论文信息 - On underdetermined source separation

On underdetermined source separation

This paper discusses some theoretical results on underdetermined source separation, i.e. when the mixing matrix is degenerate, especially when there is more sources than observations. In this case, we show that the sources can be restored up to an arbitrary additive random vector. In the particular case of discrete sources, very relevant for digital communications, we show that this vector is certain.

Christian Jutten | Anisse Taleb | C. Jutten | A. Taleb

[1] J. Marcinkiewicz. Sur une propriété de la loi de Gauß , 1939 .

[2] Petteri Pajunen,et al. A competitive learning algorithm for separating binary sources , 1997, ESANN.

[3] Georgios B. Giannakis,et al. Modeling of non-Gaussian array data using cumulants: DOA estimation of more sources with less sensors , 1993, Signal Process..

[4] D. Kendall. Random Variables and Probability Distributions (3Rd Ed.) , 1971 .

[5] G. Darmois,et al. Analyse générale des liaisons stochastiques: etude particulière de l'analyse factorielle linéaire , 1953 .

[6] J. Ord,et al. Characterization Problems in Mathematical Statistics , 1975 .

[7] H. Cramér. Random variables and probability distributions , 1937 .

[8] J. Cardoso,et al. Maximum Likelihood Source SeparationBy the Expectation-Maximization Technique : Deterministic and Stochastic Implementation , 1995 .

[9] Ruey-Wen Liu,et al. General approach to blind source separation , 1996, IEEE Trans. Signal Process..

[10] Jean-Francois Cardoso,et al. Super-symmetric decomposition of the fourth-order cumulant tensor. Blind identification of more sources than sensors , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[11] Calyampudi R. Rao,et al. Characterization Problems in Mathematical Statistics , 1976 .