In this paper, a method based on modeling and statistics is proposed to evaluate the physical properties of surface icy materials on Mars from hyperspectral images collected by the OMEGA instrument aboard the Mars Express spacecraft. The approach is based on the estimation of the functional relationship F between observed spectra and relevant physical parameters such as compound abundances and granularity. To this end, a database of synthetic spectra is generated by a radiative transfer model simulating the reflection of solar light by a granular mixture of H2O ice, CO2 ice, and dust. The database constitutes a training set used to estimate F. The high dimension of spectra is reduced by Gaussian regularized sliced inverse regression (GRSIR) to overcome the "curse of dimensionality" and, consequently, the sensitivity of the inversion to noise (ill-conditioned problems). Compared with other approaches, such as the k-NN, the partial least squares, and the support vector machines (SVM), GRSIR has the advantage of being very fast, interpretable, and accurate. For instance, on simulated test data, the same level of accuracy is obtained by GRSIR and SVM for the estimation of the proportion of dust with a normalized root-mean-square error of 13%, but GRSIR performs 100 times faster. On real data, parameter maps generated by GRSIR from a sequence of three OMEGA observations of the bright permanent polar cap (BPPC) are much smoother, detailed, and coherent than with other competing methods. They indicate that coarse-grained dry ice completely dominates (≈99.55-99.95 wt%) the material forming the top few centimeters of the BPPC with dust and water only present as traces (from 300 to 1000 ppm). The maps show clear regional variations of water and dust contamination as well as CO2 ice state of densification (mean free path around 5 cm on the average, with variations of ±50%) that must be related to meteorological and microphysical phenomena.