Advertisement

Fast Basis Searching Method of Adaptive Fourier Decomposition Based on Nelder-Mead Algorithm for ECG Signals

  • Ze Wang
  • Limin Yang
  • Chi Man Wong
  • Feng Wan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9377)

Abstract

The adaptive Fourier decomposition (AFD) is a greedy iterative signal decomposition algorithm in the viewpoint of energy. Instead of using a fixed basis for decomposition, AFD uses an adaptive basis to achieve efficient energy extraction. In the conventional searching method, a new basis is searched from a large dictionary at every decomposition level. This usually results in a slow searching speed. To improve the efficiency, a fast searching method based on Nelder-Mead algorithm is proposed in this paper. The AFD with the proposed searching method is applied for electrocardiography (ECG) signals in which the selection ranges of four key parameters in the proposed searching method are determined based on simulation results of an artificial ECG signal. The simulation results of real ECG data shows that the computational time of the AFD based on the proposed searching method is just half of that based on the conventional searching method with similar reconstruction error.

Keywords

adaptive Fourier decomposition (AFD) Nelder-Mead algorithm electrocardiography (ECG) signal 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Qian, T., Zhang, L.M., Li, Z.X.: Algorithm of Adaptive Fourier Decomposition. IEEE Trans. Signal Process. 59, 5899–5906 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Qian, T.: Adaptive Fourier Decompositions and Rational Approximations–Part I: Theory. Int. J. Wavelets Multiresolut Inf. Process. 12, 1461008 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Zhang, L., Hong, W., Mai, W., Qian, T.: Adaptive Fourier Decomposition and Rational Approximation–Part II: Software System Design and Development. Int. J. Wavelets Multiresolut Inf. Process. 12, 1461009 (2014)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Wang, Z., Wong, C.M., da Cruz, J.N., Wan, F., Mak, P.I., Mak, P.U., Vai, M.I.: Muscle and Electrode Motion Artifacts Reduction in ECG Using Adaptive Fourier Decomposition. In: 2014 IEEE International Conference on Systems, Man and Cybernetics, pp. 1456–1461. IEEE, San Diego (2014)CrossRefGoogle Scholar
  5. 5.
    Qian, T., Wang, Y.B.: Adaptive Fourier Series–a Variation of Greedy Algorithm. Adv. Comput. Math. 34, 279–293 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Qian, T., Wang, Y.B.: Remarks on Adaptive Fourier Decomposition. Int. J. Wavelets Multiresolut Inf. Process. 11, 1350007 (2013)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Zhang, L., Hong, W., Mai, W., Qian, T.: Adaptive Fourier Decomposition and Rational Approximation–Part II: Software System Design And Development. Int. J. Wavelets Multiresolut Inf. Process. 12, 1461009 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
  9. 9.
    Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, New York (2006)zbMATHGoogle Scholar
  10. 10.
    Klein, K., Neira, J.: Nelder-Mead Simplex Optimization Routine for Large-scale Problems: a Distributed Memory Implementation. Comput. Econ. 43, 447–461 (2014)CrossRefGoogle Scholar
  11. 11.
    Nelder, J.A., Mead, R.: A Simplex Method for Function Minimization. Comput. J. 7, 308–313 (1965)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Ma, J., Zhang, T., Dong, M.: A Novel ECG Data Compression Method Using Adaptive Fourier Decomposition with Security Guarantee in e-Health Applications. IEEE J. Biomed. Health Inform. 19, 986–994 (2014)Google Scholar
  13. 13.
    Qian, T.: Adaptive Fourier Decompositions and Rational Approximations, Part I: Theory. Int. J. Wavelets Multiresolut. Inf. Process. 12, 1461008 (2014)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Moody, G.B., Mark, R.G.: The Impact of the MIT-BIH Arrhythmia Database. IEEE Eng. Med. Biol. Mag. 20, 45–50 (2001)CrossRefGoogle Scholar
  15. 15.
    Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.C., Mark, R.G., Mietus, J.E., Moody, G.B., Peng, C.K., Stanley, H.E.: PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals. Circulation 101, e215–e220 (2000)CrossRefGoogle Scholar
  16. 16.
    McSharry, P.E., Clifford, G.D., Tarassenko, L., Smith, L.A.: A Dynamical Model for Generating Synthetic Electrocardiogram Signals. IEEE Trans. Biomed. Eng. 50, 289–294 (2003)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

<SimplePara><Emphasis Type="Bold">Open Access</Emphasis> This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (http://creativecommons.org/licenses/by-nc/2.5/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. </SimplePara> <SimplePara>The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.</SimplePara>

Authors and Affiliations

  • Ze Wang
    • 1
  • Limin Yang
    • 1
  • Chi Man Wong
    • 1
  • Feng Wan
    • 1
  1. 1.Department of Electrical and Computer Engineering, Faculty of Science and TechnologyUniversity of MacauMacauChina

Personalised recommendations