A Multilinear Mixing Model for Nonlinear Spectral Unmixing

In hyperspectral unmixing, bilinear and linear-quadratic models have become popular recently, and also the polynomial postnonlinear model shows promising results. These models do not consider endmember interactions involving more than two endmembers, although such interactions might compose a nontrivial part of the observed spectrum in scenarios involving bright materials and complex geometrical structures, such as vegetation and intimate mixtures. In this paper, we present an extension of these models to include an infinite number of interactions. Several technical problems, such as divergence of the resulting series, can be avoided by introducing an optical interaction probability, which becomes the only free parameter of the model in addition to the abundances. We present an unmixing strategy based on this multilinear mixing (MLM) model; present comparisons with the bilinear models and the Hapke model for intimate mixing; and show that, in several scenarios, the MLM model obtains superior results.