A novel blind source extraction algorithm for ill-conditioned mixtures

A new contrast function is proposed to solve blind extraction problem from ill-conditioned mixtures of Gaussian and sub-Gaussian signals, or mixtures of Gaussian and super-Gaussian signals. Firstly, we point out the limitation of the existing contrast function for hybrid mixtures. Then the new contrast function based on fourth order cross cumulants and the covariance is presented. In addition, it is proved that minimizing the new contrast function would lead to separation of the extractable sources, and the classic Gaussian-Newton method is applied to accomplish the minimizing process. Simulation results, for both nonsingular mixing matrix case and singular mixing matrix case (ill-conditioned case), validate the sequential blind extraction algorithm in which the proposed contrast function is used.