Bayesian separation of spectral sources under non-negativity and full additivity constraints

This paper addresses the problem of separating spectral sources which are linearly mixed with unknown proportions. The main difficulty of the problem is to ensure the full additivity (sum-to-one) of the mixing coefficients and non-negativity of sources and mixing coefficients. A Bayesian estimation approach based on Gamma priors was recently proposed to handle the non-negativity constraints in a linear mixture model. However, incorporating the full additivity constraint requires further developments. This paper studies a new hierarchical Bayesian model appropriate to the non-negativity and sum-to-one constraints associated to the sources and the mixing coefficients of linear mixtures. The estimation of the unknown parameters of this model is performed using samples obtained with an appropriate Gibbs algorithm. The performance of the proposed algorithm is evaluated through simulation results conducted on synthetic mixture data. The proposed approach is also applied to the processing of multicomponent chemical mixtures resulting from Raman spectroscopy.