ICAR: a tool for blind source separation using fourth-order statistics only

The problem of blind separation of overdetermined mixtures of sources, that is, with fewer sources than (or as many sources as) sensors, is addressed in this paper. A new method, called Independent Component Analysis using Redundancies in the quadricovariance (ICAR), is proposed in order to process complex data. This method, without any whitening operation, only exploits some redundancies of a particular quadricovariance matrix of the data. Computer simulations demonstrate that ICAR offers in general good results and even outperforms classical methods in several situations: ICAR i) succeeds in separating sources with low signal-to-noise ratios, ii) does not require sources with different second-order or/and first-order spectral densities, iii) is asymptotically not affected by the presence of a Gaussian noise with unknown spatial correlation, iv) is not sensitive to an over estimation of the number of sources.

[1]  R.C. Johnson,et al.  Introduction to adaptive arrays , 1982, Proceedings of the IEEE.

[2]  J.E. Mazo,et al.  Digital communications , 1985, Proceedings of the IEEE.

[3]  Christian Jutten,et al.  Detection de grandeurs primitives dans un message composite par une architecture de calcul neuromime , 1985 .

[4]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[5]  Zhi-Dong Bai,et al.  Remarks on certain criteria for detection of number of signals , 1987, IEEE Trans. Acoust. Speech Signal Process..

[6]  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.

[7]  Björn E. Ottersten,et al.  Sensor array processing based on subspace fitting , 1991, IEEE Trans. Signal Process..

[8]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[9]  Eric Moreau,et al.  New self-adaptative algorithms for source separation based on contrast functions , 1993, [1993 Proceedings] IEEE Signal Processing Workshop on Higher-Order Statistics.

[10]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[11]  P. Chevalier.  Performances des separateurs aveugles de sources aux ordres superieurs , 1995 .

[12]  Jerry M. Mendel,et al.  Applications of cumulants to array processing - I. Aperture extension and array calibration , 1995, IEEE Trans. Signal Process..

[13]  Nathalie Delfosse,et al.  Adaptive blind separation of independent sources: A deflation approach , 1995, Signal Process..

[14]  Antoine Souloumiac,et al.  Jacobi Angles for Simultaneous Diagonalization , 1996, SIAM J. Matrix Anal. Appl..

[15]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[16]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .

[17]  Pierre Comon,et al.  Improved contrast dedicated to blind separation in communications , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[18]  Anne Ferréol,et al.  Higher order blind source separation using the cyclostationarity property of the signals , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[19]  B. De Moor,et al.  ICA algorithms for 3 sources and 2 sensors , 1999, Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics. SPW-HOS '99.

[20]  Anne Ferréol,et al.  On the virtual array concept for the fourth-order direction finding problem , 1999, IEEE Trans. Signal Process..

[21]  Liqing Zhang,et al.  Natural gradient algorithm for blind separation of overdetermined mixture with additive noise , 1999, IEEE Signal Processing Letters.

[22]  Pierre Comon,et al.  Performance of HO Blind Source Separation Methods: Experimental Results on Ionospheric HF Links , 1999 .

[23]  Pascal Chevalier,et al.  Optimal separation of independent narrow-band sources: Concept and performance , 1999, Signal Process..

[24]  Joos Vandewalle,et al.  Fetal electrocardiogram extraction by blind source subspace separation , 2000, IEEE Transactions on Biomedical Engineering.

[25]  Anne Ferréol,et al.  On the behavior of current second and higher order blind source separation methods for cyclostationary sources , 2000, IEEE Trans. Signal Process..

[26]  Konstantinos I. Diamantaras,et al.  Blind separation of multiple binary sources using a single linear mixture , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[27]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis of Complex Valued Signals , 2000, Int. J. Neural Syst..

[28]  E. Moreau,et al.  New criteria for blind signal separation , 2000, Proceedings of the Tenth IEEE Workshop on Statistical Signal and Array Processing (Cat. No.00TH8496).

[29]  Anisse Taleb,et al.  An algorithm for the blind identification of N independent signals with 2 sensors , 2001, Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467).

[30]  Karim Abed-Meraim,et al.  Blind source-separation using second-order cyclostationary statistics , 2001, IEEE Trans. Signal Process..

[31]  Pierre Comon,et al.  From source separation to blind equalization, contrast-based approaches , 2001 .

[32]  Laurent Albera,et al.  Higher order blind separation of non zero-mean cyclostationary sources , 2002, 2002 11th European Signal Processing Conference.

[33]  Arie Yeredor,et al.  Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation , 2002, IEEE Trans. Signal Process..

[34]  Nobuhiko Kitawaki,et al.  Combined approach of array processing and independent component analysis for blind separation of acoustic signals , 2003, IEEE Trans. Speech Audio Process..

[35]  Laurent Albera,et al.  SIXTH ORDER BLIND IDENTIFICATION OF UNDERDETERMINED MIXTURES (BIRTH) OF SOURCES , 2003 .

[36]  Laurent Albera,et al.  Second-order blind separation of first- and second-order cyclostationary sources-application to AM, FSK, CPFSK, and deterministic sources , 2004, IEEE Transactions on Signal Processing.

[37]  Visa Koivunen,et al.  Identifiability, separability, and uniqueness of linear ICA models , 2004, IEEE Signal Processing Letters.

[38]  Laurent Albera,et al.  ICAR: independent component analysis using redundancies , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

[39]  Pierre Comon,et al.  Blind identification and source separation in 2×3 under-determined mixtures , 2004, IEEE Trans. Signal Process..

[40]  Laurent Albera,et al.  On the virtual array concept for higher order array processing , 2005, IEEE Transactions on Signal Processing.

[41]  Laurent Albera,et al.  Fourth-order blind identification of underdetermined mixtures of sources (FOBIUM) , 2005, IEEE Transactions on Signal Processing.