Gradient-based joint block diagonalization algorithms: Application to blind separation of FIR convolutive mixtures

Signal Processing

Volumn 90, Issue 6, 2010, Pages 1836-1849

  Ghennioui, Hicham ^a,b   Thirion Moreau, Nadège ^a   Moreau, Eric ^a   Aboutajdine, Driss ^b  

^a UNIVERSITÉ DE TOULON   (France)

^b Mohammed V University in Rabat   (Morocco)

Author keywords

Blind sources separation; Convolutive mixtures of correlated sources; Joint block diagonalization; Matrix decompositions; Spatial quadratic time frequency distributions and spectra

Indexed keywords

FIR FILTERS; IMPULSE RESPONSE; MIXTURES;

BLIND SOURCES SEPARATIONS; CORRELATED SOURCES; JOINT BLOCK DIAGONALIZATION; MATRIX DECOMPOSITION; QUADRATIC TIME-FREQUENCY;

BLIND SOURCE SEPARATION;

EID: 76749083804     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2009.12.002     Document Type: Article

References (37)

1. P. Comon, C. Jutten (Eds.), Séparation de sources, Tome 1 Concepts de base et analyse en composates indépendantes & Tome 2 : Au-delà de l'aveugle et applications, Traité IC2, Editions Hermès, Lavoisier, Mars 2007.
2. A. Belouchrani, K. Abed-Meraïm, M. Amin, A. Zoubir, Joint anti-diagonalization for blind source separation, in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'2001), Salt Lake City, Utah, May 2001.
3. Belouchrani A., and Amin M.G. Blind source separation based on time-frequency signal representations. IEEE Transactions on Signal Processing 46 11 (November 1998) 2888-2897
4. H. Bousbiah-Salah, A. Belouchrani, K. Abed-Meraïm, Blind separation of non stationary sources using joint block diagonalization, in: Proceedings of the IEEE Workshop on Statistical Signal Processing, 2001, pp. 448-451.
5. Brewer J.W. Kronecker products and matrix calculus in system theory. IEEE Transactions on Circuits and Systems 25 9 (September 1978) 772-781
6. J.-F. Cardoso, On the performance of orthogonal sources separation algorithms, in: Proceedings of the European Signal Processing Conference (EUSIPCO'94), Edinburgh, Scotland, UK, September 1994, pp. 776-779.
7. Cardoso J.-F., and Souloumiac A. Blind beamforming for non Gaussian signals. IEEE Proceedings-F 40 (1993) 362-370
8. Cardoso J.-F., and Laheld B. Equivariant adaptative source separation. IEEE Transactions on Signal Processing 44 12 (December 1996) 3017-3030
9. Chabriel G., Barrère J., Thirion-Moreau N., and Moreau E. Algebraic joint zero-diagonalization and blind source separation. IEEE Transactions on Signal Processing 56 3 (March 2008) 980-989
10. Dégerine S., and Kane E. A comparative study of approximate joint diagonalization algorithms for blind source separation in presence of additive noise. IEEE Transactions on Signal Processing 55 6 (June 2007) 3022-3031
11. L. DeLathauwer, Signal processing based on multilinear algebra, Ph.D. Thesis, Leuven Catholic University, Belgium, September 1997.
12. L. DeLathauwer, C. Févotte, B. De Moor, J. Vandewalle, Jacobi algorithm for joint block diagonalization in blind identification, in: Proceedings of the 23rd Symposium on Information Theory in the Benelux, Louvain-la-Neuve, Belgium, May 2002.
13. Fadaili E.-M., Thirion-Moreau N., and Moreau E. Non orthogonal joint diagonalization/zero-diagonalization for source separation based on time-frequency distributions. IEEE Transactions on Signal Processing 55 5 (May 2007) 1673-1687
14. C. Févotte, C. Doncarli, A unified presentation of blind source separation methods for convolutive mixtures using block-diagonalization, in: Proceedings of the ICA, Nara, Japan, 2003.
15. Flandrin P. Time-Frequency/Time-Scale analysis (1998), Academic Press, New York
16. H. Ghennioui, N. Thirion-Moreau, E. Moreau, A. Adib, D. Aboutajdine, Non unitary joint-block diagonalization of complex matrices using a gradient approach, in: M.E. Davies et al. (Eds), Proceedings of the 7th International Conference on Independent Component Analysis and Signal Separation, Lecture Notes in Computer Science, vol. 4666, Springer, Berlin, Heidelberg, London, UK, September 2007, pp. 201-208.
17. Ghennioui H., Fadaili E.-M., Thirion-Moreau N., Adib A., and Moreau E. A non-unitary joint block diagonalization algorithm for blind separation of convolutive mixtures of sources. IEEE Signal Processing Letters 14 11 (November 2007) 860-863
18. Giulieri L., Ghennioui H., Thirion-Moreau N., and Moreau E. Non-orthogonal joint diagonalization of spatial quadratic time-frequency matrices for source separation. IEEE Signal Processing Letters 12 5 (May 2005) 415-418
19. Golub G.-H., and Van Loan C.-F. Matrix Computation (1989), Johns Hopkins, University Press, Baltimore, MD
20. Gorokhov A., and Loubaton Ph. Subspace based techniques for second order blind separation of convolutive mixtures with temporally correlated sources. IEEE Transactions on Circuit and Systems 44 9 (September 1997) 813-820
21. Grenier Y., and Aboutajdine D. Comparaison des représentations temps-fréquence de signaux présentant des sauts. Annales des Télécommunications 38 11-12 (1983) 429-442
22. Hjørungnes A., and Gesbert D. Complex-valued matrix differentiation: techniques and key results. IEEE Transactions on Signal Processing 55 6 (June 2007) 2740-2746
23. M. Joho, K. Rahbar, Joint diagonalization of correlation matrices by using Newton methods with application to blind signal separation, in: IEEE Sensor Array and Multichannel Signal Processing Workshop SAM, 2002, pp. 403-407.
24. Moreau E. A generalization of joint-diagonalization criteria for source separation. IEEE Transactions on Signal Processing 49 3 (March 2001) 530-541
25. Parra L., and Spence C. Convolutive blind source separation of non-stationary sources. IEEE Transactions on Speech and Audio Processing (May 2000) 320-327
26. Pham D.-T., and Servière C. Permutation correction in the frequency domain in blind separation of speech mixtures. Eurasip Journal on Applied Signal Processing 2006 (2006) 1-16
27. Pham D.-T. Joint approximate diagonalization of positive definite matrices. SIAM Journal on Matrix Analysis and Applications 22 4 (2001) 1136-1152
28. D.-T. Pham, Blind separation of cyclostationary sources using joint block approximate diagonalization, in: M.E. Davies et al. (Eds.), Proceedings of the Independent Component Analysis and Signal Separation (ICA 2007), Lecture Notes in Computer Science, vol. 4666, Springer, Berlin, Heidelberg, London, September 2007, pp. 244-251.
29. Rahbar K., and Reilly J. A frequency domain method for blind source separation of convolutive audio mixtures. IEEE Transactions on Speech Audio Processing 13 5 (September 2005) 832-844
30. Stankovic L., and Stankovic S. Wigner distribution of noisy signals. IEEE Transactions on Signal Processing 41 2 (February 1993) 956-960
31. Smaragdis P. Blind separation of convolved mixtures in the frequency domain. Neurocomputing 22 (1998) 21-34
32. Thirion-Moreau N., and Amin M. Time-frequency domain methods. In: Comon P., and Jutten C. (Eds). Handbook of Blind Source Separation, Independent Component Analysis and Applications (2009), Academic Press, New York
33. A.-J. Van Der Veen, Joint diagonalization via subspace fitting techniques, in: Proceedings of the International Conference on Acoustic Speech and Signal Processing (ICASSP'2001), Salt Lake City, USA, May 2001, pp. 2773-2776.
34. Yeredor A. Non-orthogonal joint diagonalization in the least square sense with application in blind source separation. IEEE Transactions on Signal Processing 50 7 (July 2002) 1545-1553
35. A. Yeredor, A. Ziehe, K.-R. Müller, Approximate joint diagonalization using a natural gradient approach, in Lecture Notes in Computer Science: Independent Component Analysis and Blind Sources Separation, Proceedings ICA, vol. 3195, Granada, Spain, Springer, Berlin, September 2004, pp. 89-96.
36. V. Zarzoso, P. Comon, Blind channel equalization with algebraic optimal stepsize, in: Proceedings of the EUSIPCO, Antalya, Turkey, September 2005.
37. Ziehe A., Laskov P., Nolte G., and Müller G.K.-R. A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation. Journal of Machine Learning Research 5 (July 2004) 801-818