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

Lucas Drumetz 1, 2 Travis Meyer 3 Jocelyn Chanussot 4, 5 Andrea Bertozzi 6 Christian Jutten 7
1 Lab-STICC_IMTA_CID_TOMS
Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance
5 GIPSA-SIGMAPHY - GIPSA - Signal Images Physique
GIPSA-DIS - Département Images et Signal
7 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing
GIPSA-DIS - Département Images et Signal
Abstract : Hyperspectral images provide much more information than conventional imaging techniques, allowing a precise identification of the materials in the observed scene, but because of the limited spatial resolution, the 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 and the induced spectral variability of the endmembers, several spectra per material, constituting endmember bundles, can be considered. 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 by introducing 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 nonconvex. All the proposed penalties are compatible with the 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 classical sparse regression techniques or to the naive bundle approach.
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Submitted on : Friday, May 24, 2019 - 11:19:32 AM
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Lucas Drumetz, Travis Meyer, Jocelyn Chanussot, Andrea Bertozzi, Christian Jutten. Hyperspectral Image Unmixing with Endmember Bundles and Group Sparsity Inducing Mixed Norms. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2019, 28 (7), pp.3435-3450. ⟨10.1109/TIP.2019.2897254⟩. ⟨hal-02138874⟩

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