New hyperbolic source density models for blind source recovery score functions

We present two new hyperbolic source probability models to effectively represent sub-Gaussian and super-Gaussian families of sources for dynamic and convolutive Blind Source Recovery (BSR). Both models share a common boundary for the Gaussian density function. The proposed hyperbolic probability model for the sub-Gaussian densities is an extension of the Pearson density model. The model can represent a broader range of sub-Gaussian densities including multi-modal densities as compared to the original Pearson Model. Similarly, the proposed super-gaussian model is an extension of the generalized hyperbolic-Cauchy density function with an added degree of freedom. Combining these two proposed models we propose an adaptive score function for Blind Source Recovery from mixtures of multiple (and unknown) source densities. An adaptive algorithm, to determine the regulation parameters for the proposed score function, using the batch kurtosis of BSR output is also presented. The primary advantage of the proposed online parameter estimation is that it renders the adaptive estimation of the demixing network to be completely blind. The proposed algorithms have been extensively used in multi-distribution convolutive Blind Source Recovery problems.