  This paper introduces a robust mixing model to describe hyperspectral data
resulting from the mixture of several pure spectral signatures. This new model
not only generalizes the commonly used linear mixing model, but also allows for
possible nonlinear effects to be easily handled, relying on mild assumptions
regarding these nonlinearities. The standard nonnegativity and sum-to-one
constraints inherent to spectral unmixing are coupled with a group-sparse
constraint imposed on the nonlinearity component. This results in a new form of
robust nonnegative matrix factorization. The data fidelity term is expressed as
a beta-divergence, a continuous family of dissimilarity measures that takes the
squared Euclidean distance and the generalized Kullback-Leibler divergence as
special cases. The penalized objective is minimized with a block-coordinate
descent that involves majorization-minimization updates. Simulation results
obtained on synthetic and real data show that the proposed strategy competes
with state-of-the-art linear and nonlinear unmixing methods.
