Skip to main content

Wavelets Smoothing for Multidimensional Curves

  • Conference paper
  • First Online:
Book cover Recent Advances in Functional Data Analysis and Related Topics

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

  • 3353 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. Donoho, D.L., Johnstone, I.M., Kerkyacharian, G. and Picard, D.: Wavelet Shrinkage: Asymptopia. J. Roy. Stat. Soc. B 57, 301–369 (1995)

    MathSciNet  MATH  Google Scholar 

  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. http://mox.polimi.it/it/progetti/pubblicazioni (2010)

  4. Nason, G.P.: Wavelet Methods in Statistics with R. Springer, New York (2008)

    Book  MATH  Google Scholar 

  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. http://mox.polimi.it/it/progetti/pubblicazioni. Submitted (2010)

  6. Ramsay, J.O., Silverman, B.W.: Functional Data Analysis (Second Edition), Springer, New York (2005)

    Google Scholar 

  7. Strang, G.: Wavelets and dilation equations: a brief introduction. SIAM Review 31, 614–627 (1989)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Davide Pigoli .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pigoli, D., Sangalli, L.M. (2011). Wavelets Smoothing for Multidimensional Curves. In: Ferraty, F. (eds) Recent Advances in Functional Data Analysis and Related Topics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2736-1_40

Download citation

Publish with us

Policies and ethics