Blind unmixing of linear mixtures using a hierarchical Bayesian model. Application to spectroscopic signal analysis

Nicolas Dobigeon (1, 2) , Jean-Yves Tourneret (1, 2) , Saïd Moussaoui (3)

1 IRIT-SC - Signal et Communications
2 Toulouse INP - Institut National Polytechnique (Toulouse)
3 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

This paper addresses the problem of spectral unmixing when positivity and additivity constraints are imposed on the mixing coefficients. A hierarchical Bayesian model is introduced to satisfy these two constraints. A Gibbs sampler is then proposed to generate samples distributed according to the posterior distribution of the unknown parameters associated to this Bayesian model. Simulation results conducted with synthetic data illustrate the performance of the proposed algorithm. The accuracy of this approach is also illustrated by unmixing spectra resulting from a multicomponent chemical mixture analysis by infrared spectroscopy.

Mots clés: non-negativity constraint; spectroscopy; Source separation; Bayesian estimation; full-additivity constraint; linear mixing; Monte Carlo methods

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Nicolas Dobigeon, Jean-Yves Tourneret, Saïd Moussaoui. Blind unmixing of linear mixtures using a hierarchical Bayesian model. Application to spectroscopic signal analysis. IEEE Workshop on Statistical Signal Processing, Aug 2007, Madison, United States. pp.CDROM, ⟨10.1109/SSP.2007.4301222⟩. ⟨hal-00455587⟩