Extraction of f Waves

  • Leif Sörnmo
  • Andrius Petrėnas
  • Pablo Laguna
  • Vaidotas Marozas
Part of the Series in BioEngineering book series (SERBIOENG)


This chapter provides a comprehensive overview of methods for f wave extraction, divided into the following categories: average beat subtraction and variants, interpolation, extended Kalman filtering, adaptive filtering, principal component analysis, singular spectral analysis, autoregressive modeling and prediction error analysis, and independent component analysis. Different performance measures are described, used either for real or simulated ECG signals.


  1. 1.
    M. Holm, S. Pehrsson, M. Ingemansson, L. Sörnmo, R. Johansson, L. Sandhall, M. Sunemark, B. Smideberg, C. Olsson, S.B. Olsson, Non-invasive assessment of atrial refractoriness during atrial fibrillation in man–Introducing, validating, and illustrating a new ECG method. Cardiovasc. Res. 38, 69–81 (1998)Google Scholar
  2. 2.
    A. Bollmann, N. Kanuru, K. McTeague, P. Walter, D.B. DeLurgio, J. Langberg, Frequency analysis of human atrial fibrillation using the surface electrocardiogram and its response to ibutilide. Am. J. Cardiol. 81, 1439–1445 (1998)Google Scholar
  3. 3.
    J.L. Salinet Jr., J.P.V. Madeiro, P.C. Cortez, P.J. Stafford, G.A. Ng, F.S. Schlindwein, Analysis of QRS-T subtraction in unipolar atrial fibrillation electrograms. Med. Biol. Eng. Comput. 51, 1381–1391 (2013)Google Scholar
  4. 4.
    L. Sörnmo, P. Laguna, Bioelectrical Signal Processing in Cardiac and Neurological Applications (Elsevier (Academic Press), Amsterdam, 2005)Google Scholar
  5. 5.
    G.D. Clifford, F. Azuaje, P.E. McSharry (eds.), Advanced Methods and Tools for ECG Data Analysis (Artech House, Boston, 2006)Google Scholar
  6. 6.
    D.S. Rosenbaum, R.J. Cohen, Frequency based measures of atrial fibrillation in man, in Proceeding of International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), vol. 12 (1990), pp. 582–583Google Scholar
  7. 7.
    L. Sörnmo, M. Stridh, J.J. Rieta, Atrial activity extraction from the ECG, in Understanding Atrial Fibrillation: The Signal Processing Contribution, ed. by L.T. Mainardi, L. Sörnmo, S. Cerutti, ch. 3 (San Francisco: Morgan & Claypool, 2008), pp. 53–80Google Scholar
  8. 8.
    J.J. Rieta, F. Hornero, Comparative study of methods for ventricular activity cancellation in atrial electrograms of atrial fibrillation. Physiol. Meas. 28, 925–936 (2007)Google Scholar
  9. 9.
    L. Stark, J. Dickson, G. Whipple, H. Horibe, Remote real-time diagnosis of clinical electrograms by a digital computer system. Ann. N.Y. Acad. Sci. 127, 851–872 (1966)Google Scholar
  10. 10.
    S. Blumlein, G. Harvey, V. Murthy, J. Haywood, New technique for detection of changes in QRS morphology of ECG signals. Am. J. Physiol. 244, H560–566 (1983)Google Scholar
  11. 11.
    J. Slocum, E. Byrom, L. McCarthy, A.V. Sahakian, S. Swiryn, Computer detection of atrioventricular dissociation from surface electrocardiograms during wide QRS complex tachycardia. Circulation 72, 1028–1036 (1985)Google Scholar
  12. 12.
    J. Slocum, A.V. Sahakian, S. Swiryn, Diagnosis of atrial fibrillation from surface electrocardiograms based on computer-detected atrial activity. J. Electrocardiol. 25, 1–8 (1992)Google Scholar
  13. 13.
    S. Shkurovich, A.V. Sahakian, S. Swiryn, Detection of atrial activity from high-voltage leads of implantable ventricular defibrillators using a cancellation technique. IEEE Trans. Biomed. Eng. 45, 229–234 (1998)Google Scholar
  14. 14.
    Q. Xi, A.V. Sahakian, S. Swiryn, The effect of QRS cancellation on atrial fibrillatory wave signal characteristics in the surface electrocardiogram. J. Electrocardiol. 36, 243–249 (2003)Google Scholar
  15. 15.
    A. Fujiki, M. Sakabe, K. Nishida, K. Mizumaki, H. Inoue, Role of fibrillation cycle length in spontaneous and drug-indcued termination of human atrial fibrillation–Spectral analysis of fibrillation waves from surface electrocardiogram. Circ. J. 67, 391–395 (2003)Google Scholar
  16. 16.
    D.C. Shah, T. Yamane, K.J. Choi, M. Haïssaguerre, QRS subtraction and the ECG analysis of atrial ectopics. Ann. Noninvasive Electrocardiol. 9, 389–398 (2004)Google Scholar
  17. 17.
    F. Beckers, W. Anne, B. Verheyden, C. van der Dussen de Kestergat, E. van Herk, L. Janssens, R. Willems, H. Heidbuchel, A. E. Aubert, Determination of atrial fibrillation frequency using QRST-cancellation with QRS-scaling in standard electrocardiogram leads, in Proceedings of Computers in Cardiology, vol. 32 (IEEE Press, 2005), pp. 339–342Google Scholar
  18. 18.
    S. Petrutiu, A.V. Sahakian, S. Swiryn, Abrupt changes in fibrillatory wave characteristics at the termination of paroxysmal atrial fibrillation in humans. Europace 9, 466–470 (2007)Google Scholar
  19. 19.
    H. Grubitzsch, D. Modersohn, T. Leuthold, W. Konertz, Analysis of atrial fibrillatory activity from high-resolution surface electrocardiograms: evaluation and application of a new system. Exp. Clin. Cardiol. 13, 29–35 (2008)Google Scholar
  20. 20.
    M. Sterling, D.T. Huang, B. Ghoraani, Developing a new computer-aided clinical decision support system for prediction of successful postcardioversion patients with persistent atrial fibrillation. Comput. Math. Methods Med. (2015)Google Scholar
  21. 21.
    H. Dai, S. Jiang, Y. Li, Atrial activity extraction from single lead ECG recordings: evaluation of two novel methods. Comput. Biol. Med. 43, 176–183 (2013)Google Scholar
  22. 22.
    R. Alcaraz, J.J. Rieta, Adaptive singular value cancelation of ventricular activity in single-lead atrial fibrillation electrocardiograms. Physiol. Meas. 29, 1351–1369 (2008)Google Scholar
  23. 23.
    V.D.A. Corino, M.W. Rivolta, R. Sassi, F. Lombardi, L.T. Mainardi, Ventricular activity cancellation in electrograms during atrial fibrillation with constraints on residuals’ power. Med. Eng. Phys. 35, 1770–1777 (2013)Google Scholar
  24. 24.
    E. Bataillou, E. Thierry, H. Rix, O. Meste, Weighted averaging using adaptive estimation of the weights. Signal Process. 44, 51–66 (1995)MATHGoogle Scholar
  25. 25.
    F. Castells, J.J. Rieta, J. Millet, V. Zarzoso, Spatiotemporal blind source separation approach to atrial activity estimation in atrial tachyarrhythmias. IEEE Trans. Biomed. Eng. 52, 258–267 (2005)Google Scholar
  26. 26.
    A.L. Goldberger, L.A. Amaral, L. Glass, J.M. Hausdorff, P.C. Ivanov, R.G. Mark, J.E. Mietus, G.B. Moody, C.K. Peng, H.E. Stanley, PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals. Circulation 101, E215–220 (2000)Google Scholar
  27. 27.
    P. Laguna, L. Sörnmo, Sampling rate and the estimation of ensemble variability for repetitive signals. Med. Biol. Eng. Comput. 38, 540–546 (2000)Google Scholar
  28. 28.
    J. Malmivuo, R. Plonsey, Bioelectromagnetism (Oxford University Press, Oxford, 1995)Google Scholar
  29. 29.
    G.J.M. Huiskamp, A. van Oosterom, Heart position and orientation in forward and inverse electrocardiography. Med. Biol. Eng. Comput. 30, 613–620 (1992)Google Scholar
  30. 30.
    M. Stridh, L. Sörnmo, Spatiotemporal QRST cancellation techniques for analysis of atrial fibrillation. IEEE Trans. Biomed. Eng. 48, 105–111 (2001)Google Scholar
  31. 31.
    L. Sörnmo, Vectorcardiographic loop alignment and morphologic beat-to-beat variability. IEEE Trans. Biomed. Eng. 45, 1401–1413 (1998)Google Scholar
  32. 32.
    R. Goya-Esteban, F. Sandberg, Ó. Barquero-Pérez, A. García Alberola, L. Sörnmo, J.L. Rojo-Álvarez, Long-term characterization of persistent atrial fibrillation: wave morphology, frequency, and irregularity analysis. Med. Biol. Eng. Comput. 52, 1053–1060 (2014)Google Scholar
  33. 33.
    V.D.A. Corino, F. Sandberg, L.T. Mainardi, P.G. Platonov, L. Sörnmo, Noninvasive assessment of atrioventricular nodal function: effect of rate-control drugs during atrial fibrillation. Ann. Noninvasive Electrocardiol. 20, 534–541 (2015)Google Scholar
  34. 34.
    G.H. Golub, C.F. van Loan, Matrix Computations, 2nd edn. (The Johns Hopkins University Press, Baltimore, 1989)MATHGoogle Scholar
  35. 35.
    J. Waktare, K. Hnatkova, C.J. Meurling, H. Nagayoshi, T. Janota, A.J. Camm, M. Malik, Optimal lead configuration in the detection and subtraction of QRS and T wave templates in atrial fibrillation, in Proceedings of Computers in Cardiology, vol. 25 (IEEE Press, 1998), pp. 629–632Google Scholar
  36. 36.
    L. Mainardi, M. Matteucci, R. Sassi, On predicting the spontaneous termination of atrial fibrillation episodes using linear and nonlinear parameters of ECG signal and RR series, in Proceedings of Computers in Cardiology, vol. 31 (IEEE Press, 2004), pp. 665–668Google Scholar
  37. 37.
    M. Lemay, J.-M. Vesin, A. van Oosterom, V. Jacquemet, L. Kappenberger, Cancellation of ventricular activity in the ECG: evaluation of novel and existing methods. IEEE Trans. Biomed. Eng. 54, 542–546 (2007)Google Scholar
  38. 38.
    M. Åström, E. Carro, L. Sörnmo, P. Laguna, B. Wohlfart, Vectorcardiographic loop alignment and the measurement of morphologic beat-to-beat variability in noisy signals. IEEE Trans. Biomed. Eng. 47, 497–506 (2000)Google Scholar
  39. 39.
    R. Bailón, L. Sörnmo, P. Laguna, A robust method for ECG-based estimation of the respiratory frequency during stress testing. IEEE Trans. Biomed. Eng. 53, 1273–1285 (2006)Google Scholar
  40. 40.
    V. Jacquemet, A. van Oosterom, J.-M. Vesin, L. Kappenberger, Analysis of electrocardiograms during atrial fibrillation. A biophysical approach. IEEE Med. Biol. Eng. Mag. 25, 79–88 (2006)Google Scholar
  41. 41.
    C. Li, C. Zheng, C. Tai, Detection of ECG characteristic points using the wavelet transform. IEEE Trans. Biomed. Eng. 42, 21–28 (1995)Google Scholar
  42. 42.
    J.P. Martínez, R. Almeida, S. Olmos, A.P. Rocha, P. Laguna, A wavelet-based ECG delineator: evaluation on standard databases. IEEE Trans. Biomed. Eng. 51, 570–581 (2004)Google Scholar
  43. 43.
    R. Almeida, J.P. Martínez, A.P. Rocha, P. Laguna, Multilead ECG delineation using spatially projected leads from wavelet transform loops. IEEE Trans. Biomed. Eng. 56, 1996–2005 (2009)Google Scholar
  44. 44.
    H. Dai, L. Yin, Y. Li, QRS residual removal in atrial activity signals extracted from single lead: a new perspective based on signal extrapolation. IET Signal Process. 10, 1169–1175 (2016)Google Scholar
  45. 45.
    X. Du, N. Rao, F. Ou, G. Xu, L. Yin, G. Wang, f-wave suppression method for improvement of locating T-wave ends in electrocardiograms during atrial fibrillation. Ann. Noninvasive Electrocardiol. 18, 262–270 (2013)Google Scholar
  46. 46.
    B. Niu, Y. Zhu, X. He, H. Wu, MCPSO: A multi-swarm cooperative particle swarm optimizer. Appl. Math. Comput. 2, 1050–1062 (2007)MATHGoogle Scholar
  47. 47.
    F. Van den Bergh, A.P. Engelbrecht, A cooperative approach to particle swarm optimization. IEEE Trans. Evol. Comput. 8, 225–239 (2004)Google Scholar
  48. 48.
    P. Bonizzi, M. Stridh, L. Sörnmo, O. Meste, Ventricular activity residual reduction in remainder ECGs based on short-term autoregressive model interpolation, in Proceedings of Computers in Cardiology, vol. 36, pp. 813–816 (2009)Google Scholar
  49. 49.
    A. Ahmad, J.L. Salinet, P.D. Brown Jr., J.H. Tuan, P.J. Stafford, G.A. Ng, F.S. Schlindwein, QRS subtraction for atrial electrograms: flat, linear and spline interpolation. Med. Biol. Eng. Comput. 49, 1321–1328 (2011)Google Scholar
  50. 50.
    M. Stridh, L. Sörnmo, C.J. Meurling, S.B. Olsson, Sequential characterization of atrial tachyarrhythmias based on ECG time-frequency analysis. IEEE Trans. Biomed. Eng. 51, 100–114 (2004)Google Scholar
  51. 51.
    M. Stridh, L. Sörnmo, C. Meurling, S.B. Olsson, Characterization of atrial fibrillation using the surface ECG: time-dependent spectral properties. IEEE Trans. Biomed. Eng. 48, 19–27 (2001)Google Scholar
  52. 52.
    S.V. Vaseghi, Advanced Digital Signal Processing and Noise Reduction, 3rd edn. (Wiley, 2006)Google Scholar
  53. 53.
    S. Haykin, Adaptive Filter Theory, 5th edn. (Pearson, New Jersey, 2014)Google Scholar
  54. 54.
    B.D.O. Anderson, J.B. Moore, Optimal Filtering (Prentice-Hall, Englewood Cliffs, N.J., 1979)MATHGoogle Scholar
  55. 55.
    M. Hayes, Statistical Digital Signal Processing and Modeling (Wiley, New York, 1996)Google Scholar
  56. 56.
    E.K. Roonizi, R. Sassi, An extended Bayesian framework for atrial and ventricular activity separation in atrial fibrillation. IEEE J. Biomed. Health Inform. 21, 1573–1580 (2017)Google Scholar
  57. 57.
    M. Stridh, D. Husser, A. Bollmann, L. Sörnmo, Waveform characterization of atrial fibrillation using phase information. IEEE Trans. Biomed. Eng. 56, 1081–1089 (2009)MATHGoogle Scholar
  58. 58.
    A. Buttu, E. Pruvot, J. Van Zaen, A. Viso, A. Forclaz, P. Pascale, S.M. Narayan, J. Vesin, Adaptive frequency tracking of the baseline ECG identifies the site of atrial fibrillation termination by catheter ablation. Biomed. Signal Process. Control 8, 969–980 (2013)Google Scholar
  59. 59.
    M.E. Nygårds, J. Hulting, An automated system for ECG monitoring. Comput. Biomed. Res. 12, 181–202 (1979)Google Scholar
  60. 60.
    P.E. McSharry, G.D. Clifford, L. Tarassenko, L.A. Smith, A dynamical model for generating synthetic electrocardiogram signals. IEEE Trans. Biomed. Eng. 50, 289–294 (2003)Google Scholar
  61. 61.
    L. Sörnmo, P.O. Börjesson, M.E. Nygårds, O. Pahlm, A method for evaluation of QRS shape features using a mathematical model for the ECG. IEEE Trans. Biomed. Eng. 28, 713–717 (1981)Google Scholar
  62. 62.
    P. Laguna, R. Jané, S. Olmos, N.V. Thakor, H. Rix, P. Caminal, Adaptive estimation of QRS complex by the Hermite model for classification and ectopic beat detection. Med. Biol. Eng. Comput. 34, 58–68 (1996)Google Scholar
  63. 63.
    R. Sameni, M.B. Shamsollahi, C. Jutten, G.D. Clifford, A nonlinear Bayesian filtering framework for ECG denoising. IEEE Trans. Biomed. Eng. 54, 2172–2185 (2007)MATHGoogle Scholar
  64. 64.
    J.V. Candy, Bayesian Signal Processing: Classical, Modern, and Particle Filtering Methods, 2nd edn. (Wiley, 2016)Google Scholar
  65. 65.
    O. Sayadi, M.B. Shamsollahi, ECG denoising and compression using a modified extended Kalman filter structure. IEEE Trans. Biomed. Eng. 55, 2240–2248 (2008)Google Scholar
  66. 66.
    E. Pueyo, M. Malik, P. Laguna, A dynamic model to characterize beat-to-beat adaptation of repolarization to heart rate changes. Biomed. Signal Process. Control 3, 29–43 (2008)Google Scholar
  67. 67.
    J. Oster, J. Behar, O. Sayadi, S. Nemati, A.E.W. Johnson, G.D. Clifford, Semisupervised ECG ventricular beat classification with novelty detection based on switching Kalman filters. IEEE Trans. Biomed. Eng. 62, 2125–2134 (2015)Google Scholar
  68. 68.
    E.K. Roonizi, R. Sassi, A signal decomposition model-based Bayesian framework for ECG components separation. IEEE. Trans. Signal Process. 64, 665–674 (2016)MathSciNetGoogle Scholar
  69. 69.
    M. Rahimpour, B.M. Asl, P wave detection in ECG signals using an extended Kalman filter: an evaluation in different arrhythmia contexts. Physiol. Meas. 37, 1089–1104 (2016)Google Scholar
  70. 70.
    D.E. Gustafson, A.S. Willsky, J.Y. Wang, M.C. Lancaster, J.H. Triebwasser, ECG/VCG rhythm diagnosis using statistical signal analysis–I. Identification of persistent rhythms. IEEE Trans. Biomed. Eng. 25, 344–353 (1978)Google Scholar
  71. 71.
    S. Haykin, Neural Networks: A Comprehensive Foundation, 2nd edn. (Prentice Hall, 1998)Google Scholar
  72. 72.
    A. Petrėnas, V. Marozas, L. Sörnmo, A. Lukoševičius, An echo state neural network for QRST cancellation during atrial fibrillation. IEEE Trans. Biomed. Eng. 59, 2950–2957 (2012)Google Scholar
  73. 73.
    V. Zarzoso, Extraction of ECG characteristics using source separation techniques: Exploiting statistical independence and beyond, in Advanced Biosignal Processing, ed. by A. Naït-Ali (Springer, Berlin Heidelberg, 2013), pp. 15–47Google Scholar
  74. 74.
    N.V. Thakor, Z. Yi-Sheng, Applications of adaptive filtering to ECG analysis: noise cancellation and arrhythmia detection. IEEE Trans. Biomed. Eng. 38, 785–794 (1991)Google Scholar
  75. 75.
    P. Laguna, R. Jané, O. Meste, P.W. Poon, P. Caminal, H. Rix, N.V. Thakor, Adaptive filter for event-related bioelectric signals using an impulse correlated reference input: comparison with signal averaging techniques. IEEE Trans. Biomed. Eng. 39, 1032–1044 (1992)Google Scholar
  76. 76.
    J. Lee, M.H. Song, D.G. Shin, K.J. Lee, Event synchronous adaptive filter based atrial activity estimation in single-lead atrial fibrillation electrocardiograms. Med. Biol. Eng. Comput. 50, 801–811 (2012)Google Scholar
  77. 77.
    P. Laguna, R. Jané, E. Masgrau, P. Caminal, The adaptive linear combiner with a periodic-impulse reference input as a linear comb filter. Signal Process. 48, 193–203 (1996)MATHGoogle Scholar
  78. 78.
    C. Vásquez, A. Hernández, F. Mora, G. Carrault, G. Passariello, Atrial activity enhancement by Wiener filtering using an artificial neural network. IEEE Trans. Biomed. Eng. 48, 940–944 (2001)Google Scholar
  79. 79.
    J.L. Elman, Finding structure in time. Cogn. Sci. 14, 179–211 (1990)Google Scholar
  80. 80.
    J.A. Anderson, An Introduction to Neural Networks (MIT Press, 1995)Google Scholar
  81. 81.
    K. Doya, Bifurcations of recurrent neural networks in gradient descent learning. IEEE Trans. Neural Netw. 1, 75–80 (1993)Google Scholar
  82. 82.
    B.A. Pearlmutter, Gradient calculations for dynamic recurrent neural networks: a survey. IEEE Trans. Neural Netw. 6, 1212–1228 (1995)Google Scholar
  83. 83.
    H. Jaeger, The ‘echo state’ approach to analysing and training recurrent neural networks, GMD Report 148 (German National Research Center for Information Technology, 2001)Google Scholar
  84. 84.
    M.C. Ozturk, D. Xu, J.C. Principe, Analysis and design of echo state networks. Neural Comput. 19, 111–138 (2007)MATHGoogle Scholar
  85. 85.
    A. Petrėnas, L. Sörnmo, A. Lukoševičius, V. Marozas, Detection of occult paroxysmal atrial fibrillation. Med. Biol. Eng. Comput. 53, 287–297 (2015)Google Scholar
  86. 86.
    M. Lukoševičius, H. Jaeger, Reservoir computing approaches to recurrent neural network training. Comput. Sci. Rev. 3, 127–149 (2009)MATHGoogle Scholar
  87. 87.
    H. Jaeger, M. Lukoševičius, D. Popovici, U. Siewert, Optimization and applications of echo state networks with leaky integrator neurons. Neural Netw. 20, 335–352 (2007)MATHGoogle Scholar
  88. 88.
    M. Lukoševičius, A practical guide to applying echo state networks, in Neural Networks: Tricks of the Trade, ed. by G. Montavon, G.B. Orr, K.-R. Müller, 2nd edn. (Springer, 2012)Google Scholar
  89. 89.
    S.C. Douglas, Numerically-robust \(\cal{O}(N^2)\) RLS algorithms using least-squares prewhitening, in IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), vol. 25 (2000), pp. 412–415Google Scholar
  90. 90.
    A. Rodan, P. Tiňo, Minimum complexity echo state network. IEEE Trans. Neural Netw. 22, 131–144 (2011)Google Scholar
  91. 91.
    I.T. Joliffe, Principal Component Analysis (Springer, Berlin, 2002)Google Scholar
  92. 92.
    L.G. Horan, N.C. Flowers, D.A. Brody, Principal factor waveforms of the thoracic QRS-complex. Circ. Res. 14, 131–145 (1964)Google Scholar
  93. 93.
    F. Castells, P. Laguna, L. Sörnmo, A. Bollmann, J. Millet Roig, Principal component analysis in ECG signal processing. J. Adv. Signal Process. 2007, ID 74580 (2007)Google Scholar
  94. 94.
    F. Castells, C. Mora, J.J. Rieta, D. Moratal-Pérez, J. Millet, Estimation of atrial fibrillatory wave from single-lead atrial fibrillation electrocardiograms using principal component analysis concepts. Med. Biol. Eng. Comput. 43, 557–560 (2005)Google Scholar
  95. 95.
    A. Hyvärinen, J. Karhunen, E. Oja, Independent Component Analysis (Wiley Interscience, 2001)Google Scholar
  96. 96.
    A. Martínez, R. Alcaraz, J.J. Rieta, Ventricular activity morphological characterization: Ectopic beats removal in long term atrial fibrillation recordings. Comput. Methods Programs Biomed. 109, 283–292 (2013)Google Scholar
  97. 97.
    P. Langley, J.P. Bourke, A. Murray, Frequency analysis of atrial fibrillation, in Proceedings of Computers in Cardiology, vol. 27 (IEEE Press, 2000), pp. 65–68Google Scholar
  98. 98.
    D. Raine, P. Langley, A. Murray, A. Dunuwille, J.P. Bourke, Surface atrial frequency analysis in patients with atrial fibrillation: a tool for evaluating the effects of intervention. J. Cardiovasc. Electrophysiol. 15, 1021–1026 (2004)Google Scholar
  99. 99.
    P. Langley, M. Stridh, J.J. Rieta, J. Millet, L. Sörnmo, A. Murray, Comparison of atrial signal extraction algorithms in 12-lead ECGs with atrial fibrillation. IEEE Trans. Biomed. Eng. 53, 343–346 (2006)Google Scholar
  100. 100.
    A. van Oosterom, The dominant T wave and its significance. J. Cardiovasc. Electrophysiol. 14, S180–S187 (2003)Google Scholar
  101. 101.
    A. van Oosterom, The dominant T wave. J. Electrocardiol. 37, 193–197 (2004)Google Scholar
  102. 102.
    R. Sassi, L.T. Mainardi, An estimate of the dispersion of repolarization times based on a biophysical model of the ECG. IEEE Trans. Biomed. Eng. 58, 3396–3405 (2011)Google Scholar
  103. 103.
    P. Laguna, J.P. Martínez, E. Pueyo, Techniques for ventricular repolarization instability assessment from the ECG. Proc. IEEE 104, 392–415 (2016)Google Scholar
  104. 104.
    G.S. Wagner, Marriott’s Practical Electrocardiography, 10th edn. (Lippincott Williams & Wilkins, Baltimore, 2001)Google Scholar
  105. 105.
    P. Langley, J.P. Bourke, A. Murray, The U wave in atrial fibrillation, in Proceedings of Computing in Cardiology, vol. 42, pp. 833–836 (2015)Google Scholar
  106. 106.
    R. Sassi, V.D.A. Corino, L.T. Mainardi, Analysis of surface atrial signals: time series with missing data? Ann. Biomed. Eng. 37, 2082–2092 (2009)Google Scholar
  107. 107.
    R. Vautard, P. Yiou, M. Ghil, Singular-spectrum analysis: a toolkit for short, noisy chaotic signals. Phys. D 58, 95–126 (1992)Google Scholar
  108. 108.
    N. Golyandina, A. Zhigljavsky, Singular Spectrum Analysis for Time Series (Springer, 2013)MATHGoogle Scholar
  109. 109.
    E. Parzen, On spectral analysis with missing observations and amplitude modulation. Sankya A. 25, 383–392 (1963)MathSciNetMATHGoogle Scholar
  110. 110.
    D.H. Schoellhamer, Singular spectrum analysis for time series with missing data. Geophys. Res. Lett. 28, 3187–3190 (2001)Google Scholar
  111. 111.
    M. Stridh, L. Sörnmo, C.J. Meurling, S.B. Olsson, Detection of autonomic modulation in permanent atrial fibrillation. Med. Biol. Eng. Comput. 41, 625–629 (2003)Google Scholar
  112. 112.
    D. Kondrashov, M. Ghil, Spatio-temporal filling of missing points in geophysical data sets. Nonlinear Process. Geophys. 13, 151–159 (2006)Google Scholar
  113. 113.
    G. Wang, N. Rao, S.J. Shepherd, C.B. Beggs, Extraction of desired signal based on AR model with its application to atrial activity estimation in atrial fibrillation. J. Adv. Signal Process. 8, 1–9 (2008)MATHGoogle Scholar
  114. 114.
    W. Liu, D.P. Mandic, A. Cichocki, Blind source extraction based on a linear predictor. IET Signal Process. 1, 29–34 (2007)Google Scholar
  115. 115.
    T.K. Moon, W.C. Sterling, Mathematical Methods and Algorithms for Signal Processing (Prentice Hall, New Jersey, USA, 2000)Google Scholar
  116. 116.
    J.F. Cardoso, Blind signal separation: statistical principles. Proc. IEEE 86, 2009–2025 (1998)Google Scholar
  117. 117.
    P. Bonizzi, M. de la Salud Guillem, A.M. Climent, J. Millet, V. Zarzoso, F. Castells, O. Meste, Noninvasive assessment of the complexity and stationarity of the atrial wavefront patterns during atrial fibrillation. IEEE Trans. Biomed. Eng. 57, 2147–2157 (2010)Google Scholar
  118. 118.
    S.M. Kay, Modern Spectral Estimation, Theory and Application (Prentice-Hall, New Jersey, 1999)Google Scholar
  119. 119.
    L. Tong, R.-W. Liu, V.C. Soon, Y.-F. Huang, Indeterminacy and identifiability of blind identification. IEEE Trans. Circ. Syst. 38, 499–509 (1991)MATHGoogle Scholar
  120. 120.
    A. Hyvärinen, E. Oja, Independent component analysis: algorithms and applications. Neural Netw. 13, 411–430 (2000)Google Scholar
  121. 121.
    P. Comon, Independent component analysis–a new concept? Signal Process. 36, 287–314 (1994)MATHGoogle Scholar
  122. 122.
    A. Hyvärinen, E. Oja, A fast fixed-point algorithm for independent component analysis. Neural Comput. 9, 1483–1492 (1997)Google Scholar
  123. 123.
    J.J. Rieta, F. Castells, C. Sánchez, V. Zarzoso, J. Millet, Atrial activity extraction for atrial fibrillation analysis using blind source separation. IEEE Trans. Biomed. Eng. 51, 1176–1186 (2004)Google Scholar
  124. 124.
    M. Lemay, J.-M. Vesin, Z. Ihara, L. Kappenberger, Suppression of ventricular activity in the surface electrocardiogram of atrial fibrillation, in Proceedings of the International Conference Independent Component Analysis and Blind Signal Separation (Springer, 2004), pp. 1095–1102Google Scholar
  125. 125.
    F. Castells, J. Igual, J. Millet, J.J. Rieta, Atrial activity extraction from atrial fibrillation episodes based on maximum likelihood source separation. Signal Process. 85, 523–535 (2005)MATHGoogle Scholar
  126. 126.
    R. Phlypo, Y. D’Asseler, I. Lemahieu, V. Zarzoso, Extraction of the atrial activity from the ECG based on independent component analysis with prior knowledge of the source kurtosis signs, in Proceeding of International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), vol. 29 (2007), pp. 6499–6502Google Scholar
  127. 127.
    V. Zarzoso, O. Meste, P. Comon, D.G. Latcu, N. Saoudi, Noninvasive cardiac signal analysis using data decomposition techniques, in Modeling in Computational Biology and Biomedicine: A Multidisciplinary Endeavor ed. by F. Cazals, P. Kornprobst (Springer, Berlin Heidelberg, 2013), pp. 83–116Google Scholar
  128. 128.
    V. Zarzoso, R. Phlypo, P. Comon, A contrast for independent component analysis with priors on the source kurtosis signs. IEEE Signal Process. Lett. 15, 501–504 (2008)Google Scholar
  129. 129.
    A. Mincholé, L. Sörnmo, P. Laguna, Detection of body position changes from the ECG using a Laplacian noise model. Biomed. Signal Process. Control 14, 189–196 (2014)Google Scholar
  130. 130.
    A.J. Pullan, M.L. Buist, L.K. Cheng, Mathematically Modelling the Electrical Activity of the Heart (World Scientific, New Jersey, USA, 2005)MATHGoogle Scholar
  131. 131.
    C. Vayá, J.J. Rieta, C. Sanchez, D. Moratal, Convolutive blind source separation algorithms applied to the electrocardiogram of atrial fibrillation: study of performance. IEEE Trans. Biomed. Eng. 54, 1530–1533 (2007)Google Scholar
  132. 132.
    F.I. Donoso, R.L. Figueroa, E.A. Lecannelier, E.J. Pinoa, A.J. Rojas, Atrial activity selection for atrial fibrillation ECG recordings. Comput. Biol. Med. 43, 1628–1636 (2013)Google Scholar
  133. 133.
    A. Belouchrani, K. Abed-Meraim, J.F. Cardoso, E. Moulines, A blind source separation technique using second-order statistics. IEEE Trans. Signal Process. 45, 434–444 (1997)Google Scholar
  134. 134.
    J. Malik, N. Reed, C.-L. Wang, H.-T. Wu, Single-lead f-wave extraction using diffusion geometry. Physiol. Meas. 38, 1310–1334 (2017)Google Scholar
  135. 135.
    R. Phlypo, V. Zarzoso, I. Lemahieu, Atrial activity estimation from atrial fibrillation ECGs by blind source extraction based on a conditional maximum likelihood approach. Med. Biol. Eng. Comput. 48, 483–488 (2010)Google Scholar
  136. 136.
    R. Llinares, J. Igual, J. Miró-Borrás, A fixed point algorithm for extracting the atrial activity in the frequency domain. Comput. Biol. Med. 40, 943–949 (2010)Google Scholar
  137. 137.
    R. Llinares, J. Igual, Exploiting periodicity to extract the atrial activity in atrial arrhythmias. J. Adv. Signal Process. 134–140 (2011)Google Scholar
  138. 138.
    O.A. Rosso, S. Blanco, J. Yordanova, V. Kolev, A. Figliola, M. Schürmann, E. Başar, Wavelet entropy: a new tool for analysis of short duration brain electrical signals. J. Neurosci. Meth. 105, 65–75 (2001)Google Scholar
  139. 139.
    P. Langley, Wavelet entropy as a measure of ventricular beat suppression from the electrocardiogram in atrial fibrillation. Entropy 17, 6397–6411 (2015)Google Scholar
  140. 140.
    J. Ródenas, M. García, R. Alcaraz, J.J. Rieta, Wavelet entropy automatically detects episodes of atrial fibrillation from single-lead electrocardiograms. Entropy 17, 6179–6199 (2015)Google Scholar
  141. 141.
    J. Mateo, J.J. Rieta, Radial basis function neural networks applied to efficient QRST cancellation in atrial fibrillation. Comput. Biol. Med. 43, 154–163 (2013)Google Scholar
  142. 142.
    I. Nault, N. Lellouche, S. Matsuo, S. Knecht, M. Wright, K.T. Lim, F. Sacher, P. Platonov, A. Deplagne, P. Bordachar, N. Derval, M.D. O’Neill, G.J. Klein, M. Hocini, P. Jaïs, J. Clémenty, M. Haïssaguerre, Clinical value of fibrillatory wave amplitude on surface ECG in patients with persistent atrial fibrillation. J. Interv. Card. Electrophysiol. 26, 11–19 (2009)Google Scholar
  143. 143.
    J. Lian, G. Garner, D. Muessig, V. Lang, A simple method to quantify the morphological similarity between signals. Signal Process. 90, 684–688 (2010)MATHGoogle Scholar
  144. 144.
    J. Igual, R. Llinares, M.S. Guillem, J. Millet, Optimal localization of leads in atrial fibrillation episodes, in International Conference on Acoustics, Speech and Signal Processing (ICASSP), vol. 31 (2006), pp. II:1192–II:1195Google Scholar
  145. 145.
    D. Husser, M. Stridh, L. Sörnmo, C. Geller, H.U. Klein, S.B. Olsson, A. Bollmann, Time-frequency analysis of the surface electrocardiogram for monitoring antiarrhythmic drug effects in atrial fibrillation. Am. J. Cardiol. 95, 526–528 (2005)Google Scholar
  146. 146.
    A. Bollmann, A. Tveit, D. Husser, M. Stridh, L. Sörnmo, P. Smith, S.B. Olsson, Fibrillatory rate response to candesartan in persistent atrial fibrillation. Europace 10, 1138–1144 (2008)Google Scholar
  147. 147.
    M. Aunes-Jansson, N. Edvardsson, M. Stridh, L. Sörnmo, L. Frison, A. Berggren, Decrease of the atrial fibrillatory rate, increased organization of the atrial rhythm and termination of atrial fibrillation by AZD7009. J. Electrocardiol. 46, 29–35 (2013)Google Scholar
  148. 148.
    M. Aunes, K. Egstrup, L. Frison, A. Berggren, M. Stridh, L. Sörnmo, N. Edvardsson, Rapid slowing of the atrial fibrillatory rate after administration of AZD7009 predicts conversion of atrial fibrillation. J. Electrocardiol. 47, 316–323 (2014)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Leif Sörnmo
    • 1
  • Andrius Petrėnas
    • 2
  • Pablo Laguna
    • 3
  • Vaidotas Marozas
    • 2
  1. 1.Department of Biomedical Engineering and Center for Integrative ElectrocardiologyLund UniversityLundSweden
  2. 2.Biomedical Engineering Institute, Kaunas University of TechnologyKaunasLithuania
  3. 3.Biomedical Signal Interpretation and Computational Simulation (BSICoS), Aragón Institute of Engineering Research (I3A), Centro de Investigacíon Biomédica en Red de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN)Zaragoza UniversityZaragozaSpain

Personalised recommendations