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Robust Volterra Filter Design for Enhancement of Electroencephalogram Signal Processing

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Abstract

Electroencephalogram (EEG) recordings often experience interference by different kinds of noise, including white, muscle, and baseline, severely limiting its utility. The recent research has demonstrated that discrete-time Volterra models can be successfully applied to reduce the broadband and narrowband noise. Their usefulness is mainly because of their ability to approximate to an arbitrary precision any fading memory system and their property of linearity with respect to parameters, the kernels coefficients. The main drawback of these models is their parametric complexity implying the need to estimate a huge number of parameters. Numerical results show that the developed algorithm achieves performance improvement over the standard filtered algorithm. This paper presents a Volterra filter (VF) algorithm based on a multichannel structure for noise reduction. Several methods have been developed, but the VF appears to be the most effective for reducing muscle and baseline noise, especially when the contamination is greater in amplitude than the brain signal. The present study introduces a new method of reducing noise in EEG signals in one step with low EEG distortion and high noise reduction. Applications with different real and synthetic signals are discussed, showing the validity of the proposed method.

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References

  1. U. Aydin, Y.S. Dogrusoz, 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(9), 1003–1013 (2011)

    Article  Google Scholar 

  2. J. Bronzino, The Biomedical Engineering Handbook, 2nd edn. (CRC Press, Boca Raton, 2000)

    Google Scholar 

  3. T.G. Burton, R.A. Goubran, F. Beaucoup, Nonlinear system identification using a subband adaptive Volterra filter. IEEE Trans. Instrum. Meas. 58(5), 1389–1397 (2009)

    Article  Google Scholar 

  4. D. Callaerts et al. On-line algorithm for signal separation based on SVD (1989)

  5. N.P. Castellanos, V.A. Makarov, Recovering EEG brain signals: artifact suppression with wavelet enhanced independent component analysis. J. Neurosci. Methods 158(2), 300–312 (2006)

    Article  Google Scholar 

  6. M. Crespo-Garcia, M. Atienza, J. Cantero, Muscle artifact removal from human sleep EEG by using independent component analysis. Ann. Biomed. Eng. 36(3), 467–475 (2008)

    Article  Google Scholar 

  7. M. Ferrer, A. Gonzalez, M. de Diego, G. Piñero, Fast affine projection algorithms for filtered-x multichannel active noise control. IEEE Trans. Audio Speech Lang. Process. 50(6), 1396–1408 (2008)

    Article  Google Scholar 

  8. P. Gaydecki, A real time programmable digital filter for biomedical signal enhancement incorporating a high-level design interface. Physiol. Meas. 21(1), 187–196 (2000)

    Article  Google Scholar 

  9. G.B. Giannakis, E. Serpedin, Linear multichannel blind equalizers of nonlinear fir Volterra channels. IEEE Trans. Signal Process. 45(1), 67–81 (1997)

    Article  Google Scholar 

  10. S. Haykin, Adaptive Filter Theory (Prentice-Hall, Englewood Cliff, 1986)

    Google Scholar 

  11. C.H. Hsiang, E.J. Power, Identification of cubic systems using higher order moments of i.i.d. signals. IEEE Trans. Signal Process. 43(7), 1733–1735 (1995)

    Article  Google Scholar 

  12. N. Ille, P. Berg, M. Scherg, Artifact correction of the ongoing EEG using spatial filters based on artifact and brain signal topographies. Clin. Neurophysiol. 19(2), 113–124 (2002)

    Article  Google Scholar 

  13. C. James, M. Hagan, Multireference adaptive noise canceling applied to the EEG. IEEE Trans. Biomed. Eng. 44(8), 775–779 (1997)

    Article  Google Scholar 

  14. T. Jung, C. Humphries et al., Extended ICA removes artifacts from electroencephalographic recordings. Adv. Neural Inf. Process. Syst. 10, 894–900 (1998)

    Google Scholar 

  15. S.M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall, New York, 1993)

    MATH  Google Scholar 

  16. S.M. Kuo, D.R. Morgan, Active Noise Control Systems Algorithms and DSP Implementations (Wiley, New York, 1996)

    Google Scholar 

  17. T. Lagerlund, F. Sharbrough, N. Busacker, Spatial filtering of multichannel electroencephalographic recordings through principal component analysis by singular value decomposition. Clin. Neurophysiol. 14(1), 73–82 (1997)

    Article  Google Scholar 

  18. T. Lagerlund, F. Sharbrough, N. Busacker, Spatial filtering of multichannel electroencephalographic recordings through principal component analysis by singular value decomposition. Brain Topogr. 17(2), 73–84 (2004)

    Article  Google Scholar 

  19. S. Martens, M. Mischi, S. Oei, J. Bergmans, An improved adaptive power line interference canceller for electrocardiography. IEEE Trans. Biomed. Eng. 53(11), 2220–2231 (2006)

    Article  Google Scholar 

  20. V.J. Mathews, G.L. Sicuranza, Polynomial Signal Processing (Wiley, New York, 2000)

    Google Scholar 

  21. S. Olmos, P. Laguna, Steady-state MSE convergence of LMS adaptive filters with deterministic reference inputs with applications to biomedical signals. IEEE Trans. Signal Process. 48(8), 2229–2241 (2000)

    Article  Google Scholar 

  22. S. Olmos, L. Sörnmo, P. Laguna, Block adaptive filters with deterministic reference inputs for event-related signals: BLMS and BRLS. IEEE Trans. Signal Process. 50(5), 1102–1112 (2002)

    Article  Google Scholar 

  23. E.L. Ortiz, O.J. Tobias, R. Seara, A sparse-interpolated scheme for implementing adaptive Volterra filters. IEEE Trans. Signal Process. 58(4), 2022–2035 (2010)

    Article  MathSciNet  Google Scholar 

  24. J.S. Paul, M.R. Reddy, V.J. Kumar, A transform domain SVD filter for suppression of muscle noise artefacts in exercise ECG’s. IEEE Trans. Biomed. Eng. 47(5), 654–663 (2000)

    Article  Google Scholar 

  25. R. Rangayyan, Biomedical Signal Analysis: A Case-Study Approach. IEEE Press Series in Biomedical Engineering (2002)

    Google Scholar 

  26. G.V. Raz, B.V. Veen, Baseband Volterra filters for implementing carrier based nonlinearities. IEEE Trans. Signal Process. 46(1), 103–114 (1998)

    Article  Google Scholar 

  27. E.P. Reddy, D.P. Das, K.M.M. Prabhu, Fast adaptive algorithms for active control of nonlinear noise processes. IEEE Trans. Signal Process. 56(9), 4530–4535 (2008)

    Article  MathSciNet  Google Scholar 

  28. E.P. Reddy, D.P. Das, K.M.M. Prabhu, Adaptive polynomial filters. IEEE Trans. Signal Process. 8(3), 10–26 (1991)

    Article  Google Scholar 

  29. S. Romero, M. Mananasa, M. Barbanojb, A comparative study of automatic techniques for ocular artifact reduction in spontaneous EEG signals based on clinical target variables: a simulation case. Comput. Biol. Med. 38(3), 348–360 (2008)

    Article  Google Scholar 

  30. L.A.A. Ruiz, M. Zeller, A.R.F. Vidal, J.A. Garca, W. Kellermann, Adaptive combination of Volterra kernels and its application to nonlinear acoustic echo cancellation. IEEE Trans. Audio Speech Lang. Process. 19(1), 97–110 (2011)

    Article  Google Scholar 

  31. P.K. Sadasivan, D. Narayana Dutt, SVD based technique for noise reduction in electroencephalographic signals. Signal Process. 55(2), 179–189 (1996)

    Article  MATH  Google Scholar 

  32. R. Sameni, M. Shamsollahi, C. Jutten, Model-based Bayesian filtering of cardiac contaminants from biomedical recordings. Physiol. Meas. 29(5), 595–613 (2008)

    Article  Google Scholar 

  33. R. Sameni, M. Shamsollahi, C. Jutten, G. Clifford, A nonlinear Bayesian filtering framework for ECG denoising. IEEE Trans. Biomed. Eng. 54(12), 2172–2185 (2007)

    Article  Google Scholar 

  34. M. Sansone, L. Mirarchi, M. Bracale, Adaptive removal of gradients-induced artefacts on ECG in MRI: a performance analysis of RLS filtering. Med. Biol. Eng. Comput. 48(5), 475–482 (2010)

    Article  Google Scholar 

  35. G.M. Schetzen, Nonlinear system modeling based on the Wiener theory. Proc. IEEE 69(12), 1557–1573 (1981)

    Article  Google Scholar 

  36. S.-Y. Shao, K.-Q. Shen, C.J. Ong, E.P.V. Wilder-Smith, X.-P. Li, Automatic EEG artifact removal: a weighted support vector machine approach with error correction. IEEE Trans. Biomed. Eng. 56(2), 336–344 (2009)

    Article  Google Scholar 

  37. G.L. Sicuranza, Quadratic filters for signal processing. Proc. IEEE 80(2), 1263–1285 (1992)

    Article  Google Scholar 

  38. G.L. Sicuranza, A. Carini, A multichannel hierarchical approach to adaptive Volterra filters employing filtered-x affine projection algorithms. IEEE Trans. Signal Process. 53(4), 1463–1473 (2005)

    Article  MathSciNet  Google Scholar 

  39. L. Sörnmo, P. Laguna, Bioelectrical Signal Processing in Cardiac an Neurological Applications (Elsevier Academic, Amsterdam, 2005)

    Google Scholar 

  40. P. Strauch, B. Mulgrew, Active control of nonlinear noise processes in a linear duct. IEEE Trans. Signal Process. 46(9), 2404–2412 (1998)

    Article  Google Scholar 

  41. L. Tan, J. Jiang, Adaptive Volterra filters for active control of nonlinear noise processes. IEEE Trans. Signal Process. 49(8), 1667–1676 (2001)

    Article  Google Scholar 

  42. R.M. Udrea, D.N. Vizireanu, Quantized multiple sinusoids signal estimation algorithm. J. Instrum. 3, 1–7 (2008)

    Article  Google Scholar 

  43. D.N. Vizireanu, A fast, simple and accurate time-varying frequency estimation method for single-phase electric power systems. Measurement 45(6), 1331–1333 (2012)

    Article  Google Scholar 

  44. D.N. Vizireanu, A simple and precise real-time four point single sinusoid signals instantaneous frequency estimation method for portable DSP based instrumentation. Measurement 44(2), 500–502 (2011)

    Article  Google Scholar 

  45. S. Vorobyov, A. Cichocki, Blind noise reduction for multisensory signals using ICA and subspace filtering, with application to EEG analysis. Biol. Cybern. 86(4), 293–303 (2002)

    Article  MATH  Google Scholar 

  46. R. Vullings, B. de Vries, J. Bergmans, An adaptive Kalman filter for ECG signal enhancement. IEEE Trans. Biomed. Eng. 58(4), 1094–1103 (2011)

    Article  Google Scholar 

  47. B. Widrow, S.D. Stearns, Adaptive Signal Processing (Prentice-Hall, Englewood Cliffs, 1985)

    MATH  Google Scholar 

  48. U. Wiklund, M. Karlsson, N. Östlund, L. Berglin, K. Lindecrantz, S. Karlsson, L. Sandsjö, Adaptive spatio-temporal filtering of disturbed ECGs: a multi-channel approach to heartbeat detection in smart clothing. Med. Biol. Eng. Comput. 45(6), 515–523 (2007)

    Article  Google Scholar 

  49. Y. Wu, R.M. Rangayyan, Y. Zhouc, S.-C. Ngd, Filtering electrocardiographic signals using an unbiased and normalized adaptive noise reduction system. Med. Eng. Phys. 31(1), 17–26 (2009)

    Article  Google Scholar 

  50. L. Xu, D. Zhang, K. Wang, Wavelet-based cascaded adaptive filter for removing baseline drift in pulse waveforms. IEEE Trans. Biomed. Eng. 53(11), 1973–1975 (2005)

    Article  Google Scholar 

  51. H. Yang, S.T. Bukkapatnam, R. Komanduri, Nonlinear adaptive wavelet analysis of electrocardiogram signals. Phys. Rev. 76(2), 026214 (2007)

    Google Scholar 

  52. T. Zhang, Y. Okada, Recursive artifact windowed-single tone extraction method (raw-stem) as periodic noise filter for electrophysiological signals with interfering transients. J. Neurosci. Methods 155(2), 308–318 (2006)

    Article  Google Scholar 

  53. H. Zhao, J. Zhang, A novel adaptive nonlinear filter-based pipelined feedforward second-order Volterra architecture. IEEE Trans. Signal Process. 57(1), 237–246 (2009)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work was sponsored by University of Castilla-La Mancha and Virgen de la Luz Hospital of Cuenca (Spain).

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Correspondence to J. Mateo.

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Mateo, J., Torres, A., García, MA. et al. Robust Volterra Filter Design for Enhancement of Electroencephalogram Signal Processing. Circuits Syst Signal Process 32, 233–253 (2013). https://doi.org/10.1007/s00034-012-9447-5

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