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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
G. Battle, A block spin construction of ondelettes. I. lemarié functions. Comm. Math. Phys. 110(4), 601–615 (1987)
C.K. Chui, J.-Z. Wang, On compactly supported spline wavelets and a duality principle. Trans. Amer. Math. Soc. 330(2), 903–915 (1992)
R.R. Coifman, V.M. Wickerhauser, Entropy-based algorithms for best basis selection. IEEE Trans. Inform. Theory 38(2), 713–718 (1992)
R.A. Horn, C.R. Johnson, Topics in Matrix Analysis (Cambridge University Press, Cambridge, 1994)
P.G. Lemarié. Ondelettes à localisation exponentielle. J. Math. Pures Appl. (9), 67(3):227–236 (1988)
P. Neittaanmäki, V. Rivkind, V. Zheludev, in Periodic Spline Wavelets and Representation of Integral Operators, Preprint 177, University of Jyväskylä, Department of Mathematics, 1995
G. Plonka, M. Tasche, On the computation of periodic spline wavelets. Appl. Comput. Harmon. Anal. 2(1), 1–14 (1995)
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
N. Saito, R.R. Coifman, Local discriminant bases and their applications. J. Math. Imaging Vision 5(4), 337–358 (1995)
C.E. Shannon, W. Weaver, The Mathematical Theory of Communication (The University of Illinois Press, Urbana, IL, 1949)
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
M. Unser, A. Aldroubi, M. Eden, A family of polynomial spline wavelet transforms. Signal Process. 30(2), 141–162 (1993)
M.V. Wickerhauser, Adapted Wavelet Analysis: From Theory to Software (AK Peters, Wellesley, MA, 1994)
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
V. Zheludev, Wavelets based on periodic splines. Russian Acad. Sci. Dokl. Math. 49(2), 216–222 (1994)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-94-017-8926-4_8
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-017-8925-7
Online ISBN: 978-94-017-8926-4
eBook Packages: EngineeringEngineering (R0)