The Characterization of a Kind of Vector-Valued Multivariate Wavelet Packets with Composite Dilation Matrix


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In this article, the notion of a kind of multivariate vector-valued wavelet packets with composite dilation matrix is introduced. A new method for designing a kind of biorthogonal vector- valued wavelet packets in higher dimensions is developed and their biorthogonality property is inv- -estigated by virtue of matrix theory, time-frequency analysis method, and operator theory. Two biorthogonality formulas concerning these wavelet packets are presented. Moreover, it is shown how to gain new Riesz bases of space by constructing a series of subspace of wavelet packets.



Key Engineering Materials (Volumes 439-440)

Edited by:

Yanwen Wu






Y. H. Xia and H. Li, "The Characterization of a Kind of Vector-Valued Multivariate Wavelet Packets with Composite Dilation Matrix", Key Engineering Materials, Vols. 439-440, pp. 932-937, 2010

Online since:

June 2010





[1] 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

[2] 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

[3] 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

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

DOI: 10.1137/s0036141093243642

[5] S. Yang, et al, ``Construction of biorthogonal multiwavelets", Math. Anal. Appl, 2002, 276(1), 1-12.

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

[7] E. Weber, Orthogonal frames of translates,J. Appl. comput. Harmon. Anal., Vol. 17, pp.69-90, (2004).

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