Hyperspectral images for remote sensing provide much more information than conventional imaging techniques,allowing a precise identification of the materials in the observed scene, but their limited spatial resolution makes that observations are usually mixtures of the contributions of several materials.The spectral unmixing problem aims at recovering the spectra of the pure materials of the scene (endmembers), along with their proportions (abundances) in each pixel. In order to deal with the intra-class variability of the materials, several spectraper material, constituting end member bundles, can be considered to take into account spectral variability. However, the usual abundance estimation techniques do not take advantage of the particular structure of these bundles, organized into groups of spectra. In this paper, we propose to use group sparsity inducing mixed norms in the abundance estimation optimization problem.In particular, we propose a new penalty which simultaneously enforces group and within group sparsity, to the cost of being non convex. All the proposed penalties are compatible with the traditional abundance sum-to-one constraint, which is not the case with traditional sparse regression. We show on simulated and real datasets that well chosen penalties can significantly improve the unmixing performance compared to the naive bundle approach.
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