Hyperspectral Unmixing With Endmember Variability via Alternating Angle Minimization

Abstract

In hyperspectral unmixing applications, one typically assumes that a single spectrum exists for every endmember. In many scenarios, this is not the case, and one requires a set or a distribution of spectra to represent an endmember or class. This inherent spectral variability can pose severe difficulties in classical unmixing approaches. In this paper, we present a new algorithm for dealing with endmember variability in spectral unmixing, based on the geometrical interpretation of the resulting unmixing problem, and an alternating optimization approach. This alternating-angle-minimization algorithm uses sets of spectra to represent the variability present in each class and attempts to identify the subset of endmembers which produce the smallest reconstruction error. The algorithm is analogous to the popular multiple endmember spectral mixture analysis technique but has a much more favorable computational complexity while producing similar results. We illustrate the algorithm on several artificial and real data sets and compare with several other recent techniques for dealing with endmember variability.