A new technique for blind source separation of post nonlinear mixture

This paper presents a new method for solving post-nonlinear blind source separation (PNLBSS). It proposes a modified Gaussianization technique for recovering PNLBSS systems. The proposed technique overcomes the failure of classical Gaussianization schemes to work properly in some PNL mixture with severe nonlinearity characteristics. It is found that the failure is due to the multi-modality of the probability distributions (pdf), of the received nonlinear mixture. In order to estimate the eceived pdf, the paper proposes an accurate nonparametric evaluation of the signal´s pdf and its entropy functions . The pdf estimation is based on using Bspline wavelet transform as the smoothing filter for the data histogram distribution. The paper also proposes a pre-mapping scheme that transforms multi-modal pdf to a uni-modal one, and thereby makes them Gaussianable. Several illustrative examples are given, to verify the ability of the proposed technique to estimate signal´s pdf, recover PNLBSS mixture with severe nonlinearity characteristics.