The Characterization of a class of Multivariate Wavelet Packets with an Integer-valued Dilation Matrix

Author

Wang, Xiping ; Yu, Yumin

Author_Institution

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

fYear

2010

fDate

28-31 March 2010

Firstpage

1

Lastpage

4

Abstract

In this paper, the notion of matrix-valued multire-solution-analysis is introduced. A novel way for designing biorthogonal matrix-valued multivariate wavelet packets is presented and their properties are investigated by means of time-frequency analysis method, matrix theory and operator theory. Three biorthogonality formulas concerning these wavelet packets are obtained. Finally, new Riesz bases of three dimensional matrix-valued function space are constructed by designing a series of subspaces of biorthogonal matrix wavelet packets.

Keywords

mathematical operators; matrix algebra; wavelet transforms; Riesz bases; biorthogonal matrix-valued multivariate wavelet packets; integer-valued dilation matrix; matrix theory; matrix-valued multiresolution analysis; operator theory; three dimensional matrix-valued function space; time-frequency analysis method; Biomedical signal processing; Discrete wavelet transforms; Fractals; Image coding; Mathematics; Signal resolution; Space technology; Time frequency analysis; Wavelet analysis; Wavelet packets;

fLanguage

English

Publisher

ieee

Conference_Titel

Power and Energy Engineering Conference (APPEEC), 2010 Asia-Pacific

Conference_Location

Chengdu

Print_ISBN

978-1-4244-4812-8

Electronic_ISBN

978-1-4244-4813-5

Type

conf

DOI

10.1109/APPEEC.2010.5448538

Filename

5448538