Endmembers abundance estimators based on spectral shape similarity using genetic algorithm and generalized pattern search algorithm

Abstract

We develop two endmembers abundance estimators based on a genetic algorithm (GA) and a generalized pattern search algorithm. This development aims to estimate more accurate abundances of endmembers in cases of brightness and shading noises, which is an issue in other endmember abundance estimation methods based on the least square method, such that the estimators depend on spectral shape similarity as a matching criterion between spectral signatures, because shape similarity methods are independent on the spectral reflectance amplitude and not sensitive to brightness noise effects on it. The strategy used for unmixing problem analysis is based on the popular linear spectral mixture model. GA is used as a heuristic optimization technique, and generalized pattern search is used as a direct search algorithm. Spectral angle mapper, spectral information divergence methods, and the combination of both of these are used as objective functions for optimization techniques. All experiments have been performed on the proposed estimators and the traditional fully constrained least squares method as a state-of-the-art method. Experiments have been applied on simulated multispectral and hyperspectral datasets with different noise conditions. In addition, a hyperspectral real dataset from a cuprite region (Las Vegas, Nevada, USA) was used for testing performance. The experimental results show that proposed estimators are better than fully contained least squares method across all experiments and especially in cases of noisy datasets.