Mineralogy Analysis Using Linear Unmixing Under Group Constraint

During the past decades, remote sensing spectroscopy has led to many discoveries and new understandings of the composition of the Earth and planetary surface. Various methods have been proposed to interpret these datasets, in particular: linear unmixing under positivity and sum-to-one constraints, using a known spectral database. Given the large size of this database with potential contribution of a few spectra only, in comparison to reduced number of wavelengths, one must include a sparsity constraint.Here we show how exact sparsity constraints, combined with group exclusivity can be used to propose a valuable tool in the aim of constraining the mineralogy of planetary surfaces. Synthetic tests are performed in order to test the robustness of the methodology, and first results on real data are introduced.