A fully constrained linear unmixing method : Simplex regularization for hyperspectral imagery

With a priori information of the known endmembers in hyperspectral image, there is no closed-form solution of Least Square (LS) method for linear mixing model under the Abundance Non negativity Constraint (ANC). So many iterations which may result in big computational complexity are needed in the traditional Fully Constrained LS (FCLS) methods to obtain the optimal solution. In this paper, an analysis of impacts on abundance estimation of hyperspectal image in different simplex shapes was implemented and a fully constrained linear unmixing method based on simplex regularization was proposed which could get optimal solution under limited iteration when the hyperspectral image was spanned into a regular simplex. The proposed method was carried out by three steps. Firstly, the simplex of hyperspectral image was regularized by the known endmembers' whitening matrix. Secondly, the analytical solution of abundance coefficients was obtained under Abundance Sum-to-one Constraint (ASC). Then for every pixel, the FCLS solution was achieved by eliminating the endmembers with negative abundance coefficients and solving the ASC equation iteratively. Experiments results simulated and real hyperspectral images indicate that the proposed method can obtain consistent results with traditional FCLS method and decrease the computational burden efficiently.