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.
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