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Piecewise Modeling of ECG Signals Using Chebyshev Polynomials

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Computational Intelligence in Data Mining

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 711))

Abstract

An electrocardiogram (ECG) signal measures electrical activity of the heart which is used for cardiac-related issues. The morphology of these signals is affected by artifacts during acquisition and transmission which prevents accurate diagnosis. Also a typical ECG monitoring device generates massive volume of digital data which require huge memory and large bandwidth. So there is a need to effectively compress these signals. In this paper, a piecewise efficient model to compress ECG signals is proposed. The model is designed to perform three successive steps: denoising, segmentation, and approximation. Preprocessing is done through total variation denoising technique to reduce noise, while bottom-up time-series approach is implemented to divide the signals into various segments. The individual segments are then approximated using Chebyshev polynomials. The proposed model is compared with other compression models in terms of maximum error, root mean square error, percentage root mean difference, and normalized percentage root mean difference showing significant improvements in performance parameters.

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References

  1. Walraven, Gail: Basic arrhythmias, Pearson Higher Ed (2014).

    Google Scholar 

  2. Mainardi, L. T., Bianchi, A. M., Baselli, G., Cerutti, S.: Pole-tracking algorithms for the extraction of time-variant heart rate variability spectral parameters. J. Mol. Biol. IEEE Transactions on Biomedical Engineering 42(3), 250–259 (1995).

    Article  Google Scholar 

  3. Poungponsri, S., Yu, X. H.: Electrocardiogram (ECG) signal modeling and noise reduction using wavelet neural networks. In: ICAL’09. IEEE International Conference on Automation and Logistics, pp. 394–398, (2009).

    Google Scholar 

  4. Levkov, C., Mihov, G., Ivanov, R., Daskalov, I., Christov, I., Dotsinsky, I.: Removal of power-line interference from the ECG: a review of the subtraction procedure. BioMedical Engineering OnLine, 4(1), 50 (2005).

    Article  Google Scholar 

  5. Lu, G., Brittain, J. S., Holland, P., Yianni, J., Green, A. L., Stein, J. F., Aziz, T. Z. and Wang, S.: Removing ECG noise from surface EMG signals using adaptive filtering. Neuroscience letters 462(1), 14–19 (2009).

    Article  Google Scholar 

  6. Alfaouri, M., Daqrouq, K.: ECG signal denoising by wavelet transform thresholding. American Journal of Applied Sciences, 5(3), 276–281 (2008).

    Article  Google Scholar 

  7. Donoho, D. L., Johnstone, I. M.: Threshold selection for wavelet shrinkage of noisy data. In: In Engineering in Medicine and Biology Society, 1994. Engineering Advances: New Opportunities for Biomedical Engineers. Proceedings of the 16th Annual International Conference of the IEEE, pp. A24–A25. IEEE Press, (1994).

    Google Scholar 

  8. Rudin, L. I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena, 60(1–4), 259–268 (1992).

    Article  MathSciNet  Google Scholar 

  9. Solo, V.: Selection of regularisation parameters for total variation denoising. In: In Acoustics, Speech, and Signal Processing, IEEE International Conference pp. 1653–1655. IEEE Press, New (1999).

    Google Scholar 

  10. Bioucas-Dias, J. M., Figueiredo, M. A., Oliveira, J. P.: Total variation-based image deconvolution: a majorization-minimization approach In: IEEE International Conference on Acoustics, Speech and Signal Processing Conference (2), (2006).

    Google Scholar 

  11. Beraza, I., Romero, I.: Comparative study of algorithms for ECG segmentation. Biomedical Signal Processing and Control 34, 166–173 (2017).

    Article  Google Scholar 

  12. Khawaja, A., Sanyal, S., Dossel, O.: A wavelet-based multi-channel ECG delineator In: The 3rd European Medical and Biological Engineering Conference, (2005).

    Google Scholar 

  13. Clavier, L., Boucher, J. M., Polard, E.: idden Markov models compared to the wavelet transform for P-wave segmentation in EGC signals. In: In Signal Processing Conference (EUSIPCO’1998), 9th European, pp. 1–4. IEEE (1998).

    Google Scholar 

  14. Akhbari, M., Shamsollahi, M. B., Sayadi, O., Armoundas, A. A., Jutten, C.: ECG segmentation and fiducial point extraction using multi hidden Markov model. Computers in Biology and Medicine 79, 21–29 (2016).

    Article  Google Scholar 

  15. Zifan, A., Saberi, S., Moradi, M. H., Towhidkhah, F.: Automated ECG segmentation using piecewise derivative dynamic time warping. International Journal of Biological and Medical Sciences 1(3) (2006).

    Google Scholar 

  16. Bystricky, W., Safer, A.: Modelling T-end in Holter ECGs by 2-layer perceptrons. Computers in Cardiology, 105–108 (2002).

    Google Scholar 

  17. Sayadi, O., Shamsollahi, M. B.: A model-based Bayesian framework for ECG beat segmentation. Physiological measurement 30(3), 335 (2009).

    Article  Google Scholar 

  18. Keogh, E., Chu, S., Hart, D., Pazzani, M.: Segmenting time series: A survey and novel approach. Data Mining in Time Series Databases 57, 1–22 (2004).

    Google Scholar 

  19. Borsali, R., Nait-Ali, A., Lemoine, J.: ECG compression using an ensemble polynomial modeling: Comparison with the DCT based technique. Cardiovascular Engineering 4(3), 237–244 (2004).

    Article  Google Scholar 

  20. Karczewicz, M., Gabbouj, M.: ECG data compression by spline approximation. Signal Processing, 59(1), 43–59 (1997).

    Article  Google Scholar 

  21. Fira, C. M., Goras, L.: An ECG signals compression method and its validation using NNs. IEEE Transactions on Biomedical Engineering 55(4), 1319–1326 (2008).

    Article  Google Scholar 

  22. Nygaard, R., Haugland, D.: Compressing ECG signals by piecewise polynomial approximation. In: Proceedings of the 1998 IEEE International Conference in Acoustics, Speech and Signal Processing, pp. 1809–1812 (1998).

    Google Scholar 

  23. Abdoli, M., Ahmadian, A., Karimifard, S., Sadoughi, H., Yousefi Rizi, F.: An Efficient Piecewise Modeling of ECG Signals Based on Critical Samples Using Hermitian Basis Functions. In: In 4th European Conference of the International Federation for Medical and Biological Engineering, pp. 1188–1191. Springer Berlin Heidelberg (2009).

    Google Scholar 

  24. Tchiotsop, D., Ionita, S.: ECG Data Communication Using Chebyshev Polynomial compression methods. Telecommunicatii Numere Publicate, AN XVI. 2010(2):22–32.

    Google Scholar 

  25. Mason, J. C., Handscomb, D. C.: Chebyshev polynomials. CRC Press (2002).

    Google Scholar 

  26. Yang, W. Y., Cao, W., Chung, T. S., Morris, J.: Applied numerical methods using MATLAB. John Wiley and Sons (2005).

    Google Scholar 

  27. Cheney, E. W.: Approximation theory III (Vol. 12). Academic Press, New York (1980).

    Google Scholar 

  28. Moody, G. B., Mark, R. G.: The MIT-BIH arrhythmia database on CD-ROM and software for use with it. In: 1 In Computers in Cardiology, Proceedings, pp. 185–188. IEEE (1990).

    Google Scholar 

  29. Ustundag, M., Sengur, A., Gokbulut, M., ATA, F.: Performance comparison of wavelet thresholding techniques on weak ECG signal denoising. Przeglad Elektrotechniczny 89(5), 63–66 (2013).

    Google Scholar 

  30. Kabir, M. A., Shahnaz, C.: Denoising of ECG signals based on noise reduction algorithms in EMD and wavelet domains. Biomedical Signal Processing and Control 7(5), 481–489 (2012).

    Article  Google Scholar 

  31. Georgieva-Tsaneva, G., Tcheshmedjiev, K.: Denoising of electrocardiogram data with methods of wavelet transform. In: International Conference on Computer Systems and Technologies, pp. 9–16 (2013).

    Google Scholar 

  32. Sandryhaila, A., Saba, S., Puschel, M., Kovacevic, J.: Efficient compression of QRS complexes using Hermite expansion. IEEE Transactions on Signal Processing 60(2), 947–955 (2012).

    Article  MathSciNet  Google Scholar 

  33. Nygaard, R., Haugland, D., Husoy, J. H.: Signal Compression by Second Order Polynomials and Piecewise Non-Interpolating Approximation (1999).

    Google Scholar 

  34. Jokic, S., Delic, V., Peric, Z., Krco, S., Sakac, D.: Efficient ECG modeling using polynomial functions. Elektronika ir Elektrotechnika 110(4), 121–124 (2011).

    Google Scholar 

  35. Ktata, S., Ouni, K., Ellouze, N.: A novel compression algorithm for electrocardiogram signals based on wavelet transform and SPIHT. International Journal of Signal Processing 5(4), 32–37 (2009).

    Google Scholar 

  36. Istepanian, R. S., Petrosian, A. A.: Optimal zonal wavelet-based ECG data compression for a mobile telecardiology system. IEEE Transactions on Information Technology in Biomedicine, 4(3), 200–211 (2000).

    Article  Google Scholar 

  37. Negoita, M., Goras, L.: On a compression algorithm for ECG signals. IEEE Signal Processing Conference, 1–4, 2005.

    Google Scholar 

  38. Luong, D. T., Duc, N. M., Linh, N. T., Ha, N. T., Thuan, N. D.: Advanced Two-State Compressing Algorithm: A Versatile, Reliable and Low-Cost Computational Method for ECG Wireless Applications. American Journal of Biomedical Sciences, 8(1), 2016.

    Google Scholar 

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Correspondence to Om Prakash Yadav .

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Yadav, O.P., Ray, S. (2019). Piecewise Modeling of ECG Signals Using Chebyshev Polynomials. In: Behera, H., Nayak, J., Naik, B., Abraham, A. (eds) Computational Intelligence in Data Mining. Advances in Intelligent Systems and Computing, vol 711. Springer, Singapore. https://doi.org/10.1007/978-981-10-8055-5_26

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