Bayesian source separation with mixture of Gaussians prior for sources and Gaussian prior for mixture coefficients

Details Bayesian source separation with mixture of Gaussians prior for sources and Gaussian prior for mixture coefficients Bayesian source separation with mixture of Gaussians prior for sources and Gaussian prior for mixture coefficients

2001-11-06

arxiv.org/abs/physics/0111018v1

Physics

Data Analysis, Statistics and Probability

Presented at MaxEnt00. Appeared in Bayesian Inference and Maximum Entropy Methods, Ali Mohammad-Djafari(Ed.), AIP Proceedings

Scientific paper

10.1063/1.1381902

In this contribution, we present new algorithms to source separation for the case of noisy instantaneous linear mixture, within the Bayesian statistical framework. The source distribution prior is modeled by a mixture of Gaussians [Moulines97] and the mixing matrix elements distributions by a Gaussian [Djafari99a]. We model the mixture of Gaussians hierarchically by mean of hidden variables representing the labels of the mixture. Then, we consider the joint a posteriori distribution of sources, mixing matrix elements, labels of the mixture and other parameters of the mixture with appropriate prior probability laws to eliminate degeneracy of the likelihood function of variance parameters and we propose two iterative algorithms to estimate jointly sources, mixing matrix and hyperparameters: Joint MAP (Maximum a posteriori) algorithm and penalized EM algorithm. The illustrative example is taken in [Macchi99] to compare with other algorithms proposed in literature. Keywords: Source separation, Gaussian mixture, classification, JMAP algorithm, Penalized EM algorithm.

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