Practical method for blind inversion of Wiener systems

In this paper, firstly we show that the problem of blind inversion of Wiener systems is a special case of blind separation of post-nonlinear instantaneous mixtures approximately, and derive the learning rule for the former problem using this relationship. Secondly, we review the Gaussianization method for blind inversion of Wiener systems. Based on the fact that the convolutive mixture is close to Gaussian, this method roughly approximates the convolutive mixture by a Gaussian variable and constructs the inverse nonlinearity easily. Thirdly, in order to improve the performance, the Cornish-Fisher expansion is exploited to model the latent convolutive mixture, and then the extended Gaussianization method is developed. We show that the performance of our method is insensitive to the nonlinearity in the Wiener system. Experimental results are presented to illustrate the validity and efficiency of our method.