Title :
Researches into the Biorthogonality Property of Vector-Valued Poly-scale Wavelet Packets in Higher Dimensions
Author :
Yuan, Deyou ; Liu, Yong
Author_Institution :
Dept. of Appl. Math., Nanyang Inst. of Technol., Nanyang, China
Abstract :
We define a class of vector-valued wavelet packets for vector-valued multivariate function space, which are generalizations of univariate wavelet packets. A new approach for constructing a class of biorthogonal vector-valued multivariate wavelet packets is developed and their biorthogonality properties are characterized by means 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(Rs,Cv) from these wavelet packets.
Keywords :
matrix algebra; time-frequency analysis; wavelet transforms; biorthogonal vector-valued multivariate wavelet packet; biorthogonality formula; biorthogonality property; matrix theory; operator theory; time-frequency analysis; univariate wavelet packet; vector-valued multivariate function space; vector-valued poly-scale wavelet packet; Discrete transforms; Fractals; Image processing; Mathematics; Multiresolution analysis; Signal analysis; Space technology; Time frequency analysis; Wavelet analysis; Wavelet packets; Riesz bases; biorthogonality; matrix theory; vector-valued wavelet packets;
Conference_Titel :
Environmental Science and Information Application Technology, 2009. ESIAT 2009. International Conference on
Conference_Location :
Wuhan
Print_ISBN :
978-0-7695-3682-8
DOI :
10.1109/ESIAT.2009.398
