Fractal Models for SAR images

In this thesis the modeling of SAR (Synthetic Aperture Radar) images of natural surfaces described via fractal models is dealt with. A complete theoretical forward model linking the parameters describing the scene observed by the sensor to the stochastic characterization of the relevant SAR image is provided. The inverse problem is treated as well: a SAR image post-processing able to automatically retrieve - operating on an amplitude single SAR image - the fractal parameters of the scene, is presented. The developed imaging model is based on sound geometrical and electromagnetic models that are combined according to the SAR impulse response function. The power spectral densities of appropriate cuts of the SAR image are evaluated in closed form in terms of the surface fractal parameters. The theoretical results are here conceptually assessed, analytically derived, graphically validated and numerically verified. Moreover, based on the inversion of the forward theoretical model, an innovative SAR image post-processing for the fractal parameters estimation is implemented. It is firstly tested on simulated SAR images, then it is applied to different types of new generation (i.e. high resolution) SAR images. The generated fractal maps show themselves to be very useful for a wide range of application, e.g. prevention and monitoring of environmental disasters, geodynamic processes interpretation, land classification, rural planning, and so on.