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Introduction to Complex Systems Analysis with Wavelets

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Complexity and Nonlinearity in Cardiovascular Signals

Abstract

In this chapter the authors deal with a few methods of nonlinear wavelet analysis for the characterization of nonstationary signals. The methods herein described can be used in a wide variety of biological signals including ECG, HRV, pressure waves and heart sounds. The reader can find both conventional methods of wavelet analysis such as linear and nonlinear denoising, as well as more sophisticated methods based on fractal analysis and entropy. Applications of such algorithms to the analysis of the heartbeat dynamics are also described.

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References

  1. Porta, A., Guzzetti, S., Furlan, R., Gnecchi-Ruscone, T., Montano, N., Malliani, A.: IEEE Trans. Biomed. Eng. 54(1), 94–106 (2007)

    Article  PubMed  Google Scholar 

  2. De Melis, M., Morbiducci, U., Rietzschel, E.R., et al.: Med. Biol. Eng. Comput. 47, 165–173 (2009)

    Article  PubMed  Google Scholar 

  3. Babaei, S., Geranmayeh, A.: Comput. Biol. Med. 39, 8–15 (2009)

    Article  PubMed  Google Scholar 

  4. Işler, Y., Kuntalp, M.: Comput. Biol. Med. 37, 1502–1510 (2007)

    Article  PubMed  Google Scholar 

  5. Makowiec, D., Rynkiewicz, A., Wdowczyk-Szulc, J., et al.: Physiol. Meas. 32, 1681–1699 (2011)

    Article  PubMed  Google Scholar 

  6. Makowieca, D., Dudkowska, A., Galaska, R.: Physica A. 388, 3486–3502 (2009)

    Article  Google Scholar 

  7. Unser, M., Aldroubi, A.: Proc. IEEE. 84, 626–638 (1996)

    Article  Google Scholar 

  8. Daubechies, I.: Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics, Philadelphia (1992)

    Book  Google Scholar 

  9. Mallat, S.: A Wavelet Tour of Signal Processing. Elsevier, Amsterdam (2009)

    Google Scholar 

  10. Beck, A., Teboulle, M.: SIAM J. Imaging Sci. 2, 183–202 (2009)

    Article  Google Scholar 

  11. Donoho, D.L.: IEEE Trans. Inf. Theory. 41, 613–627 (1995)

    Article  Google Scholar 

  12. Wang, Y., Yang, J., Yin, W., Zhang, Y.: SIAM J. Imaging Sci. 1, 248–272 (2008)

    Article  Google Scholar 

  13. Daubechies, I., Defrise, M., De Mol, C.: Commun. Pure Appl. Math. 57, 1413–1541 (2004)

    Article  Google Scholar 

  14. Gamero, L.G., Risk, M., Sobh, J.F., Ramirez, A.J., Saul, J.P.: Comput. Cardiol. 1996, 177–180 (1996)

    Google Scholar 

  15. Gamero, L.G., Vila, J., Palacios, F.: Med. Biol. Eng. Comput. 40, 72–78 (2002)

    Article  CAS  PubMed  Google Scholar 

  16. Addison, P.S.: Physiol. Meas. 26, R155–R199 (2005)

    Article  PubMed  Google Scholar 

  17. Nowak, R.D., Baraniuk, R.G.: IEEE Trans. Signal Process. 47, 1852–1865 (1999)

    Google Scholar 

  18. Meyer, Y., Salinger, D.H.: Wavelets and Operators. Cambridge University Press, Cambridge (1992)

    Google Scholar 

  19. Zhang, X.-S., Zhu, Y.-S., Zhang, X.-J.: Med. Biol. Eng. Comput. 35, 467–473 (1997)

    Article  CAS  PubMed  Google Scholar 

  20. Mallat, S., Hwang, W.L.: IEEE Trans. Inf. Theory. 38, 617–643 (1992)

    Article  Google Scholar 

  21. Yang, H.: IEEE Trans. Biomed. Eng. 58, 339–347 (2011)

    Google Scholar 

  22. Yang, H., Bukkapatnam, S.T., Komanduri, R.: Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 76, 026214 (2007)

    Article  CAS  Google Scholar 

  23. Ivanov, P.C., Rosenblum, M.G., Peng, C.-K., Mietus, J., Havlin, S., Stanley, H.E., Goldberger, A.L.: Nature. 383, 323–327 (1996)

    Article  CAS  PubMed  Google Scholar 

  24. Rosso, O.A., Blanco, S., Yordanova, J., Kolev, V., Figliola, A., Schürmann, M., Baar, E.: J. Neurosci. Methods. 105, 65–75 (2001)

    Article  CAS  PubMed  Google Scholar 

  25. Zunino, L., Pérez, D.G., Garavaglia, M., Rosso, O.A.: Phys. A Stat. Mech. Appl. 379, 503–512 (2007)

    Article  Google Scholar 

  26. Eke, A., Herman, P., Kocsis, L., Kozak, L.R.: Physiol. Meas. 23, R1–R38 (2002)

    Article  CAS  PubMed  Google Scholar 

  27. Pincus, S.M.: Proc. Natl. Acad. Sci. U. S. A. 88, 2297–2301 (1991)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Ocak, H.: Expert Syst. Appl. 36, 2027–2036 (2009)

    Article  Google Scholar 

  29. Wachowiak, M.P., Hay, D.C., Johnson, M.J.: Comput. Biol. Med. 77, 222–230 (2016)

    Article  PubMed  Google Scholar 

  30. Maxim, V., Şendur, L., Fadili, J., Suckling, J., Gould, R., Howard, R., Bullmore, E.: NeuroImage. 25, 141–158 (2005)

    Article  PubMed  Google Scholar 

  31. Mandelbrot, B.B., Van Ness, J.W.: SIAM Rev. 10, 422–437 (1968)

    Article  Google Scholar 

  32. Beran, J.: Biometrika. 81, 755–766 (1994)

    Article  Google Scholar 

  33. Mandelbrot, B.B.: Fractals and Turbulence: Attractors and Dispersion. Springer-Verlag, Berlin (1977)

    Google Scholar 

  34. Wornell, G.: Signal Processing with Fractals: A Wavelet-Based Approach. Prentice Hall PTR, Upper Saddle River, NJ (1996)

    Google Scholar 

  35. Wornell, G.W., Oppenheim, A.V.: IEEE Trans. Signal Process. 40, 611–623 (1992)

    Article  Google Scholar 

  36. Duverney, D., Gaspoz, J.-M., Pichot, V., Roche, F., Brion, R., Antoniadis, A., Barthélémy, J.-C.: Pacing Clin. Electrophysiol. 25, 457–462 (2002)

    Article  PubMed  Google Scholar 

  37. Tikkanen, P.E.: Biol. Cybern. 80, 259–267 (1999)

    Article  CAS  PubMed  Google Scholar 

  38. Kabir, M.A., Shahnaz, C.: Biomed. Signal Process. Control. 7, 481–489 (2012)

    Article  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Ingegneria dell’Informazione, University of Pisa, Pisa, Italy

    Nicola Vanello & Luigi Landini

Authors
  1. Nicola Vanello
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  2. Luigi Landini
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Corresponding author

Correspondence to Nicola Vanello .

Editor information

Editors and Affiliations

  1. Department of Electronics, Informatics and Bioengineering, Politecnico di Milano, Milan, Italy

    Riccardo Barbieri

  2. Department of Information Engineering & Bioengineering and Robotics Research Center “E. Piaggio”, University of Pisa, School of Engineering, Pisa, Italy

    Enzo Pasquale Scilingo

  3. Department of Information Engineering & Bioengineering and Robotics Research Center “E. Piaggio”, University of Pisa, School of Engineering, Pisa, Italy

    Gaetano Valenza

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Vanello, N., Landini, L. (2017). Introduction to Complex Systems Analysis with Wavelets. In: Barbieri, R., Scilingo, E., Valenza, G. (eds) Complexity and Nonlinearity in Cardiovascular Signals. Springer, Cham. https://doi.org/10.1007/978-3-319-58709-7_5

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