Spectral unmixing using distance geometry

In this paper, we present a new method for solving the spectral unmixing problem which uses only the spectral distances between the data points and the endmembers. This method is obtained by reformulating every step of the recently developed SPU algorithm entirely in distance geometry, yielding a recursive algorithm based on the geometrical properties of the spectral unmixing problem. The algorithm almost always minimizes the reconstruction error while obeying the constraints on the abundances, yielding results comparable to the fully-constrained least-squares solution. The performance of the algorithm is demonstrated on an artificial data set based on the USGS spectral library.