A study of multiple vector-valued wavelet packets associated with a dilation matrix in higher dimensions

Author

Feng, Jin-Shun ; Wang, Hui

Author_Institution

Sch. of Educ., Nanyang Inst. of Technol., Nanyang

Volume

2

fYear

2008

fDate

30-31 Aug. 2008

Firstpage

507

Lastpage

512

Abstract

In this paper, the notion of multiple vector-valued multiresolution analysis of space L²(R^s,C^rtimesr) is introduced. A method for constructing biorthogonal multiple vector-valued wavelet packets in higher dimensions is presented and their properties is investigated by means of time-frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas concerning these wavelet packets are obtained. Finally, new Riesz bases of space L²(R^s,C^rtimesr) is obtained by constructing a series of subspaces of biorthogonal vector-valued wavelet packets.

Keywords

matrix algebra; time-frequency analysis; wavelet transforms; biorthogonal multiple vector-valued wavelet packets; dilation matrix; higher dimensions; matrix theory; operator theory; time-frequency analysis method; Discrete wavelet transforms; Educational technology; Functional analysis; Multiresolution analysis; Pattern analysis; Pattern recognition; Space technology; Time frequency analysis; Wavelet analysis; Wavelet packets; Biorthogonality; Multiresolution Analysis; Riesz Bases; Vector-valued; Wavelet Packets;

fLanguage

English

Publisher

ieee

Conference_Titel

Wavelet Analysis and Pattern Recognition, 2008. ICWAPR '08. International Conference on

Conference_Location

Hong Kong

Print_ISBN

978-1-4244-2238-8

Electronic_ISBN

978-1-4244-2239-5

Type

conf

DOI

10.1109/ICWAPR.2008.4635833

Filename

4635833