Supervised Planetary Unmixing with Optimal Transport

Sina Nakhostin (1) , Nicolas Courty (1) , Rémi Flamary (2) , Thomas Corpetti (3)

1 OBELIX - Environment observation with complex imagery
2 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
3 FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences

This paper is focused on spectral unmixing and presents an original technique based on Optimal Transport. Optimal Transport consists in estimating a plan that transports a spectrum onto another with minimal cost, enabling to compute an associated distance (Wasserstein distance) that can be used as an alternative metric to compare hyperspectral data. This is exploited for spectral unmixing where abundances in each pixel are estimated on the basis of their projections in a Wasserstein sense (Bregman projections) onto known end-members. In this work an over-complete dictionary is used to deal with internal variability between endmembers, while a regularization term, also based on Wasserstein distance, is used to promote prior proportion knowledge in the endmem-ber groups. Experiments are performed on real hyperspectral data of asteroid 4-Vesta.

Mots clés: Optimal Transport; Spectral Unmixing; Endmember Variability; Wassertein Distance; Bregman Pro-

Domaines: Machine Learning [stat.ML]; Traitement du signal et de l'image [eess.SP]

Sina Nakhostin, Nicolas Courty, Rémi Flamary, Thomas Corpetti. Supervised Planetary Unmixing with Optimal Transport. WHISPERS 8th workshop on Hyperspectral image and Signal Processing: Evolution in Remote Sensing, Aug 2016, Los Angeles, United States. ⟨hal-01377236⟩