Kalman Filter with Augmented Measurement Model: An ECG Imaging Simulation Study

  • Walther H. W. Schulze
  • Francesc Elies Henar
  • Danila Potyagaylo
  • Axel Loewe
  • Matti Stenroos
  • Olaf Dössel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7945)


ECG imaging is a non-invasive technique of characterizing the electrical activity and the corresponding excitation conduction of the heart using body surface ECG. The method may provide great opportunities in the planning of cardiac interventions and in the diagnosis of cardiac diseases. This work introduces an algorithm for the imaging of transmembrane voltages that is based on a Kalman filter with an augmented measurement model. In the latter, a regularization term is integrated as additional ”measurement”. The filter is trained using a-priori-knowledge from a simulation model. Two effects are investigated: the influence of the training data on the reconstruction quality and the representation of a-priori knowledge in the trained covariance matrices. The proposed algorithm shows a promising quality of reconstruction and may be used in the future to introduce generic physiological knowledge in solutions of cardiac source imaging.


Ground Truth Kalman Filter Covariance Matrice Reconstruction Quality Transmembrane Voltage 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Cuculich, P.S., Wang, Y., Lindsay, B.D., Faddis, M.N., Schuessler, R.B., Damiano, R.J., Li, L., Rudy, Y.: Noninvasive characterization of epicardial activation in humans with diverse atrial fibrillation patterns. Circulation 122, 1364–1372 (2010)CrossRefGoogle Scholar
  2. 2.
    Ramanathan, C., Jia, P., Ghanem, R., Calvetti, D., Rudy, Y.: Noninvasive electrocardiographic imaging (ecgi): Application of the generalized minimal residual (gmres) method. Ann. Biomed. Eng. 31, 981–994 (2003)CrossRefGoogle Scholar
  3. 3.
    Brooks, D.H., Ahmad, G.F., MacLeod, R.S., Maratos, G.M.: Inverse electrocardiography by simultaneous imposition of multiple constraints. IEEE Trans. Biomed. Eng. 46, 3–18 (1999)CrossRefGoogle Scholar
  4. 4.
    Zhang, Y., Ghodrati, A., Brooks, D.H.: An analytical comparison of three spatio-temporal regularization methods for dynamic linear inverse problems in a common statistical framework. Inverse Probl. 21, 357 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Joly, D., Goussard, Y., Savard, P.: Time-recursive solution to the inverse problem of electrocardiography: A model-based approach. In: Proc. IEEE/EMBS Conf., vol. 15, pp. 767–768 (1993)Google Scholar
  6. 6.
    El-Jakl, J., Champagnat, F., Goussard, Y.: Time-space regularization of the inverse problem of electrocardiography. In: Proc. IEEE/EMBS Conf., vol. 17, pp. 213–214 (1995)Google Scholar
  7. 7.
    Aydin, U., Dogrusoz, Y.S.: A kalman filter-based approach to reduce the effects of geometric errors and the measurement noise in the inverse ecg problem. Med. Biol. Eng. Comput. 49, 1003–1013 (2011)CrossRefGoogle Scholar
  8. 8.
    Berrier, K.L., Sorensen, D.C., Khoury, D.S.: Solving the inverse problem of electrocardiography using a duncan and horn formulation of the kalman filter. IEEE Trans. Biomed. Eng. 51, 507–515 (2004)CrossRefGoogle Scholar
  9. 9.
    Ghodrati, A., Brooks, D.H., Tadmor, G., MacLeod, R.S.: Wavefront-based models for inverse electrocardiography. IEEE Trans. Biomed. Eng. 53, 1821–1831 (2006)CrossRefGoogle Scholar
  10. 10.
    Liu, C., He, B.: Noninvasive estimation of global activation sequence using the extended kalman filter. IEEE Trans. Biomed. Eng. 58, 541–549 (2011)CrossRefGoogle Scholar
  11. 11.
    Wang, L., Zhang, H., Wong, K., Liu, H., Shi, P.: Physiological-model-constrained noninvasive reconstruction of volumetric myocardial transmembrane potentials. IEEE Trans. Biomed. Eng. 57, 296–315 (2010)CrossRefGoogle Scholar
  12. 12.
    Wang, L.: Computational reduction for noninvasive transmural electrophysiological imaging. Comput. Biol. Med. 43, 184–199 (2013)CrossRefGoogle Scholar
  13. 13.
    Schulze, W., Farina, D., Jiang, Y., Dössel, O.: A kalman filter with integrated tikhonov-regularization to solve the inverse problem of electrocardiography. In: IFMBE Proc., vol. 25, pp. 821–824 (2009)Google Scholar
  14. 14.
    Kaipio, J., Somersalo, E.: Nonstationary inverse problems and state estimation. J. Inverse Ill-Posed Probl. 7, 273–282 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Hiltunen, P., Särkkä, S., Nissilä, I., Lajunen, A., Lampinen, J.: State space regularization in the nonstationary inverse problem for diffuse optical tomography. Inverse Probl. 27, 025009 (2011)Google Scholar
  16. 16.
    Loewe, A., Schulze, W.H.W., Jiang, Y., Wilhelms, M., Dössel, O.: Determination of optimal electrode positions of a wearable ecg monitoring system for detection of myocardial ischemia: a simulation study. Proc. Comp. in Card. 38, 741–744 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Walther H. W. Schulze
    • 1
  • Francesc Elies Henar
    • 1
  • Danila Potyagaylo
    • 1
  • Axel Loewe
    • 1
  • Matti Stenroos
    • 2
  • Olaf Dössel
    • 1
  1. 1.Institute of Biomedical EngineeringKarlsruhe Institute of Technology (KIT)Germany
  2. 2.Dept. of Biomedical Engineering and Computational ScienceAalto UniversityEspooFinland

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