Blind source separation of independent/dependent signals using a measure on copulas

We introduce a new BSS approach, based on modified Kullback-Leibler divergence between copula densities, for both independent or dependent source component signals. In the standard case of independent source components, the proposed method improves the mutual information (between probability densities) procedure, and it has the advantage to be naturally generalized to separate mixtures of dependent source components. Simulation results are presented showing the convergence and the efficiency of the proposed algorithms.

[1]  R. Nelsen An Introduction to Copulas (Springer Series in Statistics) , 2006 .

[2]  M. Sklar Fonctions de repartition a n dimensions et leurs marges , 1959 .

[3]  Michel Verleysen,et al.  Is the General Form of Renyi's Entropy a Contrast for Source Separation? , 2007, ICA.

[4]  Yanqin Fan,et al.  Pseudo‐likelihood ratio tests for semiparametric multivariate copula model selection , 2005 .

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

[6]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[7]  Dinh-Tuan Pham,et al.  Mutual information approach to blind separation of stationary sources , 2002, IEEE Trans. Inf. Theory.

[8]  I. Gijbels,et al.  Improved kernel estimation of copulas: Weak convergence and goodness-of-fit testing , 2009, 0908.4530.

[9]  Jean-Christophe Pesquet,et al.  Cumulant-based independence measures for linear mixtures , 2001, IEEE Trans. Inf. Theory.

[10]  Ray-Bing Chen,et al.  Independent Component Analysis Via Copula Techniques , 2007 .

[11]  H. Joe Multivariate models and dependence concepts , 1998 .

[12]  Andrzej Cichocki,et al.  Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities , 2010, Entropy.

[13]  Zengqi Sun,et al.  Copula Component Analysis , 2007, ICA.

[14]  Jean-Christophe Pesquet,et al.  Quadratic Higher Order Criteria for Iterative Blind Separation of a MIMO Convolutive Mixture of Sources , 2007, IEEE Transactions on Signal Processing.

[15]  Guillaume Gelle,et al.  A penalized mutual information criterion for blind separation of convolutive mixtures , 2004, Signal Process..

[16]  H. Tsukahara Semiparametric estimation in copula models , 2005 .

[17]  Amor Keziou,et al.  New estimates and tests of independence in some copula models , 2008, 0806.4864.

[18]  Eric Moreau,et al.  A robust algorithm for convolutive blind source separation in presence of noise , 2013, Signal Process..

[19]  R. Nelsen An Introduction to Copulas , 1998 .