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Séparation de sources non-négatives : application au traitement des signaux de spectroscopie

Abstract : Spectral data sets resulting from spectroscopy analysis of a multicomponent substance are a linear combination of the unknown pure component spectra. The analysis aims at identifying these components and the determination of their concentrations. The main constraint is the non-negativity, so this a non-negative source separation problem. Source separation is a fundamental problem in signal processing where a strong hypothesis is the statistical independence of the sources signals. Due to the pure spectra overlapping, the cross-correlation of the sources becomes very important. Therefore, applying a method based on source orthogonality contraint will be inefficient. In addition, the analysis of the range of admissible solution under the non-negativity information shows that this contraint alone does not ensure the uniqueness of the solution, unless under some particular conditions. These two problems motivate the development of two methods based on jointly accounting for statistical independence hypothesis and non-negativity information. The first method is an extension of the maximum likelihood approach of source separation and the second method addresses the separation problem in a Bayesian framework. A numerical evaluation of the performances with synthetic and experimental data allow to asses the performances of these methods. Finally, the Bayesian approach is applied to physical chemistry analysis of real spectra resulting from infrared, Raman and Ultraviolet-Visible spectroscopies.
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Saïd Moussaoui. Séparation de sources non-négatives : application au traitement des signaux de spectroscopie. Autre. Université Henri Poincaré - Nancy 1, 2005. Français. ⟨NNT : 2005NAN10164⟩. ⟨tel-01748096⟩

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