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            <title xml:lang="fr">Modèles de mélange de Gaussiennes temps-fréquence pour le débruitage de signaux</title>
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            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
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              <p>On considère le problème de débruitage d'un signal engendré par des coefficients (de synthèse) dans un dictionnaire temps- fréquence, modélisés par un mélange de Gaussiennes multivariées. L'existence de corrélations é la fois dans les coefficients de synthèse et entre les éléments du dictionnaire complique singulièrement le problème de débruitage. Un algorithme de type "Majoration-Minimisation" adapté au problème posé est développé et étudié, une preuve de convergence est donnée. Cet algorithme requiert en toute généralité l'inversion de matrices de grande dimension; des cas particuliers sont considérés (dictionnaires temps-fréquence invariants par translation, et covariances possédant une structure compatible) dans lesquels la complexité peut être considérablement réduite. L'inversion se ramène à une inversion de matrices bloc-circulantes, qui peut être effectuée efficacement. Les performances de l'algorithme sont illustrées par des simulations numériques.</p>
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