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In hyperspectral image unmixing, a collection of pure spectra, the so-called endmembers, is identified and their abundance fractions are estimated at each pixel. While endmembers are often extracted using a geometric approach, the abundances are usually estimated by solving an inverse problem. In this paper, we bypass the problem of abundance estimation by using a geometric point of view. The proposed framework shows that a large number of endmember extraction techniques can be adapted to jointly estimate the abundance fractions, with no additional computational complexity. This is illustrated in this paper with the N-Findr, SGA, VCA, OSP, and ICE endmember extraction techniques. A nonlinear extension is also proposed, using non linear dimension reduction methods such as MDS, LLE and ISOMAP. These strategies maintain the geometric unmixing algorithms unchanged, for endmember extraction as well as abundance fraction estimation. The relevance of the proposed approach is illustrated through experiments on synthesized data and real hyperspectral image.
RÉSUMÉ
De récentes études ont montré l’avantage de l’approche géométrique en démélange de données hyperspectrales. Elle permet d’identifier les signatures spectrales des composants purs. Jusqu’ici, l’estimation des fractions d’abondance a toujours été réalisée dans un second temps, par résolution d’un problème inverse généralement. Dans cet article, nous montrons que les techniques géométriques d’extraction des composants purs de la littérature permettent d’estimer conjointement les fractions d’abondance, pour un coût calculatoire supplémentaire négligeable. Pour ce faire, un socle commun d’interprétations géométriques du problème est proposé, que l’on peut décliner pour mieux l’adapter à la technique d’extraction de composants purs retenue. Le caractère géométrique de l’approche lui confère une flexibilité très appréciable dans le cadre de techniques de démélange géométrique, illustrée ici avec NFindr, SGA, VCA, OSP et ICE. Une extension non linéaire est proposée, en utilisant des techniques de réduction de dimensionnalité par apprentissage de variétés, illustrée avec les algorithmes MDS, LLE et ISOMAP. Une telle approche permet de maintenir inchangés les algorithmes géométriques d’identification des composants purs et d’estimation de la proportion de ces derniers dans le mélange. La pertinence de cette approche est illustrée par des expérimentations sur des données synthétisées et réelles.
hyperspectral data processing, nonlinear unmixing, geometric unmixing methods, abundance estimation, dimensionality reduction techniques, geodesic distance
MOTS-CLÉS
traitement de données hyperspectrales, démélange non linéaire, approches géométriques, réduction de dimension, distance géodésique
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