Skip to Main content Skip to Navigation

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 processing of such data sets aims at identifying the chemical composition of the substance by estimating the pure component spectra and determining their concentrations. This is a source separation problem where the sources correspond the pure spectra and the mixing coefficients allow the evaluate the amount of each component in the substance. The main constraint is the non-negativity of both the sources signals and the mixing coefficients. Thus, mixture analysis in spectroscopy is 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 is inefficient. In addition, the analysis of the range of admissible solution under the non-negativity contraint 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 contraint. 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.
Complete list of metadata

Cited literature [150 references]  Display  Hide  Download
Contributor : Saïd Moussaoui Connect in order to contact the contributor
Submitted on : Friday, April 7, 2006 - 4:00:35 PM
Last modification on : Friday, October 23, 2020 - 8:38:04 AM
Long-term archiving on: : Saturday, April 3, 2010 - 11:08:38 PM


  • HAL Id : tel-00012096, version 1



Saïd Moussaoui. Séparation de sources non-négatives. Application au traitement des signaux de spectroscopie. Traitement du signal et de l'image [eess.SP]. Université Henri Poincaré - Nancy I, 2005. Français. ⟨tel-00012096⟩



Record views


Files downloads