The Intelligent Algorithm of the Biorthogonal Quarternary Wavelet Packs and Applications in Physics

The rise of wavelet analysis in applied mathematics is due to its applications and the flexibility. In this article, the notion of orthogonal nonseparable four-dimensional wavelet packets, which is the generalization of orthogonal univariate wavelet packets, is introduced. An approach for designing...

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Bibliographic Details
Published inAdvanced Research on Computer Education, Simulation and Modeling pp. 53 - 58
Main Authors Gao, Hailin, Liu, Ruohui
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg
SeriesCommunications in Computer and Information Science
Subjects
B-spline function
iteration method
quarternary
Riesz bases
time-frequency analysis representation
vector-valued wavelet wraps
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Summary:The rise of wavelet analysis in applied mathematics is due to its applications and the flexibility. In this article, the notion of orthogonal nonseparable four-dimensional wavelet packets, which is the generalization of orthogonal univariate wavelet packets, is introduced. An approach for designing a sort of biorthogonal vector-valued wavelet wraps in three-dimensional space is presented and their biorthogonality traits are characterized by virtue of iteration method and time-frequency representation method. The biorthogonality formulas concerning the-se wavelet wraps are established. Moreover, it is shown how to draw new Riesz bases of space L2(R4) from these wavelet wraps. The quarternary dual frames ia also discussed.
ISBN:9783642217821
3642217826
ISSN:1865-0929
1865-0937
DOI:10.1007/978-3-642-21783-8_9