A Model for High Resolution TerraSAR-X Images of Natural Scenes

In the last year, the TerraSAR-X sensor began to provide a great amount of data, thus increasing the possibility to extract valuable information from SAR images. Indeed, these high resolution images are increasingly more textured and present many details previously masked due to the low resolution of the available sensors. This certainly represents an advance for remote sensing applications, but, anyway, the interpretation of these images requires careful attention. As an example, in classification and segmentation issues the increasing in texture of the images is not so unmistakably good news, because, if adequate models for the new data are not introduced, the results may not be as reliable as they could. In this paper we present the first steps toward the modeling of high resolution SAR images relevant to natural scenes: these are the first results obtained in the framework of the MTH0183 project approved after the TerraSAR-X AO. We use fractal models to account for the geometric description of the observed surface and effective scattering models to evaluate a closed form expression for the radar cross section of a fractal surface: in fact, the combined use of these fractal geometrical and electromagnetic models allows to obtain an effective data modeling. Hence, in this work we present a mathematical model allowing the evaluation in closed form of the structure function and of the power density spectrum of the image relevant to a natural scene, in case of small slopes for the observed scene. Furthermore, a numerical study applied to simulated data and aimed to the validation of the above-mentioned theoretical results is provided. Finally. the obtained theoretical and experimental results are effectively used for the modeling of actual TerraSAR-X high resolution, amplitude only, SAR images. In particular, this analysis is performed on the Vesuvio volcano area close to Naples, Italy.