Bayesian blind separation of generalized hyperbolic processes in noisy and underdeterminate mixtures

• Published in: IEEE transactions on signal processing Vol. 54; no. 9; pp. 3257 - 3269
• Main Authors: Snoussi, H., Idier, J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Bayesian analysis; Bayesian methods; Blind source separation; Blinds; Computer Science; Covariance matrix; Decorrelation; Detection, estimation, filtering, equalization, prediction; Engineering Sciences; Exact sciences and technology; Fittings; generalized hyperbolic distributions; Gibbs sampling; Independent component analysis; Information, signal and communications theory; Mathematical models; Maximum likelihood estimation; Miscellaneous; noisy mixture; Prewhitening; Sampling; Sampling methods; Separation; Signal and communications theory; Signal and Image Processing; Signal processing; Signal processing algorithms; Signal, noise; Source separation; Statistics; Telecommunications and information theory; underdeterminate mixture; Vectors; Parameter estimation; Source separation; Signal estimation; underdeterminate mixture; Gaussian distribution; Blind source separation; Gibbs sampling; Implementation; Blind separation; MCMC algorithm; generalized hyperbolic distributions; Signal processing; Data structure; noisy mixture
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2006.877660

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