arXiv subjects

Hichem Snoussi

Publications and source records attributed to Hichem Snoussi.

21 records · Page 2Linked to original sources

arXiv2002

Blind separation of noisy Gaussian stationary sources. Application to cosmic microwave background imaging

We present a new source separation method which maximizes the likelihood of a model of noisy mixtures of stationary, possibly Gaussian, independent components. The method has been devised to address the problem of imaging CMB anisotropies. It works in the spectral domain where, thanks to two simple approximations, the likelihood assumes a simple form which is easy to handle (low dimensional sufficient statistics) and to maximize (via the EM algorithm).

astro-ph↗

arXiv2001

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

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.

physics.data-an↗

arXiv2001

Penalized maximum likelihood for multivariate Gaussian mixture

In this paper, we first consider the parameter estimation of a multivariate random process distribution using multivariate Gaussian mixture law. The labels of the mixture are allowed to have a general probability law which gives the possibility to modelize a temporal structure of the process under study. We generalize the case of univariate Gaussian mixture in [Ridolfi99] to show that the likelihood is unbounded and goes to infinity when one of the covariance matrices approaches the boundary of singularity of the non negative definite matrices set. We characterize the parameter set of these singularities. As a solution to this degeneracy problem, we show that the penalization of the likelihood by an Inverse Wishart prior on covariance matrices results to a penalized or maximum a posteriori criterion which is bounded. Then, the existence of positive definite matrices optimizing this criterion can be guaranteed. We also show that with a modified EM procedure or with a Bayesian sampling scheme, we can constrain covariance matrices to belong to a particular subclass of covariance matrices. Finally, we study degeneracies in the source separation problem where the characterization of parameter singularity set is more complex. We show, however, that Inverse Wishart prior on covariance matrices eliminates the degeneracies in this case too.

physics.data-an↗