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, Volume 88, Issue 3, pp 415–427 | Cite as

On extending the Noisy Independent Component Analysis to Impulsive Components

  • Pingxing FengEmail author
  • Liping Li
Article
  • 142 Downloads

Abstract

As an important factor in the fast fixed-point algorithm of independent component analysis (ICA), noise has a significant influence on the separate performance of ICA. Unfortunately, the traditional algorithm of noisy ICA did not address the influence of impulsive components. Because the sources were signals mixed with impulsive noise, the Gaussian noisy algorithm will be invalid for separating the sources. In general, those measurements that significantly deviate from the normal pattern of sensed data are considered impulses. In this paper, we introduce a non-linear function based on the S-estimator to identify the impulsive components in the observed data. This approach guarantees that the impulse noise can be detected from the observed signal. Furthermore, a threshold for the impulse components and methods to remove impulse noise and reconstruct the signal is proposed. The proposed technique improves the separate performance of the traditional algorithm for Gaussian noisy ICA. With the proposed method, the fast fixed-point algorithm of ICA is more reliable for noisy situations. The simulation results show the effectiveness of the proposed method.

Keywords

Independent component analysis Multidimensional signal processing Impulsive noise Signal representations 

References

  1. 1.
    Liu, K., Tian, X., & Cai, L. (2015). A noisy independent component analysis algorithm with low signal-to-noise ratio. Control Engineering of China, 2, 027.Google Scholar
  2. 2.
    Cai, L., & Tian, X. (2015). A new process monitoring method based on noisy time structure independent component analysis. Chinese Journal of Chemical Engineering, 23(1), 162–172.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Nassiri, V., Aminghafari, M., & Mohammad-Djafari, A. (2014). Solving noisy ICA using multivariate wavelet denoising with an application to noisy latent variables regression. Communications in Statistics-Theory and Methods, 43(10–12), 2297–2310.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    He, X., & Zhu, T. (2014). ICA of noisy music audio mixtures based on iterative shrinkage denoising and FastICA using rational nonlinearities. Circuits, Systems, and Signal Processing, 33(6), 1917–1956.CrossRefGoogle Scholar
  5. 5.
    Hyvärinen, A. (1999). Fast and robust fixed-point algorithms for independent component analysis. IEEE Transactions on Neural Networks, 10(3), 626–634.CrossRefGoogle Scholar
  6. 6.
    Hyvärinen, A., & Oja, E. (2000). Independent component analysis: Algorithms and applications. Neural networks, 13(4), 411–430.CrossRefGoogle Scholar
  7. 7.
    Hyvärinen, A., & Oja, E. (1997). A fast fixed-point algorithm for independent component analysis. Neural Computation, 9(7), 1483–1492.CrossRefGoogle Scholar
  8. 8.
    Hyvärinen, A., Karhunen, J., & Oja, E. (2004). Independent component analysis. London: Wiley.Google Scholar
  9. 9.
    Bell, A. J. (2000). Information theory, independent-component analysis, and applications. Unsupervised Adaptive Filtering, 1, 237–264.Google Scholar
  10. 10.
    Bell, A. J., & Sejnowski, T. J. (1995). An information–maximization approach to blind separation and blind deconvolution. Neural Computation, 7(6), 1129–1159.CrossRefGoogle Scholar
  11. 11.
    Gaeta, M., & Lacoume, J. L. (1990). Source separation without a priori knowledge: The maximum likelihood solution. Proceedings of EUSIPCO, 90, 621–624.Google Scholar
  12. 12.
    Pham, D. T. (1996). Blind separation of instantaneous mixture of sources via an independent component analysis. IEEE Transactions on Signal Processing, 44(11), 2768–2779.CrossRefGoogle Scholar
  13. 13.
    Pham, D. T., & Garat, P. (1997). Blind separation of mixture of independent sources through a quasi-maximum likelihood approach. IEEE Transactions on Signal Processing, 45(7), 1712–1725.CrossRefzbMATHGoogle Scholar
  14. 14.
    Pahm, D. T, Garrat, P., & Jutten, C. (1992). Separation of a mixture of independent sources through a ML approach. In Proceedings of European signal processing conference (p. 771).Google Scholar
  15. 15.
    Moulines, E., Cardoso, J. F., & Gassiat, E. (1997). Maximum likelihood for blind separation and deconvolution of noisy signals using mixture models. In IEEE international conference on acoustics, speech, and signal processing, 1997. ICASSP-97 (Vol. 5, pp. 3617–3620). IEEE.Google Scholar
  16. 16.
    Pajunen, P., & Karhunen, J. (1997). Least-squares methods for blind source separation based on nonlinear PCA. International Journal of Neural Systems, 8(05–06), 601–612.CrossRefGoogle Scholar
  17. 17.
    Hyvärinen, A. (1999). Fast ICA for noisy data using Gaussian moments. In Proceedings of IEEE international symposium on circuits and systems, 1999. ISCAS’99 (Vol. 5, pp. 57–61). IEEE.Google Scholar
  18. 18.
    Hyvärinen, A. (1999). Gaussian moments for noisy independent component analysis. IEEE Signal Processing Letters, 6(6), 145–147.CrossRefGoogle Scholar
  19. 19.
    Koivunen, V., Enescu, M., & Oja, E. (2001). Adaptive algorithm for blind separation from noisy time-varying mixtures. Neural Computation, 13(10), 2339–2357.CrossRefzbMATHGoogle Scholar
  20. 20.
    Koivunen, V., & Oja, E. (1999). Predictor–corrector structure for real-time blind separation from noisy mixtures. ICA, 99, 479–484.Google Scholar
  21. 21.
    Hyvärinen, A. (1999). Sparse code shrinkage: Denoising of nongaussian data by maximum likelihood estimation. Neural Computation, 11(7), 1739–1768.CrossRefGoogle Scholar
  22. 22.
    Hyvärinen, A., Hoyer, P., & Oja, E. (1999). Image denoising by sparse code shrinkage. In Intelligent signal processing. IEEE Press.Google Scholar
  23. 23.
    Rousseeuw, P. J., & Leroy, A. M. (2005). Robust regression and outlier detection. London: Wiley.zbMATHGoogle Scholar
  24. 24.
    Sengijpta, S. K. (1995). Fundamentals of statistical signal processing: Estimation theory. Technometrics, 37(4), 465–466.CrossRefGoogle Scholar
  25. 25.
    Therrien, C. W. (1992). Discrete random signals and statistical signal processing. New Jersey: Prentice Hall PTR.zbMATHGoogle Scholar
  26. 26.
    Amari, S., Cichocki, A. &, Yang, H. H. (1996). A new learning algorithm for blind signal separation. In D. Touretzky, M. Mozer, M. Hasselmo (Eds.), Advances in neural information processing systems.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Electronic EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina

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