A Study of Matrix-Valued Trivariate Wavelet Packets Associated with an Orthogonal Matrix-Valued Trivariate Scaling Function

Jian Zhang; Shui Wang Guo

doi:10.4028/www.scientific.net/KEM.439-440.1165

Paper Titles

Specific Properties of a King of Trivariable Wavelet Packets with Respect to an Integer-Valued Dilation Matrix
p.1141

The Orthogonality Character of Matrix Univariate Wavelet Packets Concerning an Integer Factor
p.1147

Statistical Properties of the Unsymmetrical P-Norm Distribution
p.1153

A Study on Characteristics of Biorthogonal Two-Dimensional Wavelet Packets
p.1159

A Study of Matrix-Valued Trivariate Wavelet Packets Associated with an Orthogonal Matrix-Valued Trivariate Scaling Function
p.1165

The Description of Two-Direction Biorthogonal Finitely Supported Wavelet Packets with Poly-Scale Dilation
p.1171

The Scheduling Algorithm of Grid Task Based on Cloud Model
p.1177

The Nice Feature of Orthogonal Vector-Valued Bivariate Wavelet Packets with Arbitrary Integer Dilation Factor
p.1184

Optimal Design for Fuzzy Controller by Ant Colony Algorithm
p.1190

HomeKey Engineering MaterialsKey Engineering Materials Vols. 439-440A Study of Matrix-Valued Trivariate Wavelet...

A Study of Matrix-Valued Trivariate Wavelet Packets Associated with an Orthogonal Matrix-Valued Trivariate Scaling Function

Abstract:

Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of matrix-valued multiresolution analysis of space is introduced. A method for constructing biorthogonal matrix–valued trivariate wavelet packets is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three biorthogonality formulas concerning these wavelet packets are provided. Finally, new Riesz bases of space is obtained by constructing a series of subspaces of biorthogonal matrix-valued wavelet packets.

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Periodical:

Key Engineering Materials (Volumes 439-440)

Pages:

1165-1170

DOI:

https://doi.org/10.4028/www.scientific.net/KEM.439-440.1165

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Online since:

June 2010

Authors:

Jian Zhang, Shui Wang Guo

Keywords:

Filter Bank, Frame Wavelet Packet, Matrix Theory, Matrix Valued Scaling Function, Matrix Valued Wavelet Packet, Refinement Equation, Riesz Base, Trivariate

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References

[1] L. Telesca, et al., Multiresolution wavelet analysis of earthquakes,. Chaos, Solitons & Fractals, Vol. 22, No. 3, PP. 741-748, (2004).

DOI: 10.1016/j.chaos.2004.02.021

Google Scholar

[2] G. Iovane, P. Giordano. Wavelet and multiresolution analysis: Nature of ε ∞ Cantorian space-time. Chaos, Solitons & Frac-tals, Vol. 32, No. 4, PP. 896-910, (2007).

DOI: 10.1016/j.chaos.2005.11.097

Google Scholar

[3] N. Zhang, X. Wu X. Lossless Compression of Color Mosaic Images,. IEEE Trans Image processing Vol. 15, No. 16, PP. 1379-1388, (2006).

DOI: 10.1109/tip.2005.871116

Google Scholar

[4] Q. Chen, etal, A study on compactly supported orthogo-nal vector-valued wavelets and wavelet packets,. Chaos, Soli-tons & Fractals. Vol. 31, No. 4, PP. 1024-1034, (2007).

DOI: 10.1016/j.chaos.2006.03.097

Google Scholar

[5] Z. Shen, Nontensor product wavelet packets in 2() s LR , , SIAM Math. Anal., Vol. 26, No. 4, PP. 1061-1074, (1995).

DOI: 10.1137/s0036141093243642

Google Scholar

[6] Q. Chen, Z. Cheng, X. Feng, ``Multivariate Biorthogonal Multiwavelet packets, MATHEMATICA APPLICATA, in Chinese, 2005, 18(3), pp.358-364.

Google Scholar