SAR Imaging of Fractal Surfaces

A complete theoretical model for synthetic aperture radar (SAR) imaging of natural surfaces is introduced in this paper. The topography of the natural scenes is described via models derived from fractal geometry; scattering evaluations are performed via fractal scattering models appropriate to the employed fractal scene description. Scattering contributions are combined according to the SAR image impulse response function. The power spectral density of appropriate cuts of the SAR image are evaluated in closed form in terms of the surface fractal parameters. Our theoretical model is here conceptually assessed, analytically derived, graphically validated, numerically verified, and also tested on simulated SAR images. The introduced model allows defining innovative postprocessing inverse techniques to retrieve fractal parameters directly from SAR images.