

978-0-7695-3571-5

Type

conf

DOI

10.1109/GCIS.2009.403

Filename

5209358