A Supervised Approach for Estimating Fractional Abundances of Binary Intimate Mixtures

In this work, we propose a supervised framework for spectral unmixing of binary intimate mixtures. The core idea is based on geodesic distance measurements and regression to estimate the fractional abundances. The main assumption is that spectral reflectances of binary mixtures form a curve between the two endmembers, and the mixture's relative position on this curve serves as an indicator of its fractional abundances. We propose four novel approaches to approximate this relative position. From this, the fractional abundances are obtained using Gaussian process regression. The proposed framework simultaneously copes with the spectral variability by hypersphere and high-dimensional simplex projections. The approach is extensively validated on real datasets, including binary mineral mixtures and industrial clay powder mixtures produced in a laboratory setting, comprising 60 binary mixtures derived from five types of clay powders: kaolin, roof clay, red clay, mixed clay, and calcium hydroxide, measured by a variety of hyperspectral sensors in the VNIR–SWIR and mid-and longwave infrared regions. A comparison with the linear mixing model and several nonlinear mixing models demonstrates the superiority of the proposed approach.