The Biorthogonality Property of Vector-Valued Multivariate Wavelet Packets with M-scale

Author

Gao, Hongwei ; Ding, Liping

Author_Institution

Dept. of Math., Yulin Univ., Yulin, China

Volume

2

fYear

2009

fDate

19-21 May 2009

Firstpage

509

Lastpage

513

Abstract

In this paper, we introduce a class of vector-valued wavelet packets for vector-valued multivariate function space, which are generalizations of univariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue 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

computational complexity; matrix algebra; wavelet transforms; biorthogonality property; m-scale; matrix theory; operator theory; time-frequency analysis method; vector-valued multivariate wavelet packets; Discrete wavelet transforms; Fractals; Image processing; Mathematics; Multiple signal classification; Signal analysis; Software engineering; Time frequency analysis; Wavelet analysis; Wavelet packets; Riesz bases; biorthogonal; multivariate; scaling function; vector-valued; wavelet packets;

fLanguage

English

Publisher

ieee

Conference_Titel

Software Engineering, 2009. WCSE '09. WRI World Congress on

Conference_Location

Xiamen

Print_ISBN

978-0-7695-3570-8

Type

conf

DOI

10.1109/WCSE.2009.364

Filename

5319533