Construction and properties of vector bivariate wavelet packets with respect to a quantity dilation matrix

Author

Wang, Huailing ; Ma, Ge

Author_Institution

Dept. of Math., Pingdingshan Coll. of Educ., Pingdingshan, China

Volume

2

fYear

2010

fDate

26-28 Feb. 2010

Firstpage

701

Lastpage

705

Abstract

In this work, the notion of vector-valued multiresolution analysis of space L²(R², C^r) is introduced. An approach for constructing biorthogonal vector-valued bivariate wavelet packets is presented and their properties are investigated by means of time-frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas regarding the wavelet packets are obtained. Finally, new Riesz bases of space L²(R², C^r) are constructed by designing a series of subspaces composed of these wavelet packets.

Keywords

matrix algebra; time-frequency analysis; wavelet transforms; Riesz bases of space; biorthogonal vector-valued bivariate wavelet packet; biorthogonality formula; matrix theory; operator theory; quantity dilation matrix; time-frequency analysis; vector-valued multiresolution analysis of space; Discrete wavelet transforms; Educational institutions; Educational technology; Functional analysis; Mathematics; Multiresolution analysis; Signal resolution; Space technology; Wavelet analysis; Wavelet packets; Riesz basis; biorthogonal, scaling function; bivariate; wavelet packets;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer and Automation Engineering (ICCAE), 2010 The 2nd International Conference on

Conference_Location

Singapore

Print_ISBN

978-1-4244-5585-0

Electronic_ISBN

978-1-4244-5586-7

Type

conf

DOI

10.1109/ICCAE.2010.5451737

Filename

5451737