A fully constraint abundance estimation algorithm with high accurateness

Abstract

Hyperspectral image provides a way to analyze component and the fraction by spectral unmixing. The classical method is Least Squares algorithm. But it is defined without any constraint on the abundance. The Fully constrained Least Squares (FCLS) algorithm allows resulted abundances satisfying sum-to-one and non-negative, which is practical. It has been widely used till now because it may work quickly with a small unmxing error. But when the number of endmembers is large, it gets much slow. And unmxing error is high if the endmembers are not found out completely. As for improving the speed of the algorithm, there have been many research works. But fewer algorithms are developed for increasing accurateness. Here in this paper, a primal-dual interior-point method is tested for the fully constraint unmixing with the linear unmixing model being modified slightly. A dual problem is established firstly, and then the process of the algorithm is designed to decrease distance between original problem and the dual problem based on result of FCLS. In order to promise high unmxing accurateness, the unmxing error of resulted abundances is added into the optimizing goal. Several algorithms of fully constraint abundance estimation are tested on both simulation and real hyperspectral images. The experimental results show that the prompted algorithm may find the optimal abundance for existing endmembers even though the endmember set is not complete. Accurateness of unmxing is increased, especially on the real image.