Blind Source Separation of Overdetermined Linear-Quadratic Mixtures

This work deals with the problem of source separation in overdetermined linear-quadratic (LQ) models. Although the mixing model in this situation can be inverted by linear structures, we show that some simple independent component analysis (ICA) strategies that are often employed in the linear case cannot be used with the studied model. Motivated by this fact, we consider the more complex yet more robust ICA framework based on the minimization of the mutual information. Special attention is given to the development of a solution that be as robust as possible to suboptimal convergences. This is achieved by defining a method composed of a global optimization step followed by a local search procedure. Simulations confirm the effectiveness of the proposal.

[1]  Erkki Oja,et al.  Independent Component Analysis , 2001 .

[2]  Yannick Deville,et al.  Blind Separation of Linear-Quadratic Mixtures of Real Sources Using a Recurrent Structure , 2009, IWANN.

[3]  Igor Vajda,et al.  Estimation of the Information by an Adaptive Partitioning of the Observation Space , 1999, IEEE Trans. Inf. Theory.

[4]  Yannick Deville,et al.  Recurrent networks for separating extractable-target nonlinear mixtures. Part I: Non-blind configurations , 2009, Signal Process..

[5]  M. Castella,et al.  Inversion of Polynomial Systems and Separation of Nonlinear Mixtures of Finite-Alphabet Sources , 2008, IEEE Transactions on Signal Processing.

[6]  C. Jutten,et al.  A Bayesian Nonlinear Source Separation Method for Smart Ion-Selective Electrode Arrays , 2009, IEEE Sensors Journal.

[7]  R. Moddemeijer On estimation of entropy and mutual information of continuous distributions , 1989 .

[8]  Christian Jutten,et al.  Bayesian source separation of linear-quadratic and linear mixtures through a MCMC method , 2009, 2009 IEEE International Workshop on Machine Learning for Signal Processing.

[9]  Jonathan Timmis,et al.  Artificial immune systems - a new computational intelligence paradigm , 2002 .

[10]  Aapo Hyvärinen,et al.  Nonlinear independent component analysis: Existence and uniqueness results , 1999, Neural Networks.

[11]  Juha Karhunen,et al.  Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixtures , 2004, Int. J. Neural Syst..

[12]  D. Pham FAST ALGORITHM FOR ESTIMATING MUTUAL INFORMATION, ENTROPIES AND SCORE FUNCTIONS , 2003 .

[13]  José R. Álvarez,et al.  Computational Methods in Neural Modeling , 2003, Lecture Notes in Computer Science.

[14]  Leandro Nunes de Castro,et al.  Artificial Immune Systems: A New Computational Approach , 2002 .

[15]  Pierre Comon,et al.  Handbook of Blind Source Separation: Independent Component Analysis and Applications , 2010 .

[16]  Karim Abed-Meraim,et al.  Blind identification of a linear-quadratic mixture of independent components based on joint diagonalization procedure , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[17]  Christian Jutten,et al.  Differential of the mutual information , 2004, IEEE Signal Processing Letters.

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

[19]  Guillermo Bedoya Jimenez Non-linear blind signal separation for chemical solid-state sensor arrays , 2006 .