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Blind Source Separation

  • V. Zarzoso
  • A. K. Nandi
Chapter

Abstract

A myriad of applications require the extraction of a set of signals which are not directly accessible. Instead, this extraction must be carried out from another set of measurements which were generated as mixtures of the initial set. Since usually neither the original signals — called sources — nor the mixing transformation are known, this is certainly a challenging problem of multichannel blind estimation. One of the most typical examples is the socalled “ cocktail party” problem. In this situation, any person attending the party can hear the speech of the speaker they want to listen to, together with surrounding sounds coming from other ’ competing’ speakers, music, background noises, etc. Everybody has experienced how the human brain is able to separate all these incoming sound signals and to ’ switch’ to the desired one. Similar results can be achieved by adequately processing the output signals of an array of microphones, as long as the signals to be extracted fulfil certain conditions [62, 63] . Wireless communications is another usual application field of signal separation techniques. In a CDMA (Code Division Multiple Access) environment several users share the same radio channel by transmitting their signal after modifying it according to an appropriate code. Traditionally, the extraction of the desired signal at the receiving end requires the knowledge of the corresponding code.

Keywords

Singular Value Decomposition Independent Component Analysis Independent Component Analysis Source Separation Blind Source Separation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    E. Bacharakis. Separation of Maternal and Foetal ECG using Blind Source Separation Methods. Master’ s thesis, University of Strathclyde, Glasgow, Scotland, UK, September 1995.Google Scholar
  2. [2]
    E. Bacharakis, A. K. Nandi, and V. Zarzoso. Foetal ECG Extraction using Blind Source Separation Methods. In Proceedings EUSIPCO’ 96, pages 395–398, Trieste, Italy, 10th-13th September 1996.Google Scholar
  3. [3]
    A. J. Bell and T. J. Sejnowski. An Information-Maximization Approach to Blind Separation and Blind Deconvolution. Neural Computation, 7(6):1129–1159, 1995.CrossRefGoogle Scholar
  4. [4]
    A. Belouchrani, K. Abed-Meraim, J.-F. Cardoso, and E. Moulines. A Blind Source Separation Technique using Second-Order Statistics. IEEE Transactions on Signal Processing, SP-45 (2):434–444, February 1997.CrossRefGoogle Scholar
  5. [5]
    A. Belouchrani and J.-F. Cardoso. Maximum Likelihood Source Separation for Discrete Sources. In Proceedings EUSIPCO’ 94, pages 768–771, Edinburgh, Scotland, UK, September 1994.Google Scholar
  6. [6]
    E. Biglieri and K. Yao. Some Properties of Singular Value Decomposition and their Applications to Digital Signal Processing. Signal Processing, 18(3):277–289, November 1989.MathSciNetCrossRefGoogle Scholar
  7. [7]
    D. R. Brillinger. Time Series. Data Analysis and Theory. Holden-Day Inc., San Francisco, 1981.zbMATHGoogle Scholar
  8. [8]
    D. Callaerts, B. D. Moor, J. Vandewalle, W. Sansen, G. Vantrappen, and J. Janssens. Comparison of SVD Methods to Extract the Foetal Electrocardiogram from Cutaneous Electrode Signals. Medical & Biological Engineering & Computing, 28:217–224, May 1990.CrossRefGoogle Scholar
  9. [9]
    X.-R. Cao and R. Liu. General Approach to Blind Source Separation. IEEE Transactions on Signal Processing, SP-44 (3):562–571, March 1996.Google Scholar
  10. [10]
    J.-F. Cardoso. Blind Identification of Independent Components with Higher-Order Statistics. In Proceedings Workshop on Higher-Order Spectral Analysis, pages 157–160, Vail, Colorado, June 1989.CrossRefGoogle Scholar
  11. [11]
    J.-F. Cardoso. Source Separation using Higher-Order Moments. In Proceedings ICASSP’ 89, pages 2109–2112, Glasgow, Scotland, UK, 23rd— 26th May 1989.Google Scholar
  12. [12]
    J.-F. Cardoso. On the Performance of Orthogonal Source Separation Algorithms. In Proceedings EUSIPCO’ 94, pages 776–779, Edinburgh, Scotland, UK, September 1994.Google Scholar
  13. [13]
    J.-F. Cardoso. The Invariant Approach to Source Separation. In Proceedings NOLTA ’ 95, pages 55–60, 1995.Google Scholar
  14. [14]
    J.-F. Cardoso. Performance and Implementation of Invariant Source Separation Algorithms. In Proceedings ISCAS’ 96, 1996.Google Scholar
  15. [15]
    J.-F. Cardoso. Infomax and Maximum Likelihood in Blind Source Separation. IEEE Signal Processing Letters, 4(4):112–114, April 1997.CrossRefGoogle Scholar
  16. [16]
    J.-F. Cardoso. Statistical Principles of Source Separation. In Proceedings IFAC SYSID’ 97, pages 1837–1844, Fukuoka, Japan, 1997.Google Scholar
  17. [17]
    J.-F. Cardoso and B. H. Laheld. Equivariant Adaptive Source Separation. IEEE Transactions on Signal Processing, SP-44(12):3017–3030, December 1996.CrossRefGoogle Scholar
  18. [18]
    J.-F. Cardoso and A. Souloumiac. Blind Beamforming for non-Gaussian Signals. IEE Proceedings-F, 140(6):362–370, December 1993.Google Scholar
  19. [19]
    E. Chaumette, P. Comon, and D. Muller. ICA-Based Technique for Radiating Sources Estimation: Application to Airport Surveillance. IEE Proceedings-F, 140(6):395–401, December 1993.Google Scholar
  20. [20]
    R. M. Clemente and J. I. Acha. Blind Separation of Sources using a New Polynomial Equation. IEE Electronics Letters, 33(3):176–177, 30th January 1997.CrossRefGoogle Scholar
  21. [21]
    P. Comon. Separation of Sources using Higher-Order Cumulants. In SPIE Vol. 1152 Advanced Algorithms and Architectures for Signal Processing IV, pages 170–181, 1989.CrossRefGoogle Scholar
  22. [22]
    P. Comon. Separation of Stochastic Processes. In Proceedings Workshop on Higher-Order Spectral Analysis, pages 174–179, Vail, Colorado, June 1989.CrossRefGoogle Scholar
  23. [23]
    P. Comon. Statistical Approach to the Jutten-Herault Algorithm. In Proceedings NATO Workshop on Neuro-Computing, Les Arcs, France, 27th February — 3rd March 1989. Republished in: Neurocomputing. Algorithms, Architectures and Applications, F. Fogelman and J. Herault (Eds.), NATO ASI Series, pp. 81–88, Springer Verlag, 1990.Google Scholar
  24. [24]
    P. Comon. Independent Component Analysis, A New Concept? Signal Processing, 36 (3): 287–314, April 1994.zbMATHCrossRefGoogle Scholar
  25. [25]
    P. Comon. Tensor Diagonalization, A Useful Tool in Signal Processing. In Proceedings IFAC SYSID’ 94, pages 77–82, Copenhagen, July 1994.Google Scholar
  26. [26]
    P. Comon, C. Jutten, and J. Herault. Blind Separation of Sources, Part II: Problems Statement. Signal Processing, 24(1):11–20, November 1991.zbMATHCrossRefGoogle Scholar
  27. [27]
    T. M. Cover and J. A. Thomas. Elements of Information Theory. John Wiley & Sons, Inc., New York, 1991.zbMATHCrossRefGoogle Scholar
  28. [28]
    M. Gaeta and J.-L. Lacoume. Sources Separation without a priori Knowledge: the Maximum Likelihood Solution. In Proceedings EU-SIPCO’ 90, pages 621–624, Barcelona, 1990.Google Scholar
  29. [29]
    G. H. Golub and C. F. V. Loan. Matrix Computations. The Johns Hopkins University Press, Baltimore, Maryland, 2nd edition, 1989.zbMATHGoogle Scholar
  30. [30]
    F. Harroy and J.-L. Lacoume. Maximum Likelihood Estimators and Cramer-Rao Bounds in Source Separation. Signal Processing, 55:167–177, December 1996.zbMATHCrossRefGoogle Scholar
  31. [31]
    F. Harroy, J.-L. Lacoume, and M. A. Lagunas. A General Adaptive Algorithm for nonGaussian Source Separation without any Constraint. In Proceedings EUSIPCO’ 94, pages 1161–1164, Edinburgh, Scotland, UK, September 1994.Google Scholar
  32. [32]
    R. A. Johnson and D. W. Wichern. Applied Multivariate Statistical Analysis. Prentice Hall, Englewood Cliffs, New Jersey, 2nd edition, 1988.zbMATHGoogle Scholar
  33. [33]
    C. Jutten and J. Herault. Une Solution Neuromimétique au Problème de Séparation de Sources. Traitement du Signal, 5(6):389–404, 1989.Google Scholar
  34. [34]
    C. Jutten and J. Herault. Blind Separation of Sources, Part I: An Adaptive Algorithm Based on Neuromimetic Architecture. Signal Processing, 24 (1) :1–10, November 1991.zbMATHCrossRefGoogle Scholar
  35. [35]
    J.-L. Lacoume and P. Ruiz. Sources Identification: A Solution Based on the Cumulants. In Proceedings IEEE ASSP Workshop, Minneapolis, August 1988.Google Scholar
  36. [36]
    J.-L. Lacoume and P. Ruiz. Separation of Independent Sources from Correlated Inputs. IEEE Transactions on Signal Processing, SP-40(12):3074–3078, December 1992.CrossRefGoogle Scholar
  37. [37]
    B. H. Laheld and J.-F. Cardoso. Adaptive Source Separation with Uniform Performance. In Proceedings EUSIPCO’ 94, pages 183–186, Edinburgh, Scotland, UK, September 1994.Google Scholar
  38. [38]
    L. D. Lathauwer, D. Callaerts, B. D. Moor, and J. Vandewalle. Fetal Electrocardiogram Extraction by Source Subspace Separation. In Proceedings IEEE/ATHOS Signal Processing Conference on Higher-Order Statistics, pages 134–138, Spain, June 1995.Google Scholar
  39. [39]
    L. D. Lathauwer, B. D. Moor, and J. Vandewalle. Blind Source Separation by Higher-Order Singular Value Decomposition. In Proceedings EU-SIPCO’ 94, pages 175–178, Edinburgh, Scotland, UK, September 1994.Google Scholar
  40. [40]
    A. Mansour and C. Jutten. Fourth-Order Criteria for Blind Sources Separation. IEEE Transactions on Signal Processing, SP-43(8):2022–2025, August 1995.CrossRefGoogle Scholar
  41. [41]
    A. Mansour and C. Jutten. A Direct Solution for Blind Separation of Sources. IEEE Transactions on Signal Processing, SP-44(3):746–748, March 1996.CrossRefGoogle Scholar
  42. [42]
    K. V. Mardia, J. T. Tent, and J. M. Bibby. Multivariate Analysis. Academic Press, London, 1979.zbMATHGoogle Scholar
  43. [43]
    P. McCullagh. Tensor Methods in Statistics. Monographs on Statistics and Applied Probability. Chapman and Hall, London, 1987.zbMATHGoogle Scholar
  44. [44]
    J. M. Mendel. Tutorial on Higher-Order Statistics (Spectra) in Signal Processing and System Theory: Theoretical Results and Some Applications. Proceedings of the IEEE, 79(3):278–305, March 1991.CrossRefGoogle Scholar
  45. [45]
    A. K. Nandi and V. Zarzoso. Fourth-Order Cumulant Based Blind Source Separation. IEEE Signal Processing Letters, 3(12):312–314, December 1996.CrossRefGoogle Scholar
  46. [46]
    A. K. Nandi and V. Zarzoso. Foetal ECG Separation. In IEE Colloquium on the Use of Model Based Digital Signal Processing Techniques in the Analysis of Biomedical Signals, pages 8/1–8/6, Savoy Place, London, 16th April 1997.Google Scholar
  47. [47]
    C. L. Nikias and A. P. Petropulu. Higher-Order Spectra Analysis. A Nonlinear Signal Processing Framework. Signal Processing Series. Prentice Hall, Englewood Cliffs, New Jersey, 1993.zbMATHGoogle Scholar
  48. [48]
    T. Oostendorp. Modelling the Fetal ECG. PhD thesis, K. U. Nijmegen, The Netherlands, 1989.Google Scholar
  49. [49]
    D. T. Pham. Blind Separation of Instantaneous Mixture of Sources via an Independent Component Analysis. IEEE Transactions on Signal Processing, SP-44(11):2768–2779, November 1996.CrossRefGoogle Scholar
  50. [50]
    D. T. Pham, P. Garat, and C. Jutten. Separation of a Mixture of Independent Sources through a Maximum-Likelihood Approach. In Proceedings EUSIPCO’ 92, pages 771–774, Brussels, 1992.Google Scholar
  51. [51]
    R. Plonsey. Bioelectric Phenomena. McGraw-Hill, New York, 1969.Google Scholar
  52. [52]
    R. Plonsey and R. C. Barr. Bioelectricity: A Quantitative Approach. Plenum Press, New York, 1988.Google Scholar
  53. [53]
    R. Roy and T. Kailath. ESPRIT — Estimation of Signal Parameters via Rot a t io nal I nva r ia nce Techniques. IEEE Trans ac t ions on Aco u st ics, Speech, and Signal Processing, ASSP-37(7):984–995, July 1989.CrossRefGoogle Scholar
  54. [54]
    L. L. Scharf. Statistical Signal Processing. Detection, Estimation and Time Series Analysis. Addison-Wesley, Inc., 1991.zbMATHGoogle Scholar
  55. [55]
    R. O. Schmidt. Multiple Emitter Location and Signal Parameter Estimation. IEEE Transactions on Antennas and Propagation, AP-34(3):276–280, March 1986.CrossRefGoogle Scholar
  56. [56]
    E. Sorouchyari. Blind Separation of Sources, Part III: Stability Analysis. Signal Processing, 24(1) :21–29, November 1991.zbMATHCrossRefGoogle Scholar
  57. [57]
    A. Stuart and J. K. Ord. Kendall’ s Advanced Theory of Statistics, volume I. Edward Arnold, London, 6th edition, 1994.Google Scholar
  58. [58]
    L. Tong, Y. Inouye, and R. Liu. Waveform-Preserving Blind Estimation of Multiple Independent Sources. IEEE Transactions on Signal Processing, SP-41(7):2461–2470, July 1993.CrossRefGoogle Scholar
  59. [59]
    L. Tong, R. Liu, V. C. Soon, and Y.-F. Huang. Indeterminacy and Identifiability of Blind Identification. IEEE Transactions on Signal Processing, SP-38(5):499–509, May 1991.Google Scholar
  60. [60]
    L. Tong, S. Yu, Y. Inouye, and R. Liu. A Necessary and Sufficient Condition of Blind Identification. In Proceedings International Signal Processing Workshop on Higher-Order Statistics, pages 261–264, Chamrousse, France, 10th-12th July 1991.Google Scholar
  61. [61]
    J. Vanderschoot, D. Callaerts, W. Sansen, J. Vandewalle, G. Vantrappen, and J. Janssens. Two Methods for Optimal MECG Elimination and FECG Detection from Skin Electrode Signals. IEEE Transactions on Biomedical Engineering, BME-34(3):233–243, March 1987.CrossRefGoogle Scholar
  62. [62]
    E. Weinstein, M. Feder, and A. V. Oppenheim. Multi-Channel Signal Separation by Decorrelation. IEEE Transactions on Speech and Audio Processing, SAAP-1(4):405–413, October 1993.CrossRefGoogle Scholar
  63. [63]
    D. Yellin and E. Weinstein. Criteria for Multichannel Signal Separation. IEEE Transactions on Signal Processing, SP-42(8):2158–2168, August 1994.CrossRefGoogle Scholar
  64. [64]
    D. Yellin and E. Weinstein. Multichannel Signal Separation: Methods and Analysis. IEEE Transactions on Signal Processing, SP-44(1):106–118, January 1996.CrossRefGoogle Scholar
  65. [65]
    V. Zarzoso and A. K. Nandi. The Potential of Decorrelation in Blind Separation of Sources Based on Cumulants. In Proceedings ECSAP’ 97, pages 293–296, Prague, Czech Republic, 24th-27th June 1997.Google Scholar
  66. [66]
    V. Zarzoso and A. K. Nandi. Generalization of a Maximum-Likelihood Approach to Blind Source Separation. In Proceedings EUSIPCO’ 98, volume IV, pages 2069–2072, Rhodes, Greece, 8th-11th September 1998.Google Scholar
  67. [67]
    V. Zarzoso and A. K. Nandi. Modelling Signals of Arbitrary Kurtosis for Testing BSS Methods. IEE Electronics Letters, 34(1):29–30, 8th January 1998. Errata: Vol. 34, No. 7, 2nd April 1998, p. 703.CrossRefGoogle Scholar
  68. [68]
    V. Zarzoso, A. K. Nandi, and E. Bacharakis. Maternal and Foetal ECG Separation using Blind Source Separation Methods. IMA Journal of Mathematics Applied in Medicine & Biology, 14:207–225, 1997.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • V. Zarzoso
  • A. K. Nandi

There are no affiliations available

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