On Characteristics of Biorthogonal Vector-Valued Multivariate Wavelet Packets Associated with a Quantity Dilation Matrix

Author

Du, Shude ; Yuan, Deyou

Author_Institution

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

Volume

1

fYear

2009

fDate

4-5 July 2009

Firstpage

611

Lastpage

614

Abstract

Wavelet analysis has been a widely applied one method for analyzing signal. In this work, the notion of vector-valued wavelet packets for space L²(Rⁿ)^s is proposed, which are generalizations of univariate wavelet packets. A constructive method for a class of biorthogonal vector-valued multivariate wavelet packets is formulated and their biorthogonality properties are discussed by virtue of matrix theory, and operator theory. Three biorthogonality formulas concerning these wavelet packets are provided. Furthermore, new Riesz bases of space L²(Rⁿ)^s from these wavelet packets are obtained.

Keywords

computational complexity; matrix algebra; signal processing; time-frequency analysis; wavelet transforms; biorthogonal vector-valued multivariate wavelet packets; operator theory; quantity dilation matrix; signal analysis; signal processing; time-frequency localization property; univariate wavelet packets; Aggregates; Discrete transforms; Information analysis; Mathematics; Pixel; Signal analysis; Space technology; Time frequency analysis; Wavelet analysis; Wavelet packets; biorthogonality formulas; scaling functions; vector-valued; wavelet packets;

fLanguage

English

Publisher

ieee

Conference_Titel

Environmental Science and Information Application Technology, 2009. ESIAT 2009. International Conference on

Conference_Location

Wuhan

Print_ISBN

978-0-7695-3682-8

Type

conf

DOI

10.1109/ESIAT.2009.399

Filename

5200196