  Spectral variability in hyperspectral images can result from factors
including environmental, illumination, atmospheric and temporal changes. Its
occurrence may lead to the propagation of significant estimation errors in the
unmixing process. To address this issue, extended linear mixing models have
been proposed which lead to large scale nonsmooth ill-posed inverse problems.
Furthermore, the regularization strategies used to obtain meaningful results
have introduced interdependencies among abundance solutions that further
increase the complexity of the resulting optimization problem. In this paper we
present a novel data dependent multiscale model for hyperspectral unmixing
accounting for spectral variability. The new method incorporates spatial
contextual information to the abundances in extended linear mixing models by
using a multiscale transform based on superpixels. The proposed method results
in a fast algorithm that solves the abundance estimation problem only once in
each scale during each iteration. Simulation results using synthetic and real
images compare the performances, both in accuracy and execution time, of the
proposed algorithm and other state-of-the-art solutions.
