Researches into the Biorthogonality Property of Vector-Valued Poly-scale Wavelet Packets in Higher Dimensions

Author

Yuan, Deyou ; Liu, Yong

Author_Institution

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

Volume

3

fYear

2009

fDate

4-5 July 2009

Firstpage

489

Lastpage

492

Abstract

We define a class of vector-valued wavelet packets for vector-valued multivariate function space, which are generalizations of univariate wavelet packets. A new approach for constructing a class of biorthogonal vector-valued multivariate wavelet packets is developed and their biorthogonality properties are characterized by means of matrix theory, time-frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are derived. Moreover, it is shown how to gain new Riesz bases of space L²(R^s,C^v) from these wavelet packets.

Keywords

matrix algebra; time-frequency analysis; wavelet transforms; biorthogonal vector-valued multivariate wavelet packet; biorthogonality formula; biorthogonality property; matrix theory; operator theory; time-frequency analysis; univariate wavelet packet; vector-valued multivariate function space; vector-valued poly-scale wavelet packet; Discrete transforms; Fractals; Image processing; Mathematics; Multiresolution analysis; Signal analysis; Space technology; Time frequency analysis; Wavelet analysis; Wavelet packets; Riesz bases; biorthogonality; matrix theory; 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.2009.398

Filename

5199737