Estimation of Mars surface physical properties from hyperspectral images using the SIR method
Résumé
Visible and near infrared imaging spectroscopy is a key remote sensing technique to study and monitor planet Mars. Indeed it allows the detection, mapping and characterization of minerals as well as volatile species that often constitute the first step toward the resolution of key climatic and geological issues.
These tasks are carried out by the spectral analysis of the solar light reflected in different directions by the materials forming the top few millimeters or centimetres of the ground. The chemical composition, granularity, texture, physical state, etc. of the materials determine the morphology of the hundred thousands spectra that typically constitute an image. Radiative transfer models simulating the propagation of solar light through the martian atmosphere and surface and then to the sensor aim at evaluating numerically the direct and quantitative link between parameters and spectra. Then techniques must be applied to the models in order to invert the link and evaluate the properties of atmospheric and surface materials from the spectra. Processing of all the pixels of an image finally provides physical and structural maps. We use the SIR method (K.C. Li, Sliced Inverse Regression for dimension reduction, Journal of the American Statistical Association, 86:316-327, 1991) combined to a nonparametric regression to reverse the previous numerical link in order to estimate some Mars surface physical parameters from spectra. For that purpose we first generate numerous corresponding pairs of parameters - synthetic spectra by direct radiative transfer modeling in order to constitute a learning database. The SIR step allows to reduce the dimension of the spectra (usually several hundreds) in order to overcome the curse of dimensionality in the regression step. The latter provides multivariate functions each relating the reduced components of a spectrum to a given physical parameter value. Such inverted link is applied to a real dataset of hyperspectral images collected by the OMEGA instrument (Mars Express mission).
These tasks are carried out by the spectral analysis of the solar light reflected in different directions by the materials forming the top few millimeters or centimetres of the ground. The chemical composition, granularity, texture, physical state, etc. of the materials determine the morphology of the hundred thousands spectra that typically constitute an image. Radiative transfer models simulating the propagation of solar light through the martian atmosphere and surface and then to the sensor aim at evaluating numerically the direct and quantitative link between parameters and spectra. Then techniques must be applied to the models in order to invert the link and evaluate the properties of atmospheric and surface materials from the spectra. Processing of all the pixels of an image finally provides physical and structural maps. We use the SIR method (K.C. Li, Sliced Inverse Regression for dimension reduction, Journal of the American Statistical Association, 86:316-327, 1991) combined to a nonparametric regression to reverse the previous numerical link in order to estimate some Mars surface physical parameters from spectra. For that purpose we first generate numerous corresponding pairs of parameters - synthetic spectra by direct radiative transfer modeling in order to constitute a learning database. The SIR step allows to reduce the dimension of the spectra (usually several hundreds) in order to overcome the curse of dimensionality in the regression step. The latter provides multivariate functions each relating the reduced components of a spectrum to a given physical parameter value. Such inverted link is applied to a real dataset of hyperspectral images collected by the OMEGA instrument (Mars Express mission).