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Abstract

This chapter presents wavelets and wavelet packets in the spaces of periodic splines of arbitrary order, which, in essence, are the multiple generators for these spaces. The SHA technique provides explicit representation of the wavelets and wavelet packets and fast implementation of the transforms in one and several dimensions.

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References

  1. A. Averbuch, E. Hulata, V. Zheludev, I. Kozlov, A wavelet packet algorithm for classification and detection of moving vehicles. Multidimension. Syst. Signal Process. 12(1), 9–31 (2001)

    Article  MATH  Google Scholar 

  2. G. Battle, A block spin construction of ondelettes. I. lemarié functions. Comm. Math. Phys. 110(4), 601–615 (1987)

    Article  MathSciNet  Google Scholar 

  3. C.K. Chui, J.-Z. Wang, On compactly supported spline wavelets and a duality principle. Trans. Amer. Math. Soc. 330(2), 903–915 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. R.R. Coifman, V.M. Wickerhauser, Entropy-based algorithms for best basis selection. IEEE Trans. Inform. Theory 38(2), 713–718 (1992)

    Article  MATH  Google Scholar 

  5. R.A. Horn, C.R. Johnson, Topics in Matrix Analysis (Cambridge University Press, Cambridge, 1994)

    MATH  Google Scholar 

  6. P.G. Lemarié. Ondelettes à localisation exponentielle. J. Math. Pures Appl. (9), 67(3):227–236 (1988)

    Google Scholar 

  7. P. Neittaanmäki, V. Rivkind, V. Zheludev, in Periodic Spline Wavelets and Representation of Integral Operators, Preprint 177, University of Jyväskylä, Department of Mathematics, 1995

    Google Scholar 

  8. G. Plonka, M. Tasche, On the computation of periodic spline wavelets. Appl. Comput. Harmon. Anal. 2(1), 1–14 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. N. Saito, R.R. Coifman, in Improved Discriminant Bases Using Empirical Probability Density Estimation. Proceedings of the Statistical Computing Section of Amer. Statist. Assoc., (Washington, DC, 1997), pp. 312–321

    Google Scholar 

  10. N. Saito, R.R. Coifman, Local discriminant bases and their applications. J. Math. Imaging Vision 5(4), 337–358 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  11. C.E. Shannon, W. Weaver, The Mathematical Theory of Communication (The University of Illinois Press, Urbana, IL, 1949)

    MATH  Google Scholar 

  12. J.-O. Strömberg, in A Modified Franklin System and Higher-Order Spline Systems of \(R^n\) as Unconditional Bases for Hardy Spaces. Conference on Harmonic Analysis in Honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981), Belmont, 1983, pp. 475–494

    Google Scholar 

  13. M. Unser, A. Aldroubi, M. Eden, A family of polynomial spline wavelet transforms. Signal Process. 30(2), 141–162 (1993)

    Article  MATH  Google Scholar 

  14. M.V. Wickerhauser, Adapted Wavelet Analysis: From Theory to Software (AK Peters, Wellesley, MA, 1994)

    MATH  Google Scholar 

  15. V. Zheludev. Periodic Splines, Harmonic Analysis, and Wavelets, ed. by Y.Y. Zeevi, R. Coifman. Signal and Image Representation in Combined Spaces, volume 7 of Wavelet Anal. Appl. ( Academic Press, San Diego, CA, 1998) pp. 477–509

    Google Scholar 

  16. V. Zheludev, Wavelets based on periodic splines. Russian Acad. Sci. Dokl. Math. 49(2), 216–222 (1994)

    MathSciNet  Google Scholar 

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Correspondence to Amir Z. Averbuch .

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Averbuch, A.Z., Neittaanmaki, P., Zheludev, V.A. (2014). Periodic Spline Wavelets and Wavelet Packets. In: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8926-4_8

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  • DOI: https://doi.org/10.1007/978-94-017-8926-4_8

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-8925-7

  • Online ISBN: 978-94-017-8926-4

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