- Research Article
- Open Access
Underdetermined Blind Audio Source Separation Using Modal Decomposition
EURASIP Journal on Audio, Speech, and Music Processing volume 2007, Article number: 085438 (2007)
This paper introduces new algorithms for the blind separation of audio sources using modal decomposition. Indeed, audio signals and, in particular, musical signals can be well approximated by a sum of damped sinusoidal (modal) components. Based on this representation, we propose a two-step approach consisting of a signal analysis (extraction of the modal components) followed by a signal synthesis (grouping of the components belonging to the same source) using vector clustering. For the signal analysis, two existing algorithms are considered and compared: namely the EMD (empirical mode decomposition) algorithm and a parametric estimation algorithm using ESPRIT technique. A major advantage of the proposed method resides in its validity for both instantaneous and convolutive mixtures and its ability to separate more sources than sensors. Simulation results are given to compare and assess the performance of the proposed algorithms.
Nandi AK (Ed): Blind Estimation Using Higher-Order Statistics. Kluwer Academic, Boston, Mass, USA; 1999.
Cichocki A, Amari S: Adaptive Blind Signal and Image Processing. John Wiley & Sons, Chichester, UK; 2003.
Cardoso J-F: Blind signal separation: statistical principles. Proceedings of the IEEE 1998,86(10):2009-2025. 10.1109/5.720250
Sugden P, Canagarajah N: Underdetermined noisy blind separation using dual matching pursuits. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '04), May 2004, Montreal, Que, Canada 5: 557-560.
Sugden P, Canagarajah N: Underdetermined blind separation using learned basis function sets. Electronics Letters 2003,39(1):158-160. 10.1049/el:20030101
Comon P: Blind identification and source separation in 2 × 3 under-determined mixtures. IEEE Transactions on Signal Processing 2004,52(1):11-22. 10.1109/TSP.2003.820073
Belouchrani A, Cardoso JF: A maximum likelihood source separation for discrete sources. Proceedings of the 7th European Signal Processing Conference (EUSIPCO '94), September 1994, Scotland, UK 2: 768-771.
Peterson JM, Kadambe S: A probabilistic approach for blind source separation of underdetermined convolutive mixtures. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '03), April 2003, Hong Kong 6: 581-584.
Low SY, Nordholm S, Togneri R: Convolutive blind signal separation with post-processing. IEEE Transactions on Speech and Audio Processing 2004,12(5):539-548. 10.1109/TSA.2004.832993
Khor LC, Woo WL, Dlay SS: Non-sparse approach to underdetermined blind signal estimation. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 5: 309-312.
Georgiev P, Theis F, Cichocki A: Sparse component analysis and blind source separation of underdetermined mixtures. IEEE Transactions on Neural Networks 2005,16(4):992-996. 10.1109/TNN.2005.849840
Takigawa I, Kudo M, Toyama J: Performance analysis of minimum ℓ 1 -norm solutions for underdetermined source separation. IEEE Transactions on Signal Processing 2004,52(3):582-591. 10.1109/TSP.2003.822284
Linh-Trung N, Belouchrani A, Abed-Meraim K, Boashash B: Separating more sources than sensors using time-frequency distributions. EURASIP Journal on Applied Signal Processing 2005,2005(17):2828-2847. 10.1155/ASP.2005.2828
Yilmaz Ö, Rickard S: Blind separation of speech mixtures via time-frequency masking. IEEE Transactions on Signal Processing 2004,52(7):1830-1846. 10.1109/TSP.2004.828896
Li Y, Amari S-I, Cichocki A, Ho DWC, Xie S: Underdetermined blind source separation based on sparse representation. IEEE Transactions on Signal Processing 2006,54(2):423-437.
Huang NE, Shen Z, Long SR, et al.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proceedings of the Royal Society of London. Series A 1998,454(1971):903-995. 10.1098/rspa.1998.0193
Flandrin P, Rilling G, Gonçalvès P: Empirical mode decomposition as a filter bank. IEEE Signal Processing Letters 2004,11(2, part 1):112-114. 10.1109/LSP.2003.821662
Boyer R, Abed-Meraim K: Audio modeling based on delayed sinusoids. IEEE Transactions on Speech and Audio Processing 2004,12(2):110-120. 10.1109/TSA.2003.819953
Nieuwenhuijse J, Heusens R, Deprettere EdF: Robust exponential modeling of audio signals. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '98), May 1998, Seattler, Wash, USA 6: 3581-3584.
Nuzillard D, Nuzillard J-M: Application of blind source separation to 1-D and 2-D nuclear magnetic resonance spectroscopy. IEEE Signal Processing Letters 1998,5(8):209-211. 10.1109/97.704974
Park H, Van Huffel S, Elden L: Fast algorithms for exponential data modeling. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '94), April 1994, Adelaide, SA, Australia 4: 25-28.
Serviere C, Capdevielle V, Lacoume J-L: Separation of sinusoidal sources. Proceedings of IEEE Signal Processing Workshop on Higher-Order Statistics, July 1997, Banff, Canada 344-348.
O'Grady PD, Pearlmutter BA, Rickard ST: Survey of sparse and non-sparse methods in source separation. International Journal of Imaging Systems and Technology 2005,15(1):18-33. 10.1002/ima.20035
Frank IE, Todeschini R: The Data Analysis Handbook. Elsevier Science, Amsterdam, The Netherlands; 1994.
Rilling G, Flandrin P, Gonçalvès P: Empirical mode decomposition. http://perso.ens-lyon.fr/patrick.flandrin/emd.html
Kung SY, Arun KS, Bhaskar Rao DV: State space and singular value decomposition based on approximation methods for harmonic retrieval. Journal of the Optical Society of America 1983,73(12):1799-1811. 10.1364/JOSA.73.001799
Rosier J, Grenier Y: Unsupervised classification techniques for multipitch estimation. Proceedings of the 116th Convention of the Audio Engineering Society (AES '04), May 2004, Berlin, Germany
Huang Y, Benesty J, Chen J: A blind channel identification-based two-stage approach to separation and dereverberation of speech signals in a reverberant environment. IEEE Transactions on Speech and Audio Processing 2005,13(5, part 2):882-895.
Albouy B, Deville Y: Alternative structures and power spectrum criteria for blind segmentation and separation of convolutive speech mixtures. Proceedings of the 4th International Symposium on Independent Component Analysis and Blind Signal Separation (ICA '03), April 2003, Nara, Japan 361-366.
Wax M, Kailath T: Detection of signals by information theoretic criteria. IEEE Transactions on Acoustics, Speech, and Signal Processing 1985,33(2):387-392. 10.1109/TASSP.1985.1164557
Xu G, Liu H, Tong L, Kailath T: A least-squares approach to blind channel identification. IEEE Transactions on Signal Processing 1995,43(12):2982-2993. 10.1109/78.476442
Aïssa-El-Bey A, Grebici M, Abed-Meraim K, Belouchrani A: Blind system identification using cross-relation methods: further results and developments. Proceedings of the 7th International Symposium on Signal Processing and Its Applications (ISSPA '03), July 2003, Paris, France 1: 649-652.
Ahmad R, Khong AWH, Naylor PA: Proportionate frequency domain adaptive algorithms for blind channel identification. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '06), May 2006, Toulouse, France 5: 29-32.
De Lathauwer L, De Moor B, Vandewalle J: ICA techniques for more sources than sensors. Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, June 1999, Caesarea, Israel 121-124.
Jensen J, Heusdens R: A comparison of sinusoidal model variants for speech and audio representation. Proceedings of the 11th European Signal Processing Conference (EUSIPCO '02), September 2002, Toulouse, France 1: 479-482.
Ikram MZ: Blind separation of delayed instantaneous mixtures: a cross-correlation based approach. Proceedings of the 2nd IEEE International Symposium on Signal Processing and Information Technology (ISSPIT '02), December 2002, Marrakesh, Morocco
Qiu W, Hua Y: Performance comparison of subspace and cross-relation methods for blind channel identification. Signal Processing 1996,50(1-2):71-81. 10.1016/0165-1684(96)00010-2
Aïssa-El-Bey A, Abed-Meraim K, Grenier Y: Blind separation of audio sources using modal decomposition. Proceedings of the 8th International Symposium on Signal Processing and Its Applications (ISSPA '05), August 2005, Sydney, Australia 2: 451-454.
Aïssa-El-Bey A, Abed-Meraim K, Grenier Y: Séparation aveugle sous-déterminée de sources audio par la méthode EMD (Empirical Mode Decomposition). Actes 20e Colloque GRETSI sur le Traitement du Signal et des Images, September 2005, Louvain-La-Neuve, Belgium 2: 1233-1236.