Abstract
Wavelet analysis has become a developing branch of mathematics for over twenty years. In this paper, the notion of orthogonal nonseparable bivariate wavelet packs, which is the generalization of orthogonal univariate wavelet packs, is proposed by virtue of analogy method and iteration method. Their biorthogonality traits are researched by using time-frequency analysis approach and variable separation approach. Three orthogonality formulas regarding these wavelet wraps are obtained. Moreover, it is shown how to draw new orthonormal bases of space L 2(R 4) from these wavelet wraps. A procedure for designing a class of orthogonal vector-valued finitely supported wavelet functions is proposed by virtue of filter bank theory and matrix theory.
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References
Telesca, L., et al.: Multiresolution wavelet analysis of earthquakes. Chaos, Solitons & Fractals 22(3), 741–748 (2004)
Iovane, G., Giordano, P.: Wavelet and multiresolution analysis:Nature of ε ∞ Cantorian space-time. Chaos, Solitons & Fractals 32(4), 896–910 (2007)
Zhang, N., Wu, X.: Lossless Compression of Color Mosaic Images. IEEE Trans. Image Processing 15(16), 1379–1388 (2006)
Chen, Q., et al.: A study on compactly supported orthogonal vector-valued wavelets and wavelet packets. Chaos, Solitons & Fractals 31(4), 1024–1034 (2007)
Shen, Z.: Nontensor product wavelet packets in. SIAM Math. Anal. 26(4), 1061–1074 (1995)
Chen, Q., Qu, X.: Characteristics of a class of vector-valued nonseparable higher-dimensional wavelet packet bases. Chaos, Solitons & Fractals 41(4), 1676–1683 (2009)
Chen, Q., Wei, Z.: The characteristics of orthogonal trivariate wavelet packets. Information Technology Journal 8(8), 1275–1280 (2009)
Chen, Q., Huo, A.: The research of a class of biorthogonal compactly supported vector-valued wavelets. Chaos, Solitons & Fractals 41(2), 951–961 (2009)
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© 2011 Springer-Verlag Berlin Heidelberg
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Luo, P., Wang, S. (2011). Generation and Characteristics of Vector-Valued Quarternary Wavelets with Poly-scale Dilation Factor*. In: Lin, S., Huang, X. (eds) Advances in Computer Science, Environment, Ecoinformatics, and Education. CSEE 2011. Communications in Computer and Information Science, vol 214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23321-0_7
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DOI: https://doi.org/10.1007/978-3-642-23321-0_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23320-3
Online ISBN: 978-3-642-23321-0
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