Skip to main content

ECG Segmentation by Adaptive Rational Transform

  • Conference paper
  • First Online:
Computer Aided Systems Theory – EUROCAST 2019 (EUROCAST 2019)

Abstract

We propose a novel method to delineate and segment ECG heartbeats, i.e. to provide model curves for the P, QRS, and T waves, and to extract the fiducial points of them. The main idea of our method is to apply an adaptive transformation by means of rational functions to model the heartbeats and their waveforms. We suggest to represent the heartbeats with a linear combination of rational functions that are selected adaptively to the ECG signals through a non-linear optimization. This leads to a simple, yet morphologically accurate description of the heartbeats, and results a direct segmentation of them. Then, we derived the fiducial points based on the analytical model curves extracted from the rational representation. Multiple geometric concepts and their combination is discussed to this order. The evaluations were performed on the QT Database, and the results are compared to the previous ones, proving the efficiency of our method.

G. Bognár—Supported by the ÚNKP-18-3 New National Excellence Program of the Ministry of Human Capacities of Hungary.

S. Fridli—EFOP-3.6.3-VEKOP-16-2017-00001: Talent Management in Autonomous Vehicle Control Technologies - The Project is supported by the Hungarian Government and co-financed by the European Social Fund.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

References

  1. Bognár, G., Fridli, S.: Heartbeat classification of ECG signals using rational function systems. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2017. LNCS, vol. 10672, pp. 187–195. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-74727-9_22

    Chapter  Google Scholar 

  2. Bognár, G., Fridli, S.: ECG heartbeat classification by means of variable rational projection (to appear)

    Google Scholar 

  3. Bognár, G., Schipp, F.: Geometric interpretation of QRS complexes in ECG signals by rational functions. Ann. Univ. Sci. Bp. Sect. Comput. 47, 155–166 (2018)

    MathSciNet  MATH  Google Scholar 

  4. Fridli, S., Kovács, P., Lócsi, L., Schipp, F.: Rational modeling of multi-lead QRS complexes in ECG signals. Ann. Univ. Sci. Bp. Sect. Comput. 37, 145–155 (2012)

    MathSciNet  MATH  Google Scholar 

  5. Fridli, S., Lócsi, L., Schipp, F.: Rational function systems in ECG processing. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2011. LNCS, vol. 6927, pp. 88–95. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-27549-4_12

    Chapter  Google Scholar 

  6. Fridli, S., Schipp, F.: Biorthogonal systems to rational functions. Ann. Univ. Sci. Bp. Sect. Comput. 35, 95–105 (2011)

    MathSciNet  MATH  Google Scholar 

  7. Goldberger, A.L., et al.: PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals. Circulation 101(23), e215–e220 (2000)

    Article  Google Scholar 

  8. Golub, G.H., Pereyra, V.: The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. SIAM J. Numer. Anal. 10(2), 413–432 (1973)

    Article  MathSciNet  Google Scholar 

  9. Heuberger, P.S.C., van den Hof, P.M.J., Wahlberg, B. (eds.): Modelling and Identification with Rational Orthogonal Basis Functions. Springer, London (2005). https://doi.org/10.1007/1-84628-178-4

    Book  Google Scholar 

  10. Kovács, P.: Transformation methods in signal processing. Ph.D. thesis, ELTE Eötvös Loránd University, Budapest, Hungary, May 2016

    Google Scholar 

  11. Kovács, P.: Rational variable projection methods in ECG signal processing. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2017. LNCS, vol. 10672, pp. 196–203. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-74727-9_23

    Chapter  Google Scholar 

  12. Kovács, P., Böck, C., Meier, J., Huemer, M.: ECG segmentation using adaptive Hermite functions. In: 2017 51st Asilomar Conference on Signals, Systems, and Computers, pp. 1476–1480, October 2017

    Google Scholar 

  13. Kovács, P., Lócsi, L.: RAIT: the rational approximation and interpolation toolbox for Matlab, with experiments on ECG signals. Int. J. Adv. Telecom. Elect. Sign. Syst. 1(2–3), 67–752 (2012)

    Google Scholar 

  14. Laguna, P., Mark, R.G., Goldberg, A., Moody, G.B.: A database for evaluation of algorithms for measurement of QT and other waveform intervals in the ECG. In: IEEE Computers in Cardiology, pp. 673–676, September 1997

    Google Scholar 

  15. Laguna, P., Jané, R., Caminal, P.: Automatic detection of wave boundaries in multilead ECG signals: validation with the CSE database. Comput. Biomed. Res. 27(1), 45–60 (1994)

    Article  Google Scholar 

  16. Lócsi, L.: A hyperbolic variant of the Nelder–Mead simplex method in low dimensions. Acta Univ. Sapientiae Math. 5(2), 169–183 (2013)

    Article  MathSciNet  Google Scholar 

  17. Martinez, J.P., Almeida, R., Olmos, S., Rocha, A.P., Laguna, P.: A wavelet-based ECG delineator: evaluation on standard databases. IEEE Trans. Biomed. Eng. 51(4), 570–581 (2004)

    Article  Google Scholar 

  18. Zhang, D.: Wavelet approach for ECG baseline wander correction and noise reduction. In: Proceedings of International Conference of the IEEE Engineering in Medicine and Biology Society, pp. 1212–1215 (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gergő Bognár .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bognár, G., Fridli, S. (2020). ECG Segmentation by Adaptive Rational Transform. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2019. EUROCAST 2019. Lecture Notes in Computer Science(), vol 12014. Springer, Cham. https://doi.org/10.1007/978-3-030-45096-0_43

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-45096-0_43

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-45095-3

  • Online ISBN: 978-3-030-45096-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics