Fractal analysis and validation of a sea-surface fractal model for SAR imagery

A fractal model for sea surfaces is proposed, discussed and validated by fractal analysis on synthetic 2D reflectivity maps derived from live recorded data, and on a real ERS-1 SAR image. The proposed dynamic fractal model of the surface is based on the use of the band-limited WM functions. The model takes into account for the multistructure of the sea, it includes the time-evolution of sea waves, and it gives a realistic representation of the sea wave surface since it uses the sea hydrodynamic-differential equations describing the sea wave motion. A suitable data analysis technique is defined for the estimation of the fractal model parameters. This methodology is based on fractal and multifractal analysis of the SAR image and allows to directly estimating the sea model parameters from a fractal analysis of the radar data. In particular, a method to obtain the fractal dimension D, based on the multiscale decomposition provided by the normalized Laplacian pyramid (NLP) is used. Multifractal analysis is also used to evaluate the "local regularity" of the model by means of the Holder exponent spectra. Experiments on measured sea spectra, simulated radar reflectivity maps and real SAR images of the sea surface corroborate the underlying modeling assumptions and show promising results to strictly validate the proposed fractal model on a large class of SAR images of the sea surface.