Massive hyperspectral images analysis by inverse regression of physical models

Keywords :

• apprentissage statistique
• problème inverse
• modèle photométrique

The objective of the thesis is to develop a statistical learning technique suitable for the inversion of complex physical models. The two main difficulties addressed are on the one hand the massive amount of observations to be analyzed and on the other hand the need to quantify the uncertainty on the inversion, which can come from the physical model or from the measurements. In a Bayesian inversion framework, we therefore propose a two-step approach : a learning step of a parametric statistical model (GLLiM), common to all the observations, then a prediction step, repeated for each measurement, but fast enough to support a large dataset. We show that the posterior distribution, which takes the form of a Gaussian mixture, can be exploited to detect and estimate possible multiple solutions. In addition, we explore sampling techniques to seek the best the trade-off between computation time and inversion precision.

Although general, the proposed approach is applied mainly to a complex inverse problem in planetary remote sensing. This involves using a semi-empirical photometric model (Hapke's model) to analyze spectral bidirectional reflectance measurements and indirectly find the textural characterization of the material examined. Several datasets are studied, both from laboratory measurements and a large collection of multi-angular hyperspectral satellite images.

Finally, we exploit the versatility of the GLLiM model to explore several issues related to Bayesian inversion. In particular, we propose an indicator to assess the influence of the choice of the direct model on the quality of the inversion. We also use the GLLiM model to take into account a priori information, making it suitable for solving data assimilation problems. 

Directors:

• Florence Forbes (Université Grenoble Alpes )
• Sylvain Douté (Université Grenoble Alpes )

Raporteurs:

• Nicolas Dobigeon (INP - ENSEEIGHT Toulouse )
• Frédéric Schmidt (Université Paris-Saclay )

Examinators:

• Saïd Moussaoui (Ecole Centrale Nantes )
• Clémentine Prieur (Université Grenoble Alpes )
• Cédric Pilorget (Université Paris-Saclay )