A theoretical discussion on the foundation of Stone's blind source separation

Signal, Image and Video Processing

Volumn 5, Issue 3, 2011, Pages 379-388

  Khosravy, Mahdi ^a   Asharif, Mohammad Reza ^a   Yamashita, Katsumi ^b  

^a UNIVERSITY OF THE RYUKYUS   (Japan)

^b Osaka Prefecture University   (Japan)

Author keywords

Blind source separation; General eigenvalue decomposition; Simultaneous diagonalization; Stone's BSS

Indexed keywords

COVARIANCE MATRICES; EIGENVALUE DECOMPOSITION; GENERALIZED EIGENVALUE DECOMPOSITION; IMAGE MIXTURE; LINEAR FILTERS; NOISE LEVELS; SECOND ORDER STATISTICS; SIMULTANEOUS DIAGONALIZATION; SOURCE SIGNALS; STONE'S BSS; THEORETICAL FOUNDATIONS;

COVARIANCE MATRIX; EIGENVALUES AND EIGENFUNCTIONS; FIR FILTERS; INDEPENDENT COMPONENT ANALYSIS;

BLIND SOURCE SEPARATION;

EID: 80051915799     PISSN: 18631703     EISSN: 18631711     Source Type: Journal    
DOI: 10.1007/s11760-010-0161-0     Document Type: Article

References (37)

1. Stone J. V.: Blind source separation using temporal predictability. Neural. Comput. 13(7), 1559-1574 (2001).
2. Stone J. V.: Independent Component Analysis: A Tutorial Introduction. A Bradford Book, London (2004).
3. Common P.: Independent component analysis, a new concept?. Signal Process 36, 287-314 (1994).
4. Haykin S.: Unsupervised Adaptive Filtering. Volume 1: Blind Source Separation. Wiley, New York (2000).
5. Cichocki A., Amari S.: Adaptive Blind Signal and Image Processing. Wiley, New York (2000).
6. Friedman J.: Exploratory projection pursuit. J. Am. Stat. Assoc. 82(397), 249-266 (1987).
7. DeGroot M. H.: Probability and Statistics. 2nd edn. Addison-Wesley, London (1986).
8. Jutten, C., Herault, J.: Independent component analysis versus PCA. In: Proceedings of EUSIPCO, pp. 643-646 (1988).
9. Bell A. J., Sejnowski T. J.: An information-maximization approach to blind separation and blind deconvolution. Neural. Comput. 7, 1129-1159 (1995).
10. Cardoso J. F.: Infomax and maximum likelihood for blind source separation. IEEE Signal Process. Lett. 4(4), 112-114 (1997).
11. Cardoso, J. F.: Eigen-structure of the fourth-order cumulant tensor with application to the blind source separation problem. In: Internationl Conference on Acoustics Speech and Signal Processing, pp. 2655-2658, Albuquerque, NM, USA (1990).
12. Belouchrani A., Amin M. G.: New approach for blind source separation using time-frequency distributions. Proc. SPIE 2846, 193-203 (1996).
13. Boumahdi, M., Lacoume, J. L.: Blind identification using the kurtosis: Results of field data processing. In Proceedings of the 1995 IEEE International Conference on Acoustics, Speech, and Signal Processing, volume 3, pp 1980-1983, Detroit, Michigan USA, (1995).
14. Jafari M. G., Vincent E., Abdallah S. A., Plumbley M. D., Davies M. E.: An adaptive stereo basis method for convolutive blind audio source separation. Neurocomputing 71, 2087-2097 (2008).
15. Davies, M. E., Jafari, M. J., Abdallah, S. A., Vincent, E., Plumbley, M. D.: Blind speech separation using space-time independent component analysis. In: Makino, S., Lee, T. W., Sawada, H. (eds.) Blind Speech Separation, Springer (2007).
16. Hyvfarinen, A.: Complexity pursuit: Combining nongaussinity and autocorrelations of signal separation. In: Proceedings of International Workshop on Independent Component Analysis and Blind Signal Separation (ICA2000), Helsinki, Finland, pp. 175-180 (2000).
17. Tong, L., Soon, V. C., Huang, Y. F., Liu, R.: AMUSE: A new blind identification algorithm. In Proceedings of IEEE ISCAS, pp 1784-1787 vol. 3, New Orleans, LA (1990).
18. Molgedey L., Schuster H. G.: Separation of a mixture of independent signals using time delayed correlations. Phys. Rev. Lett. 72(23), 3634-3637 (1994).
19. Belouchrani, A., Amin, M. G., Abed-Meraim, K.: Direction finding in correlated noise fields based on joint block-diagonalization of spatio-temporal correlation matrices. IEEE Signal Process. Lett. 4(9), September (1997).
20. Belouchrani A., Meraim K. A., Cardoso J. F., Moulines E.: A blind source separation technique using second-order statistics. IEEE Trans. Signal Process. 45(2), 434-444 (1997).
21. Cardoso J. F., Souloumiac A.: Blind beamforming for non-Gaussian signals. IEE Proc. F (Radar Signal Process.) 140(6), 362-370 (1993).
22. Meraim K. A., Moulines E., Loubaton P.: Prediction error method for second-order blind identification. IEEE Trans. Signal Process. 45, 694-705 (1997).
23. Cichocki A., Thawonmas R.: On-line algorithm for blind signal extraction of arbiturarily distributed, but temporally correlated sources using second order statistics. Neural Process. Lett. 12, 91-98 (2000).
24. Choi S., Cichocki A., Belouchrani A.: Second order nonstationary source separation. J. VLSI Signal Process. 32(1-2), 93-104 (2002).
25. Liu W., Mandic D., Cichocki A.: Blind Second-Order Source Extraction of Instantaneous Noisy Mixtures. IEEE Trans. Circuits Syst. II: Express Briefs 53(9), 931-935 (2006).
26. Vaseghi, S. V.: Linear Prediction Models, chapter. 8 of Advanced digital signal processing and noise reduction, 3rd edn Wiley, Ltd, (2006).
27. Jia, S., Qian, Y.: Improved Stone's Complexity Pursuit for Hyperspectral Imagery Unmixing. In: 18th International Conference on Pattern Recognition (ICPR'06), vol. 4, pp. 817-820 (2006).
28. Stone J. V.: Blind deconvolution using temporal predictability. Neurocomputing 49, 79-86 (2002).
29. Martinez D., Bray A.: Nonlinear blind source separation using kernels. IEEE Trans. Neural Netw. 14(1), 228-235 (2003).
30. Xie S., He Z., Fu Y.: A note on Stone's conjecture of blind signal separation. Neural. Comput. 17(2), 321-330 (2005).
31. Peterson G. L., Sochacki J. S.: Linear Algebra and Differential Equation. Addison-Wesley Publishing Company, Boston (2002).
32. Wax M., Kailath T.: Detection of signals by information theoretic criteria IEEE Trans. Acoustics Speech Signal Process. 33, 387-392 (1985).
33. Papoulis A.: Probability, Random Variables, and Stochastic Processes. 3rd edn. McGraw-Hill, NY (1991).
34. Nandi A. K.: Blind Estimation Using Higher-Order Statistics. Kluwer, Dordrecht (1999).
35. Waheed, K., Salam, F. M.: A data-derived quadratic independence measure for adaptive blind source recovery in practical applications. In: 45th IEEE International Midwest Symposium on Circuits and Systems, vol. 3, pp. 473-476 (2002).
36. Moreau, E., Macchi, O.: High-order contrasts for self-adaptive source separation, vol. 20, pp. 19-46 (1996).
37. Moreau E.: A generalization of joint-diagonalization criteria for source separation. IEEE Trans. Signal Process. 49, 530-541 (2001).