Bayesian Blind Separation of Generalized Hyperbolic Processes in Noisy and Underdeterminate Mixtures

摘要

In this paper, we propose a Bayesian sampling solution to the noisy blind separation of generalized hyperbolic signals. Generalized hyperbolic 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 Markov chain Monte Carlo method applied to source separation. The incomplete data structure of the generalized hyperbolic distribution is indeed compatible with the hidden variable nature of the source separation problem. Both overdeterminate and underdeterminate noisy mixtures are solved by the same algorithm without a prewhitening step. Our algorithm involves hyperparameters estimation as well. Therefore, it can be used, independently, to fitting the parameters of the generalized hyperbolic distribution to real data.