Blind source separation via the second characteristic function with asymptotically optimal weighting

2004 ◽  
Author(s):  
E. Eidinger ◽  
A. Yeredor
Keyword(s):  
Characteristic Function ◽  
Blind Source Separation ◽  
Source Separation ◽  
Asymptotically Optimal ◽  
Optimal Weighting

A New Concept for Separability Problems in Blind Source Separation

2004 ◽  
Vol 16 (9) ◽  
pp. 1827-1850 ◽  
Author(s):  
Fabian J. Theis
Keyword(s):  
Characteristic Function ◽  
Blind Source Separation ◽  
Random Vector ◽  
Nonlinear Models ◽  
Source Separation ◽  
Direct Proof ◽  
Logarithmic Density ◽  
Know How ◽  
Linear Separability ◽  
Mixing Matrix

The goal of blind source separation (BSS) lies in recovering the original independent sources of a mixed random vector without knowing the mixing structure. A key ingredient for performing BSS successfully is to know the indeterminacies of the problem—that is, to know how the separating model relates to the original mixing model (separability). For linear BSS, Comon (1994) showed using the Darmois-Skitovitch theorem that the linear mixing matrix can be found except for permutation and scaling. In this work, a much simpler, direct proof for linear separability is given. The idea is based on the fact that a random vector is independent if and only if the Hessian of its logarithmic density (resp. characteristic function) is diagonal everywhere. This property is then exploited to propose a new algorithm for performing BSS. Furthermore, first ideas of how to generalize separability results based on Hessian diagonalization to more complicated nonlinear models are studied in the setting of postnonlinear BSS.

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