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Hyperspectral images provide much more information than conventional imagingtechniques, allowing a precise identification of the materials in the observedscene, but because of the limited spatial resolution, the observations areusually mixtures of the contributions of several materials. The spectralunmixing problem aims at recovering the spectra of the pure materials of thescene (endmembers), along with their proportions (abundances) in each pixel. Inorder to deal with the intra-class variability of the materials and the inducedspectral variability of the endmembers, several spectra per material,constituting endmember bundles, can be considered. However, the usual abundanceestimation techniques do not take advantage of the particular structure ofthese bundles, organized into groups of spectra. In this paper, we propose touse group sparsity by introducing mixed norms in the abundance estimationoptimization problem. In particular, we propose a new penalty whichsimultaneously enforces group and within group sparsity, to the cost of beingnonconvex. All the proposed penalties are compatible with the abundancesum-to-one constraint, which is not the case with traditional sparseregression. We show on simulated and real datasets that well chosen penaltiescan significantly improve the unmixing performance compared to the naive bundleapproach.

Hyperspectral Image Unmixing with Endmember Bundles and Group Sparsity Inducing Mixed Norms