Advertisement

Noninvasive Electroardiographic Imaging: Application of Hybrid Methods for Solving the Electrocardiography Inverse Problem

  • Mingfeng Jiang
  • Ling Xia
  • Guofa Shou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4466)

Abstract

Computing the epicardial potentials from the body surface potentials constitutes one form of the ill-posed inverse problem of electrocardiography (ECG). In this paper, we employ hybrid methods combining the least square QR (LSQR) with truncated singular-value decomposition (TSVD) to solve the inverse problem of ECG. Hybrid methods are based on the Lanczos process, which yields a sequence of small bidiagonal systems approximating the original ill-posed problem, and on another additional direct regularization (the truncated SVD method is used in the present investigation), which is used to stabilize the iteration. The results show that determining of regularization parameters based on the final projected problem rather than on the original discretization one has firmer justification and it takes much less computational cost. The computation time could be reduced by several tenfolds typically, while the performance of the hybrid method is maintained well compared with TSVD, LSQR and GMRes methods. In addition, comparing with LSQR method, the hybrid method can obtain the inverse solutions without facing the “semi-convergence” problem.

Keywords

Hybrid Method Regularization Parameter Inverse Solution GMRes Method Project Problem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Rudy, Y., Messinger-Rapport,: The inverse problem in electrocardiography: Solutions in terms of epicardial potentials. CRC Crit. Rev. Biomed. Eng. 16, 215–268 (1988)Google Scholar
  2. 2.
    Seger, M., Fischer, G., Modre, R., Messnarz, B., Hanser, F., Tilg, B.: Lead field computation for the electrocardiographic inverse problem-finite elements versus boundary elements. Computer Methods and Programs in Biomedicine 77, 241–252 (2005)CrossRefGoogle Scholar
  3. 3.
    Kilmer, M.E., O’Leary, D.P.: Choosing Regularization Parameters in Iterative Methods for Ill-posed Problems. SIAM J. Matrix Anal. Appl. 22, 1204–1221 (2001)zbMATHCrossRefGoogle Scholar
  4. 4.
    Hanke, M.: On Lanczos Based Methods for the Regularization of Discrete Ill-posed Problems. BIT 41, 1008–1018 (2001)CrossRefGoogle Scholar
  5. 5.
    Brianzi, P., Favati, P., Menchi, O., Romani, F.: A framework for studying the regularizing properties of Krylov subspace methods. Inverse Problems 22, 1007–10216 (2006)zbMATHCrossRefGoogle Scholar
  6. 6.
    Jiang, M., Xia, L., Shou, G., Tang, M.: Combination of the LSQR method and a genetic algorithm for solving the electrocardiography inverse problem. Phys. Med. Biol. 52, 1277–1294 (2007)CrossRefGoogle Scholar
  7. 7.
    Ramanathan, C., Jia, P., Ghamen, R., Calvetti, D., Rudy, Y.: Noninvasive Electrocardiographic Imaging (ECGI): Application of the Generalized Minimal Residual (GMRes) Method. Annals of Biomed. Eng. 31, 981–994 (2003)CrossRefGoogle Scholar
  8. 8.
    Hansen, P.C.: Rank-Deficient and Discrete Ill-Posed Problems. Numerical Aspects of Linear Inversion, SIAM Monogr. Math. Model Comput. SIAM, Philadelphia (1998)Google Scholar
  9. 9.
    O’Leary, D.P., Simmons, J.A.: A bidiagonalization-regularization procedure for large scale discretization of ill-posed problems. SIAM J.Sci. Statist. Comput. 2, 474–489 (1981)zbMATHCrossRefGoogle Scholar
  10. 10.
    Paige, C.C., Saunders, M.A.: LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software 8, 43–71 (1982)zbMATHCrossRefGoogle Scholar
  11. 11.
    Golub, G.H., von Matt, U.: Generalized cross-validation for large-scale problems. J. Comput. Graph. Statist. 6, 1–34 (1997)CrossRefGoogle Scholar
  12. 12.
    Xia, L., Huo, M., Wei, Q., Liu, F., Crozier, S.: Analysis of cardiac ventricular wall motion based on a three-dimensional electromechanical biventricular model. Phys. Med. Biol. 50, 1901–1917 (2005)CrossRefGoogle Scholar
  13. 13.
    Xia, L., Huo, M., Wei, Q., Liu, F., Crozier, S.: Electrodynamic Heart Model Construction and ECG Simulation. Methods of Information in Medicine 45, 564–573 (2006)Google Scholar
  14. 14.
    Xia, L., Zhang, Y., Zhang, H., Wei, Q., Liu, F., Crozier, S.: Simulation of Brugada syndrome using cellular and three-dimensional whole-heart modeling approaches. Phsiological Measurement 27, 1125–1142 (2006)CrossRefGoogle Scholar
  15. 15.
    Johnston, P.R., Gulrajani, R.M.: A New Method for Regularization Parameter Determination in the Inverse Problem of Electrocardiography. IEEE Tran. Biomed. Eng. 44, 19–39 (1997)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Mingfeng Jiang
    • 1
    • 2
  • Ling Xia
    • 1
  • Guofa Shou
    • 1
  1. 1.Department of Biomedical Engineering, Zhejiang University, Hangzhou, 310027P.R. China
  2. 2.The College of Electronics and Informatics, Zhejiang Sci-Tech University, Hangzhou, 310018P.R. China

Personalised recommendations