IEEE Trans Image Process - Multivariate slow feature analysis and decorrelation filtering for blind source separation.

Tópicos

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{ method(2212) result(1239) propos(1039) }
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{ gene(2352) biolog(1181) express(1162) }
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Resumo

We generalize the method of Slow Feature Analysis (SFA) for vector-valued functions of several variables and apply it to the problem of blind source separation, in particular to image separation. It is generally necessary to use multivariate SFA instead of univariate SFA for separating multi-dimensional signals. For the linear case, an exact mathematical analysis is given, which shows in particular that the sources are perfectly separated by SFA if and only if they and their first-order derivatives are uncorrelated. When the sources are correlated, we apply the following technique called Decorrelation Filtering: use a linear filter to decorrelate the sources and their derivatives in the given mixture, then apply the unmixing matrix obtained on the filtered mixtures to the original mixtures. If the filtered sources are perfectly separated by this matrix, so are the original sources. A decorrelation filter can be numerically obtained by solving a nonlinear optimization problem. This technique can also be applied to other linear separation methods, whose output signals are decorrelated, such as ICA. When there are more mixtures than sources, one can determine the actual number of sources by using a regularized version of SFA with decorrelation filtering. Extensive numerical experiments using SFA and ICA with decorrelation filtering, supported by mathematical analysis, demonstrate the potential of our methods for solving problems involving blind source separation.

Resumo Limpo

general method slow featur analysi sfa vectorvalu function sever variabl appli problem blind sourc separ particular imag separ general necessari use multivari sfa instead univari sfa separ multidimension signal linear case exact mathemat analysi given show particular sourc perfect separ sfa firstord deriv uncorrel sourc correl appli follow techniqu call decorrel filter use linear filter decorrel sourc deriv given mixtur appli unmix matrix obtain filter mixtur origin mixtur filter sourc perfect separ matrix origin sourc decorrel filter can numer obtain solv nonlinear optim problem techniqu can also appli linear separ method whose output signal decorrel ica mixtur sourc one can determin actual number sourc use regular version sfa decorrel filter extens numer experi use sfa ica decorrel filter support mathemat analysi demonstr potenti method solv problem involv blind sourc separ

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