Spectral unmixing algorithms

This document presents the sparse Bayesian unmixing algorithms recently developed in the framework of the “HSI-MARS ” research project. The un-mixing process is formulated as a linear regression problem, where the abun-dance’s physical constraints are taken into account. Based on this formu-lation, a hierarchical Bayesian model is presented and suitable priors are selected for the model parameters such that, on the one hand, they ensure the non-negativity of the abundances, while on the other hand they favor sparse solutions for the abundances ’ vector. To perform Bayesian inference based on the proposed hierarchical Bayesian model, we resort to the vari-ational Bayes methodology. Hence, a computationally efficient variational Bayes algorithm is then presented, where approximating posteriors for all model parameters are derived. Experimental results on both synthetic and real hyperspectral data illustrate that the proposed method converges fast, favors sparsity in the abundances ’ vector, and offers improved estimatio