Non-linear fully-constrained spectral unmixing

In hyperspectral unmixing, one often observes that the inter actions between the endmember spectra can contain strong non-linear effects. Recently, a new endmember extraction algorithm has been proposed that is capable of dealing with a non-linearly shaped data manifold, based upon a combination of geodesic distances and a volume-maximizing search algorithm. Once the endmembers have been found, the pixels have to be decomposed into their abundances, which within the lin ear mixing assumption becomes a constrained least-squares problem. These techniques are however not fit for dealing with non-linearly mixed data. In this work, we present an algorithm that is capable of unmixing non-linearly mixed data, and which obeys the positivity and sum-to-one constraint usually imposed on the abundance vectors. The algorithm is based upon a reformulation of the recently developed SPU algorithm in terms of distance geometry. A demonstration of the algorithm on the Cuprite data set is provided.