Analysis and acceleration strategy of endmember extraction algorithms based on convex geometry

Under a linear mixture model with non-negativity and sum-to-one constraints, the spectral unmixing problem can be seen as a convex geometry problem. This article first analyses three commonly used endmember extraction criteria including the extreme projection criterion, the maximum simplex volume criterion and the minimum volume enclosing simplex criterion, which are derived from the geometrical explanation of the linear mixture model. And then an acceleration strategy is introduced to shorten the computing time of endmember extraction algorithms. The acceleration strategy exploits two facts: (1) the endmembers corresponding to the vertices of a simplex composed of the mixed pixels can be determined only by the boundary points, with little or no affect by the interior points; (2) the boundary points can be found in a series of two-dimensional subspace. Experiments using simulated data on eight popular endmember extraction algorithms show that the proposed acceleration strategy can reduce the computing time and then improve the speed of endmember extraction, while maintaining the same results or little sacrifice of computing precision.