Blind Identification of Complex Under-Determined Mixtures

  • Pierre Comon
  • Myriam Rajih
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3195)


Linear Mixtures of independent random variables (the so-called sources) are sometimes referred to as Under-Determined Mixtures (UDM) when the number of sources exceeds the dimension of the observation space. The algorithm proposed is able to identify algebraically a complex mixture of complex sources. It improves an algorithm proposed by the authors for mixtures received on a single sensor, also based on characteristic functions. Computer simulations demonstrate the ability of the algorithm to identify mixtures with typically 3 complex sources received on 2 sensors.


Source Separation Blind Source Separation Source Distribution Complex Source Linear Mixture 
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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  1. 1.
    Lewicki, M.S., Sejnowski, T.J.: Learning overcomplete representations. Neural Computation 12, 337–365 (2000)CrossRefGoogle Scholar
  2. 2.
    Kagan, A.M., Linnik, Y.V., Rao, C.R.: Characterization Problems in Mathematical Statistics. Prob. Math. Stat. Wiley, New York (1973)Google Scholar
  3. 3.
    Comon, P.: Tensor decompositions. In: McWhirter, J.G., Proudler, I.K. (eds.) Mathematics in Signal Processing V, pp. 1–24. Clarendon Press, Oxford (2002)Google Scholar
  4. 4.
    Sidiropoulos, N.D., Bro, R.: On the uniqueness of multilinear decomposition of N-way arrays. Jour. Chemo. 14, 229–239 (2000)CrossRefGoogle Scholar
  5. 5.
    Kruskal, J.B.: Three-way arrays: Rank and uniqueness of trilinear decompositions. Linear Algebra and Applications 18, 95–138 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Comon, P., Rajih, M.: Blind Identification of Under-Determined Complex Mixtures of Independent Sources. In: IEEE SAM Conf., Barcelona (2004)Google Scholar
  7. 7.
    Cardoso, J.F.: Super-symmetric decomposition of the fourth-order cumulant tensor. Blind identification of more sources than sensors. In: ICASSP, Toronto, pp. 3109–3112 (1991)Google Scholar
  8. 8.
    Cao, X.R., Liu, R.W.: General approach to blind source separation. IEEE Trans. Sig. Proc. 44, 562–570 (1996)CrossRefGoogle Scholar
  9. 9.
    Comon, P.: Blind identification and source separation in 2x3 under-determined mixtures. IEEE Trans. Signal Processing, 11–22 (2004)Google Scholar
  10. 10.
    Taleb, A., Jutten, C.: On underdetermined source separation. In: ICASSP 1999, Phoenix, Arizona (1999)Google Scholar
  11. 11.
    Taleb, A.: An algorithm for the blind identification of N independent signals with 2 sensors. In: Sixth International Symposium on Signal Processing and its Applications (ISSPA 2001), Kuala-Lumpur, Malaysia, IEEE, Los Alamitos (2001)Google Scholar
  12. 12.
    De Lathauwer, L., Demoor, B., Vandewalle, J.: ICA techniques for more sources than sensors. In: Sixth Sig. Proc. Workshop on Higher Order Statistics, Caesarea, Israel (1999)Google Scholar
  13. 13.
    Szekely, G.J.: Identifiability of distributions of independent random variables by linear combinations and moments. Sankhya, Indian Jour. Stat. 62, 193–202 (2000)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Eriksson, J., Koivunen, V.: Identifiability and separability of linear ICA models revisited. In: 4th Int. Symp. ICA, Nara, Japan (2003)Google Scholar
  15. 15.
    Grellier, O., Comon, P.: Performance of blind discrete source separation. In: Eusipco, vol. IV, Rhodes, Greece, pp. 2061–2064 (1998) (invited session)Google Scholar
  16. 16.
    Albera, L., Ferreol, A., et al.: Sixth order blind identification of underdetermined mixtures - BIRTH. In: 4th Int. Symp. ICA, Nara, Japan (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Pierre Comon
    • 1
  • Myriam Rajih
    • 1
  1. 1.Lab. I3S, Algorithms/Euclide/BSophia-Antipolis cedexFrance

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