Blind source extraction in various ill-conditioned cases

The paper discusses blind source extraction in various ill-conditioned cases based on a simple extraction network model. Extractability is first analyzed for the following ill-conditioned cases: the mixing matrix is square but-singular; the number of sensors is smaller than that of sources; the number of sensors is larger than that of sources, but the column rank of the mixing matrix is deficient; the number of sources is unknown and the column rank of the mixing matrix is deficient. A necessary and sufficient condition for extractability is obtained. A cost function and an unsupervised learning algorithm for the extraction network model are developed. Simulation results are also presented to show the validity of the theoretical results and the performance and characteristics of the learning algorithm.

[1]  Shun-ichi Amari,et al.  Blind signal extraction using self-adaptive nonlinear Hebbian learning rule , 1996 .

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

[3]  Erkki Oja,et al.  Independent component analysis: algorithms and applications , 2000, Neural Networks.

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

[5]  Dong-Jo Park,et al.  Blind separation of sources using higher-order cumulants , 1999, Signal Process..

[6]  Jean-François Cardoso,et al.  Equivariant adaptive source separation , 1996, IEEE Trans. Signal Process..

[7]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[8]  E. Oja,et al.  Independent Component Analysis , 2013 .

[9]  Andrzej Cichocki,et al.  Adaptive Blind Signal and Image Processing - Learning Algorithms and Applications , 2002 .

[10]  S. Amari,et al.  A Cascade Neural Network for Blind Signal Extraction without Spurious Equilibria , 1998 .

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

[12]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[13]  Pierre Comon,et al.  Blind separation of sources, part II: Problems statement , 1991, Signal Process..

[14]  Christian Jutten,et al.  Fourth-order criteria for blind sources separation , 1995, IEEE Trans. Signal Process..

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

[16]  Esfandiar Sorouchyari,et al.  Blind separation of sources, part III: Stability analysis , 1991, Signal Process..

[17]  Andrzej Cichocki,et al.  Robust neural networks with on-line learning for blind identification and blind separation of sources , 1996 .

[18]  Pierre Comon.  Independent component analysis - a new concept? signal processing , 1994 .

[19]  Pierre Comon,et al.  Separation Of Sources Using Higher-Order Cumulants , 1989, Optics & Photonics.

[20]  Jacek M. Zurada,et al.  Blind extraction of singularly mixed source signals , 2000, IEEE Trans. Neural Networks Learn. Syst..

[21]  Zied Malouche,et al.  Adaptive unsupervised extraction of one component of a linear mixture with a single neuron , 1998, IEEE Trans. Neural Networks.

[22]  V. Koivunen,et al.  Identifiability and Separability of Linear Ica Models Revisited , 2003 .

[23]  Andrzej Cichocki,et al.  Neural networks for blind decorrelation of signals , 1997, IEEE Trans. Signal Process..

[24]  Andrzej Cichocki,et al.  Adaptive blind signal and image processing , 2002 .

[25]  Eric Moreau,et al.  Self-adaptive source separation. II. Comparison of the direct, feedback, and mixed linear network , 1998, IEEE Trans. Signal Process..

[26]  Jun Wang,et al.  Sequential blind extraction of instantaneously mixed sources , 2002, IEEE Trans. Signal Process..

[27]  Erkki Oja,et al.  Simple Neuron Models for Independent Component Analysis , 1996, Int. J. Neural Syst..

[28]  Deepa Kundur,et al.  A novel blind deconvolution scheme for image restoration using recursive filtering , 1998, IEEE Trans. Signal Process..

[29]  Andrzej Cichocki,et al.  Blind extraction of source signals with specified stochastic features , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[30]  Shun-ichi Amari,et al.  Adaptive Online Learning Algorithms for Blind Separation: Maximum Entropy and Minimum Mutual Information , 1997, Neural Computation.