| Title:
             | 
Fast and accurate methods of independent component analysis: A survey (English) | 
| Author:
             | 
Tichavský, Petr | 
| Author:
             | 
Koldovský, Zbyněk | 
| Language:
             | 
English | 
| Journal:
             | 
Kybernetika | 
| ISSN:
             | 
0023-5954 | 
| Volume:
             | 
47 | 
| Issue:
             | 
3 | 
| Year:
             | 
2011 | 
| Pages:
             | 
426-438 | 
| Summary lang:
             | 
English | 
| . | 
| Category:
             | 
math | 
| . | 
| Summary:
             | 
This paper presents a survey of recent successful algorithms for blind separation of determined instantaneous linear mixtures of independent sources such as natural speech or biomedical signals. These algorithms rely either on non-Gaussianity, nonstationarity, spectral diversity, or on a combination of them. Performance of the algorithms will be demonstrated on separation of a linear instantaneous mixture of audio signals (music, speech) and on artifact removal in electroencephalogram (EEG). (English) | 
| Keyword:
             | 
Blind source separation | 
| Keyword:
             | 
probability distribution | 
| Keyword:
             | 
score function | 
| Keyword:
             | 
autoregressive random processes | 
| Keyword:
             | 
audio signal processing | 
| Keyword:
             | 
electroencephalogram | 
| Keyword:
             | 
artifact rejection | 
| MSC:
             | 
92-02 | 
| MSC:
             | 
92-04 | 
| MSC:
             | 
92-08 | 
| MSC:
             | 
94A12 | 
| . | 
| Date available:
             | 
2011-06-23T12:58:31Z | 
| Last updated:
             | 
2013-09-22 | 
| Stable URL:
             | 
http://hdl.handle.net/10338.dmlcz/141594 | 
| . | 
| Reference:
             | 
[1] Belouchrani, A., Abed-Meraim, K., Cardoso, J.-F., Moulines, E.: A blind source separation technique using second-order statistics.IEEE Trans. Signal Processing 45 (1997), 434–444. 10.1109/78.554307 | 
| Reference:
             | 
[2] Boscolo, R., Pan, H., Roychowdhury, V. P.: Independent component analysis based on nonparametric density estimation.IEEE Trans. Neural Networks 15 (2004), 55–65. 10.1109/TNN.2003.820667 | 
| Reference:
             | 
[3] Cardoso, J.-F.: Blind signal separation: statistical principles.Proc. IEEE 90 (1998), 2009–2026. | 
| Reference:
             | 
[4] Cardoso, J.-F., Pham, D. T.: Separation of non stationary sources.Algorithms and performance., In: Independent Components Analysis: Principles and Practice (S. J. Roberts and R. M. Everson, eds.), Cambridge University Press 2001, pp. 158–180. | 
| Reference:
             | 
[5] Chambers, J., Cleveland, W., Kleiner, B., Tukey, P.: Graphical Methods for Data Analysis.Wadsworth, 1983. Zbl 0532.65094 | 
| Reference:
             | 
[6] Cruces, S., Cichocki, A., Lathauwer, L. De: Thin QR and SVD factorizations for simultaneous blind signal extraction.In: Proc. European Signal Processing Conference (EUSIPCO), Vienna 2004, pp. 217–220. | 
| Reference:
             | 
[7] Dégerine, S., Zaïdi, A.: Separation of an instantaneous mixture of Gaussian autoregressive sources by the exact maximum likelihood approach.IEEE Trans. Signal Processing 52 (2004), 1492–1512. MR 2068987, 10.1109/TSP.2004.827195 | 
| Reference:
             | 
[8] Delorme, A., Sejnowski, T., Makeig, S.: Enhanced detection of artifacts in EEG data using higher-order statistics and independent component analysis. Neuroimage 34 (2007) 1443–1449. 10.1016/j.neuroimage.2006.11.004 | 
| Reference:
             | 
[9] Hyvärinen, A., Oja, E.: A fast fixed-point algorithm for independent component analysis. Neural Computation 9 (1997), 1483–1492. 10.1162/neco.1997.9.7.1483 | 
| Reference:
             | 
[10] Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis.John Wiley & Sons, 2001. | 
| Reference:
             | 
[11] James, C. J., Hesse, C. W.: Independent component analysis for biomedical signals.Physiol. Meas. 26 (2005), R15–R39. 10.1088/0967-3334/26/1/R02 | 
| Reference:
             | 
[12] Koldovský, Z., Tichavský, P., Oja, E.: Efficient variant of algorithm FastICA for independent component analysis attaining the Cramér–Rao lower bound.IEEE Trans. Neural Networks 17 (2006), 1265–1277. 10.1109/TNN.2006.875991 | 
| Reference:
             | 
[13] Koldovský, Z., Málek, J., Tichavský, P., Deville, Y., Hosseini, S.: Blind separation of piecewise stationary nonGaussian Sources.Signal Process. 89 (2009), 2570–2584. | 
| Reference:
             | 
[14] Koldovský, Z., Tichavský, P.: A comparison of independent component and independent subspace analysis algorithms.In: Proc. European Signal Processing Conference (EUSIPCO), Glasgow 2009, pp. 1447–1451. | 
| Reference:
             | 
[15] Koldovský, Z., Tichavský, P.: Time-domain blind separation of audio sources based on a complete ICA decomposition of an observation space. IEEE Trans. Audio, Speech and Language Processing 19 (2011), 406–416. 10.1109/TASL.2010.2049411 | 
| Reference:
             | 
[16] Learned-Miller, E. G., III, J. W. Fisher: ICA using spacings estimates of entropy.J. Machine Learning Research 4 (2004), 1271–1295. MR 2103630 | 
| Reference:
             | 
[17] Lee, Te-Won: Independent Component Analysis, Theory and Applications.Kluwer Academic Publishers, 1998. Zbl 0910.94004 | 
| Reference:
             | 
[18] Pham, D. T., Garat, P.: Blind separation of mixture of independent sources through a quasi-maximum likelihood approach, IEEE Trans.Signal Process. 45 (1997), 1712–1725. 10.1109/78.599941 | 
| Reference:
             | 
[19] Pham, D.-T.: Joint approximate diagonalization of positive definite Hermitian matrices.SIAM J. Matrix Anal. Appl. 22 (2001), 1136–1152. Zbl 1008.65020, MR 1824062, 10.1137/S089547980035689X | 
| Reference:
             | 
[20] Pham, D.-T.: Blind separation of instantaneous mixture of sources via the Gaussian mutual information criterion.Signal Process. 81 (2001), 855–870. Zbl 1098.94576, 10.1016/S0165-1684(00)00260-7 | 
| Reference:
             | 
[21] Pham, D.-T., Cardoso, J.-F.: Blind separation of instantaneous mixtures of nonstationary sources.IEEE Trans. Signal Process. 49 (2001), 1837–1848. MR 1852133, 10.1109/78.942614 | 
| Reference:
             | 
[22] Tichavský, P., Koldovský, Z., Oja, E.: Performance analysis of the FastICA algorithm and Cramér-Rao bounds for linear independent component analysis.IEEE Trans. Signal Process. 54 (2006), 1189–1203. 10.1109/TSP.2006.870561 | 
| Reference:
             | 
[23] Tichavský, P., Koldovský, Z., Oja, E.: Corrections to “Performance analysis of the FastICA algorithm and Cramér–Rao Bounds for linear independent component analysis, TSP 04/06".IEEE Tran. Signal Process. 56 (2008), 1715–1716. MR 2516583, 10.1109/TSP.2007.910503 | 
| Reference:
             | 
[24] Tichavský, P., Koldovský, Z., Oja, E.: Speed and accuracy enhancement of linear ICA techniques using rational nonlinear functions.Lecture Notes in Comput. Sci. 4666 (2007), 285–292. Zbl 1172.94493 | 
| Reference:
             | 
[25] Tichavský, P., Koldovský, Z., Yeredor, A., Gomez-Herrero, G., Doron, E.: A hybrid technique for blind non-Gaussian and time-correlated sources using a multicomponent approach.IEEE Trans. Neural Networks 19 (2008), 421–430. 10.1109/TNN.2007.908648 | 
| Reference:
             | 
[26] Tichavský, P., Yeredor, A.: Fast approximate joint diagonalization incorporating weight matrices.IEEE Trans. Signal Process. 57 (2009), 878–891. MR 3027773, 10.1109/TSP.2008.2009271 | 
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