Blind separation of statistically independent signals with mixed sub-Gaussian and super-Gaussian probability distributions

In the context of independent component analysis (ICA), we propose a simple method for online estimation of activation functions in order to separate blindly instantaneous mixtures of sub-Gaussian and super-Gaussian signals. An adequate choice of these activation functions is necessary, not only for successful source separation (using a relative gradient algorithm), but also to achieve a sufficient level of crosstalk index. To accomplish this, we employ a simple parameterized model for the probability density functions of the sources. The parameter of this distribution model (for each estimated source signal) is adapted online by minimizing the mutual information while the activation functions are obtained as the associated score functions. Furthermore, a modified relative gradient algorithm is derived that exhibits an isotropic convergence (near the desired solution) independent of the statistics of the sources. Simulation results are given to demonstrate the effectiveness of the presented methods.