Title :
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
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;
Conference_Titel :
Intelligent Systems, 2009. GCIS '09. WRI Global Congress on
Conference_Location :
Xiamen
Print_ISBN :
978-0-7695-3571-5
DOI :
10.1109/GCIS.2009.408