Title :
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
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;
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
DOI :
10.1109/APPEEC.2010.5448538
