Matrix-group algorithm via improved whitening process for extracting statistically independent sources from array signals

IEEE Transactions on Signal Processing

Volumn 55, Issue 3, 2007, Pages 962-977

  Feng, Da Zheng ^a   Zheng, Wei Xing ^b   Cichocki, Andrzej ^c  

^a XIDIAN UNIVERSITY   (China)

^b UNIVERSITY OF WESTERN SYDNEY   (Australia)

^c RIKEN BRAIN SCIENCE INSTITUTE   (Japan)

Author keywords

Biquadratic contrast function; Blind source separation; Cyclic maximizer; Cyclic minimizer; Diagonalization; Eigenvalue decomposition (EVD); Independent components; JADE; Signal subspace extraction; Whitening technique

Indexed keywords

ARRAY PROCESSING; ASYMPTOTIC ANALYSIS; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; STATISTICAL METHODS;

BIQUADRATIC CONTRAST FUNCTION; DIAGONALIZATION; EIGENVALUE DECOMPOSITION; WHITENING TECHNIQUE;

BLIND SOURCE SEPARATION;

EID: 33947393175     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2006.887126     Document Type: Article

References (47)

1. C. Jutten and J. Herault, "Blind separation of sources, Part I: An adaptive algorithm based on neuromatic architecture," Signal Process., vol. 24, no. 1, pp. 1-10, Jul. 1991.
2. P. Comon, "Independent component analysis: A new concept?," Signal Process., vol. 36, no. 3, pp. 287-314, Apr. 1994.
3. A. Cichocki, R. Unbehauen, and E. Rummert, "Robust learning algorithm for blind separation of signals," Electron. Lett., vol. 30, no. 17, pp. 1386-1387, Aug. 1994.
4. A. Cichocki and R. Unbehauen, "Robust neural networks with on-line learning for blind identification and blind separation of sources," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 43, no. 11, pp. 894-906, Nov. 1996.
5. S. Amari, A. Cichocki, and H. H. Yang, "A new learning algorithm for blind sources separation," in Advances in Neural Information Processing, D. Touretzky, M. Mozer, and M. Hasselmo, Eds. Cambridge, MA: MIT Press, 1996, vol. 8, pp. 757-763.
6. S. Amari and A. Cichocki, "Adaptive blind signal processing-neural network approaches," Proc. IEEE, vol. 86, no. 10, pp. 2026-2048, Oct. 1998.
7. S. A. Cruces-Alvarez, A. Cichocki, and S. Amari, "From blind signal extraction to blind instantaneous signal separation: Contrast function, algorithms, and stability," IEEE Trans. Neural Netw., vol. 15, no. 4, pp. 859-873, Jul. 2004.
8. A. J. Bell and T. J. Sejnowski, "An information-maximization approach to blind separation and blind disconsolation," Neural Comput., vol. 7, no. 6, pp. 1129-1159, Nov. 1995.
9. A. Cichocki and S. Amari, Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications. West Sussex, U.K.: Wiley, 2003.
10. J. Karhunen, E. Oja, L. Wang, R. Vigario, and J. Joutsensalo, "A class of neural networks for independent component analysis," IEEE Trans. Neural Netw., vol. 8, no. 3, pp. 486-504, May 1997.
11. A. Hyvarinen and E. Oja, "Independent component analysis by general nonlinear Hebbian like learning rules," Signal Process., vol. 64, no. 3, pp. 301-313, Feb. 1998.
12. J. F. Cardoso and B. Laheld, "Equivariant adaptive source separation," IEEE Trans. Signal Process., vol. 44, no. 12, pp. 3017-3030, Dec. 1996.
13. J. F. Cardoso, "Source separation using higher order moments," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), Glasgow, UK, May 1989, vol. 4, pp. 2109-2112.
14. J. F. Cardoso and A. Souloumiac, "Blind signal separation for non-Gaussian signals," Proc. Inst. Elect. Eng. - F, vol. 140, no. 6, pp. 362-370, Dec. 1993.
15. A. Belouchrani, K. Abed-Meraim, J. F. Cardoso, and E. Moulines, "A blind source separation technique using second-order statistics," IEEE Trans. Signal Process., vol. 45, no. 2, pp. 434-444, Feb. 1997.
16. E. Moreau, "A generalization of joint-diagonalization contrast function for source separation," IEEE Trans. Signal Process., vol. 49, no. 3, pp. 530-541, Mar. 2001.
17. M. Wax and Y. Anu, "A least squares approach to blind signal separation," IEEE Trans. Signal Process., vol. 47, no. 1, pp. 231-234, Jan. 1999.
18. L. Tong, R.-W. Liu, V. C. Soon, and Y.-F. Huang, "Indeterminacy and identifiability of blind source separation," IEEE Trans. Circuits Syst., vol. 38, no. 5, pp. 499-509, May 1991.
19. Z. Malouche and O. Macchi, "Adaptive unsupervised extraction of one component of a linear mixture with a single neuron," IEEE Trans. Neural Netw., vol. 9, no. 1, pp. 123-138, Jan. 1998.
20. N. Delfosse and P. Loubaton, "Adaptive blind separation of independent sources: A deflation approach," Signal Process., vol. 45, no. 1, pp. 59-83, Jul. 1995.
21. A. Hyvarinen and E. Oja, "A fast fixed-point algorithm for independent component analysis," Neural Comput., vol. 9, no. 7, pp. 1483-1492, Jul. 1997.
22. A. Hyvarinen, "Fast and robust fixed-point algorithms for independent component analysis," IEEE Trans. Neural Netw., vol. 10, no. 3, pp. 626-634, May 1999.
23. Z. Ding and T. Nguyen, "Stationary points of a kurtosis maximization algorithm for blind signal separation and antenna signal separation," IEEE Trans. Signal Process., vol. 48, no. 6, pp. 1587-1596, Jun. 2000.
24. C. B. Papadias, "Globally convergent blind source separation based on a multi-user kurtosis maximization criterion," IEEE Trans. Signal Process., vol. 48, no. 12, pp. 3508-3519, Dec. 2000.
25. C. Chang, Z. Ding, S. F. Yau, and F. H. Y. Chan, "A matrix-pencil approach to blind separation of colored nonstationary signals," IEEE Trans. Signal Process., vol. 48, no. 3, pp. 900-907, Mar. 2000.
26. L. Tong, V. C. Soon, Y.-F. Huang, and R. Liu, "AMUSE: A new blind source separation algorithm," in Proc. IEEE Int. Symp. Circuits Systems (ISCAS), New Orleans, LA, May 1990, vol. 3, pp. 1784-1887.
27. D.-Z. Feng, X.-D. Zhang, and Z. Bao, "An efficient multistage decomposition approach for independent components," Signal Process., vol. 83, no. 1, pp. 181-197, Jan. 2003.
28. D.-Z. Feng, Z. Bao, H.-Q. Zhang, and X.-D. Zhang, "An efficient algorithm for extracting independent components one by one," in Proc. 16th IFIP World Computer Congr. (ICSP), Beijing, China, Aug. 2000, vol. 1, pp. 421-424.
29. L. Para and C. Spence, "Convolutive blind separation of nonstationary sources," IEEE Trans. Speech Audio Process., vol. 8, no. 3, pp. 320-327, May 2000.
30. H. Sawada, R. Mukai, S. Araki, and S. Makino, "A robust and precise method for solving the permutation problem of frequency-domain blind sources separation," IEEE Trans. Speech Audio Process., vol. 12, no. 5, pp. 530-538, Sep. 2004.
31. K.-B. Yu, "Recursive updating the eigenvalue decomposition of a covariance matrix," IEEE Trans. Signal Process., vol. 39, no. 5, pp. 1136-1145, May 1991.
32. B. Champagne and Q. G. Liu, "Plane rotation-based updating schemes for efficient subspace tracking," IEEE Trans. Signal Process., vol. 46, no. 7, pp. 1886-1900, Jul. 1998.
33. P. Stoica and Y. Selen, "Cyclic minimizers, majorization techniques, and the expectation maximization algorithm: A refresher," IEEE Signal Process. Mag., vol. 21, no. 1, pp. 112-114, Jan. 2004.
34. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed. Baltimore, MD: The John Hopkins Univ. Press, 1989.
35. A. Belouchrani and A. Cichocki, "Robust whitening procedure in blind source separation context," Electron. Lett., vol. 36, no. 24, pp. 2050-2951, Nov. 2000.
36. S. Choi, A. Cichocki, and A. Belouchrani, "Second order nonstationary source separation," J. VLSI Signal Process., vol. 32, no. 1-2, pp. 93-104, Aug. 2002.
37. R. Roy and T. Kailath, "ESPRIT-estimation of signal parameters via rotational invariance techniques," IEEE Trans. Acoust., Speech, Signal Process., vol. 37, no. 7, pp. 984-995, Jul. 1989.
38. R. Schmidt, "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas Propag., vol. 34, no. 3, pp. 276-280, Mar. 1986.
39. M. Wax and T. Kailath, "Detection of signals by information theoretic contrast function," IEEE Trans. Acoust., Speech, Signal Process., vol. 33, no. 2, pp. 387-392, Apr. 1985.
40. A. Belouchrani, M. G. Amin, and K. Abed-Meraim, "Direction finding in correlated noise fields based on joint block-diagonalization of spatio-temporal correlation matrices," IEEE Signal Process. Lett., vol. 4, no. 9, pp. 266-268, Sep. 1997.
41. J. Yang and M. Kaveh, "Adaptive eigenspace algorithms for direction or frequency estimation and tracking," IEEE Trans. Acoust., Speech, Signal Process., vol. 36, no. 2, pp. 241-251, Feb. 1988.
42. B. Yang, "Projection approximation subspace tracking," IEEE Trans. Signal Process., vol. 43, no. 1, pp. 95-107, Jan. 1995.
43. J. J. Hopfield, "Neural networks and physical systems with emergent collective computational abilities," Proc. Nat. Acad. Sci. USA, vol. 79, pp. 2554-2558, 1982.
44. J. P. LaSalle, The Stability of Dynamical Systems. Philadelphia, PA: SIAM, 1976.
45. M. Viberg, P. Stoica, and B. Ottersten, "Array processing in correlated noise fields based on instrumental variables and subspace fitting," IEEE Trans. Signal Process., vol. 43, no. 5, pp. 1187-1199, May 1995.
46. D.-Z. Feng, X.-D. Zhang, and Z. Bao, "A neural network leaning for adaptively extracting cross-correlation features between two high-dimensional data stream," IEEE Trans. Neural Netw., vol. 15, no. 6, pp. 1541-1554, Nov. 2004.
47. J. R. Magnus and H. Neudecker, Matrix Differential Calculus With Applications in Statistics and Econometrics, 2nd ed. New York: Wiley, 1991.