A simple scheme for unmixing hyperspectral data based on the geometry of the N-dimensional simplex

In this paper, we study the problem of decomposing spectra in hyperspectral data into the sum of pure spectra, or endmembers. We propose to jointly extract the endmembers and estimate the corresponding fractions, or abundances. For this purpose, we show that these abundances can be easily computed using volume of simplices, from the same information used in the classical N-Findr algorithm. This results into a simple scheme for unmixing hyperspectral data, with low computational complexity. Experimental results show the efficiency of the proposed method.