In the context of hyperspectral image analysis in planetology, we show how to estimate the physical parameters that generate the spectral infrared signal reflected by Mars. The training approach we develop is based on the estimation of the functional relationship between parameters and spectra, using a database of synthetic spectra generated by a physical model. The high dimension of spectra is reduced by using Gaussian regularized inverse regression to overcome the curse of dimensionality. Compared with a basic k-nearest neighbors approach or a Partial Least Square (PLS) regression, estimates are more accurate and are thus promising.