  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.

Data Analysis, Statistics and Probability