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

TL;DR

This paper introduces a hierarchical Bayesian model with a Gibbs sampling algorithm to effectively separate spectral sources under non-negativity and full additivity constraints, demonstrated on synthetic and real Raman spectroscopy data.

Contribution

It develops a new hierarchical Bayesian framework that incorporates both non-negativity and sum-to-one constraints for spectral source separation.

Findings

The proposed method accurately separates sources in synthetic simulations.

It successfully processes real Raman spectroscopy data.

The Gibbs sampler efficiently estimates model parameters.

Abstract

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 regressors and regression coefficients of linear mixtures. The estimation of the unknown parameters of this model is performed using samples generated using an appropriate Gibbs sampler. The performance of the proposed algorithm is evaluated through simulation results conducted on synthetic mixture models. The proposed approach is also applied to the processing of multicomponent chemical mixtures resulting from Raman spectroscopy.