Supervised fully constrained linear spectral unmixing using evolutionary strategy

Spectral Unmixing algorithms use two linear and non-linear mixing models to determine the relative abundances of the materials in a remotely sensed image. Hyperspectral images are often treated as a Linear Mixture Model (LMM), where the image pixels are described by a linear combination of the spectra of pure materials. In LMM, the abundances are non-negative and sum of them must be one. Linear Unmixing with these two constraints which termed as Fully Constraint Linear Spectral Unmixing (FCLSU) leads to some inequalities that are difficult to carry out. FCLSU can be considered as a constrained optimization problem and Evolutionary Computation (EC) techniques are good problem solving tools for it. In this paper, we use Evolutionary Strategy (ES) to solve FCLSU with the assumption that the pure materials are known. The abundances estimated by ES are converted to a hyper spherical coordinate system to cope with the constraints. The results are compared based on different spectral similarity measures both on simulated and real data.