Blind Unmixing of Linear Mixtures using a Hierarchical Bayesian Model. Application to Spectroscopic Signal Analysis

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.