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The estimation of abundance maps in hyperspectral imaging requires the resolution of an optimization problem under non-negativity and sum to one constraints. Assuming that the spectral signatures of the image components have been previously determined by an endmember extraction algorithm, we propose in this paper a primal-dual interior point algorithm for the estimation of their fractional abundances. In comparison with the reference method FCLS, our algorithm has the advantage of a reduced computational cost. Moreover, it allows to deal with a penalized criterion favoring the spatial smoothness of abundance maps. The performances of the proposed approach are discussed with the help of synthetic and real examples.
RÉSUMÉ
L’estimation des cartes d’abondances en imagerie hyperspectrale nécessite de ré-soudre un problème d’optimisation sous des contraintes de positivité et d’additivité. Nous nous plaçons dans le cadre où les spectres des composants présents au sein de l’image ont été pré-alablement estimés par un algorithme d’extraction des pôles de mélange. Afin de réduire le temps de calcul, nous proposons un algorithme rapide de points intérieurs de type primal-dual pour l’estimation de ces cartes. En comparaison avec la méthode de référence FCLS, l’algorithme proposé présente l’avantage d’un coût de calcul réduit. Un second avantage est de pouvoir traiter le cas d’un critère pénalisé favorisant la régularité spatiale des cartes d’abondances. Des exemples sur des données synthétiques et réelles illustrent les performances de cet algorithme.
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