Wavelets Smoothing for Multidimensional Curves

Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


We describe a wavelet-based method that provides accurate estimates of curves in more than one dimension and of their derivatives. The method is particularly attractive when the curves to be estimated have a varying smoothness and present strongly localized features. The proposed multidimensional wavelet estimation technique is thus applied to multi-lead electrocardiogram records, where strongly localized features are indeed expected.


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  1. 1.
    Boudaoud, S., Rix, H., Meste, O., Heneghan, C., ÓBrien, C.: Corrected Integral Shape Averaging Applied to Obstructive Sleep Apnea Detection from the Electrocardiogram. EURASIP Journal on Advances in Signal Processing 41, 909–996 (2007)Google Scholar
  2. 2.
    Donoho, D.L., Johnstone, I.M., Kerkyacharian, G. and Picard, D.: Wavelet Shrinkage: Asymptopia. J. Roy. Stat. Soc. B 57, 301–369 (1995)MathSciNetMATHGoogle Scholar
  3. 3.
    Ieva, F., Paganoni, A.M., Pigoli, D., Vitelli, V.: Statistics on ECGs: wavelet smoothing, registration and classification. Tech. Rep. No. 04/2011 MOX, Dipartimento di Matematica, Politecnico di Milano. (2010)
  4. 4.
    Nason, G.P.: Wavelet Methods in Statistics with R. Springer, New York (2008)MATHCrossRefGoogle Scholar
  5. 5.
    Pigoli, D., Sangalli, L.M.: Wavelets in Functional Data Analysis: estimation of multidimensional curves and their derivatives. Tech. Rep. No. 09/2011 MOX, Dipartimento di Matematica, Politecnico di Milano. Submitted (2010)
  6. 6.
    Ramsay, J.O., Silverman, B.W.: Functional Data Analysis (Second Edition), Springer, New York (2005)Google Scholar
  7. 7.
    Strang, G.: Wavelets and dilation equations: a brief introduction. SIAM Review 31, 614–627 (1989)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Politecnico di MilanoMilanItaly

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