Complex blind source extraction from noisy mixtures using second-order statistics

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 57, Issue 7, 2010, Pages 1404-1416

  Javidi, Soroush ^a   Mandic, Danilo P ^a   Cichocki, Andrzej ^b,c  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b RIKEN BRAIN SCIENCE INSTITUTE   (Japan)

^c POLISH ACADEMY OF SCIENCES   (Poland)

Author keywords

Augmented complex least mean square (ACLMS); blind source extraction (BSE); complex noncircularity; complex pseudocovariance; electroencephalogram (EEG) artifact removal; noisy mixtures; widely linear (WL) model

Indexed keywords

ELECTROENCEPHALOGRAPHY; EXTRACTION; MIXTURES; PROBABILITY DISTRIBUTIONS;

AUGMENTED COMPLEX LEAST MEAN SQUARES; BLIND SOURCE EXTRACTION (BSE); COMPLEX NONCIRCULARITY; COMPLEX PSEUDOCOVARIANCE; ELECTROENCEPHALOGRAM ARTIFACT REMOVALS; NOISY MIXTURES; WIDELY LINEAR MODELS;

BLIND SOURCE SEPARATION;

EID: 77954865416     PISSN: 15498328     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2010.2043985     Document Type: Article

References (41)

1. J. Anemüller, T. J. Sejnowski, and S. Makeig, "Complex independent component analysis of frequency-domain electroencephalographic data," Neural Netw., vol.16, no.9, pp. 1311-1323, Nov. 2003.
2. A. Cichocki and S. Amari, Adaptive Blind Signal and Image Processing, Learning Algorithms and Applications. Hoboken, NJ: Wiley, 2002.
3. A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis. Hoboken, NJ: Wiley, 2001.
4. J. Särelä and H. Valpola, "Denoising source separation," J. Mach. Learn. Res., vol.6, pp. 233-272, 2005.
5. J. Cardoso, "Blind signal separation: Statistical principles," Proc. IEEE, vol.86, no.10, pp. 2009-2025, Oct. 1998.
6. S. Douglas, "Blind signal separation and blind deconvolution," in Handbook of Neural Network Signal Processing. Boca Raton, FL: CRC Press, 2002, ch. 7.
7. W. Leong and D. Mandic, "Noisy component extraction (NoiCE)," IEEE Trans. Circuits Syst. I, Reg. Papers, vol.57, no.3, pp. 664-671, Mar. 2010.
8. A. J. Bell and T. J. Sejnowski, "An information-maximisation approach to blind separation and blind deconvolution," Neural Comput., vol.7, no.6, pp. 1129-1159, Nov. 1995.
9. S. Amari, A. Cichocki, and H. Yang, "A new learning algorithm for blind signal separation," in Advances in Neural Information Processing Systems. Cambridge, MA: MIT Press, 1996, pp. 757-763.
10. Q. Shi, R.Wu, and S.Wang, "A novel approach to blind source extraction based on skewness," in Proc. ICSP, 2006 , vol.4, pp. 3187-3190.
11. P. Georgiev and A. Cichocki, "Robust blind source separation utilizing second and fourth order statistics," in Proc. ICANN, New York, 2002, vol.2415, pp. 1162-1167.
12. A. Cichocki, R. Thawonmas, and S. Amari, "Sequential blind signal extraction in order specified by stochastic properties," Electron. Lett., vol.33, no.1, pp. 64-65, Jan. 1997.
13. W. Liu and D. P. Mandic, "A normalised kurtosis-based algorithm for blind source extraction from noisy measurements," Signal Process., vol.86, no.7, pp. 1580-1585, Jul. 2006.
14. D. P. Mandic and A. Cichocki, "An online algorithm for blind extraction of sources with different dynamical structures," in Proc. 4th Int. Symp. Ind. Compon. Anal. Blind Signal Separation (ICA), 2003, pp. 645-650.
15. B.-Y. Wang and W. Zheng, "Blind extraction of chaotic signal from an instantaneous linear mixture," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol.53, no.2, pp. 143-147, Feb. 2006.
16. W. Liu, D. P. Mandic, and A. Cichocki, "Blind source extraction of instantaneous noisy mixtures using a linear predictor," in Proc. IEEE Int. Symp. Circuits Syst., 2006, pp. 4199-4202. (Pubitemid 47132481)
17. W. Liu, D. P. Mandic, and A. Cichocki, "Blind second-order source extraction of instantaneous noisy mixtures," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol.53, no.9, pp. 931-935, Sep. 2006. (Pubitemid 46511481)
18. W. Y. Leong, W. Liu, and D. P. Mandic, "Blind source extraction: Standard approaches and extensions to noisy and post-nonlinear mixing," Neurocomputing, vol.71, no.10-12, pp. 2344-2355, Jun. 2008.
19. D. P. Mandic, S. Javidi, G. Souretis, and S. L. Goh, "Why a complex valued solution for a real domain problem," in Proc. IEEE Workshop Mach. Learn. Signal Process., Aug. 2007, pp. 384-389.
20. D. P. Mandic and S. L. Goh, Complex Valued Nonlinear Adaptive Filters: Noncircularity, Widely Linear and Neural Models. Hoboken, NJ: Wiley, 2009.
21. B. Picinbono, "On circularity," IEEE Trans. Signal Process., vol.42, no.12, pp. 3473-3482, Dec. 1994.
22. B. Picinbono and P. Bondon, "Second-order statistics of complex signals," IEEE Trans. Signal Process., vol.45, no.2, pp. 411-420, Feb. 1997.
23. F. Neeser and J. Massey, "Proper complex random processes with applications to information theory," IEEE Trans. Inf. Theory, vol.39, no.4, pp. 1293-1302, Jul. 1993.
24. W. Wirtinger, "Zur formalen theorie der funktionen von mehr komplexen veränderlichen," Mathematische Annalen, vol.97, no.1, pp. 357-375, Dec. 1927.
25. K. Kreutz-Delgado, The complex gradient operator and the-calculus Dept. Elect. Comput. Eng., Univ. California, San Diego, CA, Course Lecture Supplement No. ECE275A, 2006.
26. S. Javidi, M. Pedzisz, S. Goh, and D. P. Mandic, "The augmented complex least mean square algorithm with application to adaptive prediction problems," in Proc. 1st IARP Workshop Cogn. Inf. Process., 2008, pp. 54-57.
27. Y. Xia, C. Cheong-Took, S. Javidi, and D. Mandic, "A widely linear affine projection algorithm," in Proc. IEEE Workshop Stat. Signal Process., 2009, pp. 373-376.
28. C. Cheong-Took and D. Mandic, "Adaptive IIR filtering of noncircular complex signals," IEEE Trans. Signal Process., vol.57, no.10, pp. 4111-4118, Oct. 2009.
29. M. Novey and T. Adal?, "On extending the complex FastICA algorithm to noncircular sources," IEEE Trans. Signal Process., vol.56, no.5, pp. 2148-2154, May 2008.
30. S. Douglas, J. Eriksson, and V. Koivunen, "Fixed-point complex ICA algorithms for the blind separation of sources using their real or imaginary components," in Independent Component Analysis and Blind Signal Separation. New York: Springer-Verlag, 2006, pp. 343-351.
31. A. Erdogan, "On the convergence of ICA algorithms with symmetric orthogonalization," IEEE Trans. Signal Process., vol.57, no.6, pp. 2209-2221, Jun. 2009.
32. E. Bingham and A. Hyvärinen, "A fast fixed point algorithm for independent component analysis of complex valued signals," Int. J. Neural Syst., vol.10, no.1, pp. 1-8, Feb. 2000.
33. S. Javidi, B. Jelfs, and D. P. Mandic, "Blind extraction of noncircular signals using a widely linear predictor," in Proc. IEEE Workshop Stat. Signal Process., 2009, pp. 501-504.
34. J. Eriksson and V. Koivunen, "Complex random vectors and ICA models: Identifiability, uniqueness, and separability," IEEE Trans. Inf. Theory, vol.52, no.3, pp. 1017-1029, Mar. 2006.
35. E. Ollila and V. Koivunen, "Complex ICA using generalized uncorrelating transform," Signal Process., vol.89, no.4, pp. 365-377, Apr. 2009.
36. P. Schreier, "Bounds on the degree of impropriety of complex random vectors," IEEE Signal Process. Lett., vol.15, pp. 190-193, 2008 .
37. A.Walden and P. Rubin-Delanchy, "On testing for impropriety of complex-valued Gaussian vectors," IEEE Trans. Signal Process., vol.57, no.3, pp. 825-834, Mar. 2009.
38. B. Picinbono and P. Chevalier, "Widely linear estimation with complex data," IEEE Trans. Signal Process., vol.43, no.8, pp. 2030-2033, Aug. 1995.
39. D. P. Mandic, S. Javidi, S. L. Goh, A. Kuh, and K. Aihara, "Complexvalued prediction of wind profile using augmented complex-valued statistics," Renew. Energy, vol.34, pp. 196-201, Nov. 2007.
40. S. Haykin, Adaptive Filter Theory. Englewood Cliffs, NJ: Prentice-Hall, 1996.
41. P. Georgiev, A. Cichocki, and H. Bakardjian, "Optimization techniques for independent component analysis with applications to EEG data," in Quantitative Neuroscience: Models, Algorithms, Diagnostics, and Therapeutic Applications. Norwell, MA: Kluwer, 2004, ch. 3, pp. 53-68.