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Calculation of the Spatial Distribution of Scatterers in a Diffuse Scene from Sar Data

One practical use of synthetic aperture radar (SAR) images is to segment large areas of land into various geophysical classes; crop types, tree types, or urban versus suburban areas for example. Since large amounts of data are usually involved automatic algorithms are the only practical approach. It would make such algorithms easier to implement if the probability density functions (pdf's) of the various classes could be modeled beforehand; in fact if the pdf's are known optimal detection algorithms can be implemented. In addition, knowledge about the distribution of scattered energy from a given scene can give information about the physical structure of the scattering surface, namely the spatial distribution of scatterers within the scene. For reasons such as these it is useful to develop a parametric model for the pdf of diffuse scenes in SAR images. Much work has been done in this area already [1,2,3] , mainly in attempting to fit pdf's with known analytical forms to histograms generated from SAR data. Unfortunately, as SAR resolutions become better (thus generating more independent samples of a diffuse scene) and SAR calibration procedures become more refined (thus removing uncertainties in backscattered values due to system effects) the analytical forms do a poorer job of fitting the actual histogram data. This indicates that a more complicated pdf model is necessary, one that includes the physical aspects of the terrain being imaged, rather then just continuing to search for other analytical forms. This paper will present a model that essentially divides the SAR pdf into a part due to speckle and a part due to the spatial distribution of the scatterers within the scene allowing a better fit to the SAR histogram values and allowing the spatial distribution function to be extracted from the SAR data. A specific form of this model was presented in ref. 2, but our approach is to generalize that model to multi-looked SAR data and to extract the spatial density function directly in addition to assuming a functional form for it.