Underdetermined blind source separation based on subspace representation

IEEE Transactions on Signal Processing

Volumn 57, Issue 7, 2009, Pages 2604-2614

  Kim, SangGyun ^a   Yoo, Chang D ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Generalized Gaussian distribution; Single source detection; Subspace representation; Underdetermined blind source separation (BSS)

Indexed keywords

CONVENTIONAL ALGORITHMS; DISTRIBUTION PARAMETERS; EXPECTATION-MAXIMIZATION ALGORITHMS; GENERALIZED GAUSSIAN DISTRIBUTION; GENERALIZED GAUSSIAN DISTRIBUTIONS; LOWER COMPLEXITY; MEAN SQUARE ERROR CRITERIONS; MIXING MATRIX; NOVEL ALGORITHM; ORTHOGONAL COMPONENTS; PSEUDO-INVERSE; SIGNAL TO INTERFERENCE RATIO; SINGLE SOURCE; SINGLE SOURCE DETECTION; SUBSPACE REPRESENTATION; SUPER-GAUSSIAN SOURCE DISTRIBUTION; SUPER-GAUSSIAN SOURCES; TIME FREQUENCY; UNDER-DETERMINED MIXTURES; UNDERDETERMINED BLIND SOURCE SEPARATION (BSS);

APARTMENT HOUSES; GAUSSIAN DISTRIBUTION; INDEPENDENT COMPONENT ANALYSIS; MEAN SQUARE ERROR; MIXING; SEPARATION; SIGNAL ANALYSIS; SIGNAL DETECTION; SPEECH ANALYSIS; STRAIN ENERGY;

BLIND SOURCE SEPARATION;

EID: 67650178769     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2017570     Document Type: Article

References (39)

1. S. Amari and A. Cichocki, "Adaptive blind signal processing, neural network approaches," Proc. IEEE, vol. 86, pp. 2026-2048, Oct. 1998.
2. A. Mansour, A. K. Barros, and N. Ohnishi, "Blind separation of sources: Methods, assumptions and applications," IEICE Trans. Fund. Electron., Commun., Comput. Sci., vol. E83-A, pp. 1498-1512, 2000.
3. A. Cichocki and S. Amari, Adaptive Blind Signal and Image Processing New York: Wiley, 2003.
4. T. W. Lee, Independent Component Analysis. Norwell, MA: Kluwer, 1998.
5. 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, 1995.
6. J. F. Cardoso, "Blind signal processing: Statistical principles," Proc. IEEE, pp. 2009-2025, 1998.
7. 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.
8. S. Degerine and R. Malki, "Second-order blind separation of sources based on canonical partial innovations," IEEE Trans. Signal Process. vol. 48, no. 3, pp. 629-641, Mar. 2000.
9. S. Choi and A. Cichocki, "Blind separation of non-stationary sources in noisy mixtures," Electron. Lett., vol. 36, no. 9, pp. 849-850, 2000.
10. D. T. Pham and J. F. Cardoso, "Blind separation of instantaneous mixtures of non-stationary sources," IEEE Trans. Signal Process., vol. 49, no. 9, pp. 1837-1848, Sep. 2001.
11. S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol. 20, no. 1, pp. 33-61, 1998.
12. D. L. Donoho and M, Elad, "Maximal sparsity representation via l 1 minimization," Proc. Nat. Acad. Sci., vol. 100, pp. 2197-2202, 2003.
13. M. S. Lewicki and T. J. Sejnowski, "Learning overcomplete representations," Neural Comput., vol. 12, pp. 337-365, 2000.
14. T. W. Lee, M. S. Lewicki, M. Girolami, and T. J. Sejnowski, "Blind source separation of more sources than mixtures using overcomplete representation," IEEE Signal Process. Lett, vol. 6, no. 4, pp, 87-90, 1999.
15. M. Zibulevsky and B. A. Pearlmutter, "Blind source separation by sparse decomposition," Neural Comput., vol. 13, no. 4, pp. 863-882, 2001.
16. M. Girolami, "A variational method for learning sparse and overcomplete representations," Neural Comput., vol. 13, pp. 2517-2532, 2001.
17. Y, Li, A. Cichocki, and S. Amari, "Sparse component analysis for blind source separation with less sensors than sources," in Proc. 4th Int. Symp. Independent Component Analysis Blind Signal Separation, 2003, pp. 89-94.
18. O. Yilmaz and S. Rickard, "Blind separation of speech mixtures via time-frequency masking," IEEE Trans. Signal Process., vol. 52, no. 7, pp. 1830-1847, Jul. 2004.
19. A. Aissa-El-Bey, N. Linh-Trung, K. Abed-Meraim, A. Belouchrani, and Y. Grenier, "Underdetermined blind separation of nondisjoint sources in the time-frequency domain," IEEE Trans. Signal Process., vol. 55, no. 3, pp. 897-907, Mar. 2007.
20. A. T. Cemgil, C. Fevotte, and S. J. Godsill, "Variational and stochastic inference for Bayesian source separation," Digit. Signal Process., vol. 17, pp. 891-913, 2007.
21. A. T. Cemgil, C. Fevotte, and S. J. Godsill, "Blind separation of sparse sources using variational EM," in Proc. 13th Eur. Signal Process. Conf., 2005.
22. H. Snoussi and J. Idier, "Bayesian blind separation of generalized hyperbolic processes in noisy and underdetermined mixtures," IEEE Trans. Signal Process., vol. 54, no. 9, pp. 3257-3269, Sep. 2006.
23. S. G. Kim and C. D. Yoo, "Underdetermined independent component analysis by data generation," in Proc. ICA, Granada, Spain, 2004, pp. 445-452.
24. S. G. Kim and C. D. Yoo, "Underdetermined blind source separation based on generalized Gaussian distribution," presented at the IEEE Int. Workshop MLSP, Maynooth, Ireland, 2006.
25. C. R. Rao and S. K. Mitra, Generalized Inverse of Matrices and its Applications. New York: Wiley, 1971.
26. D. Donoho, "The simplest solution to an underdetermined system of linear equations," in Proc. IEEE Int. Symp. Inform. Theory, 2006, pp. 1924-1928,
27. G. Strang, Introduction to Linear Algebra. Cambridge, MA: Wellesley-Cambridge, 2003.
28. T. K. Moon and W. C. Stirling, Mathematical Methods and Algorithms for Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 2000.
29. Y. Li, A. Cichocki, and S. Amari, "Analysis of sparse representation and blind source separation," Neural Comput., vol. 16, pp. 1193-1234, 2004.
30. Y. Li, S. Amari, A. Cichocki, D. W. C. Ho, and S. Xie, "Underdetermined blind source separation based on sparse representation," IEEE Trans. Signal Process., vol. 54, no. 2, pp. 423-437, Feb. 2006.
31. F. Abrard and Y. Deville, "A time-frequency blind signal separation method applicable to underdetermined mixtures of dependent sources," Signal Process., vol. 85, no. 7, pp. 1389-1403, 2005.
32. S. Choi, A. Cichocki, and S. Amari, "Flexible independent component analysis," J. VLSI Signal Process, vol. 26, pp. 25-38, 2000.
33. G. E. P. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis. Reading, MA: Addison-Wesley, 1973.
34. K. Kokkinakis and A. k. Nandi, "Exponent parameter estimation for generalized Gaussian probability density functions with application to speech modeling," Signal Process., vol. 85, pp. 1852-1858, 2005.
35. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via EM algorithm," J. Roy. Stat. Soc., vol. 39, no. Ser. B, pp. 1-38, 1977.
36. G. C. Wei and M. A. Tanner, "A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms," J. Amer. Stat. Assoc., vol. 85, no. 411, pp. 699-704, 1990.
37. G. S. Fishman, Monte Carlo: Concepts, Algorithms, and Applications New York: Springer-Verlag, 1995.
38. J. L. Melsa and D. L. Cobri, Decision and Estimation Theory. New York: McGraw-Hill, 1978.
39. I. F. Gorodnitsky and B. D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process, vol. 45, no. 3, pp. 600-616, Mar. 1997.