The Properties of Biorthogonal Vector-valued Bivariate Wavelet Packets

Author

Wang, Junqiu ; Wang, Jian-Guo

Author_Institution

Sch. of Sci., Xi´´an Univ. of Arch, & Tech., Xi´´an, China

Volume

4

fYear

2009

fDate

19-21 May 2009

Firstpage

547

Lastpage

551

Abstract

In this paper, we introduce a class of vector-valued wavelet packets of space L²(R²)^u, which are generalizations of bivariable 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. Furthermore, it is shown how to obtain new Riesz bases of space L²(R²)^u from these wavelet packets.

Keywords

matrix algebra; signal processing; time-frequency analysis; wavelet transforms; biorthogonal vector-valued bivariate wavelet packet; matrix theory; operator theory; signal processing; time-frequency analysis method; Aggregates; Discrete wavelet transforms; Fourier transforms; Hydrogen; Intelligent systems; Mathematics; Pixel; Time frequency analysis; Wavelet analysis; Wavelet packets; biorthogonal; bivariate; refinable equation; scaling function; vector-valued; 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.2009.408

Filename

5209223