Blind separation of generalized hyperbolic processes: unifying approach to stationary non Gaussianity and Gaussian non stationarity

In this contribution, we propose a Bayesian sampling solution to the problem of noisy blind separation of generalized hyperbolic (GH) signals. GH models, introduced by Barndorff-Nielsen in 1977, represent a parametric family able to cover a wide range of real signal distributions. The alternative construction of these distributions as a normal mean-variance (continuous) mixture leads to an efficient implementation of the MCMC method applied to source separation. The incomplete data structure of the GH distribution is indeed compatible with the hidden variable nature of the source separation problem. Our algorithm involves hyperparameters estimation as well. Therefore, it can be used, independently, to fit the parameters of the GH distribution to real data.