Modeling of extremely heterogeneous radar backscatter

A new class of G-distributions has been proposed to characterize the statistical properties of multi-look processed SAR data over the wide range of homogeneous, heterogeneous and extremely heterogeneous backscattering of terrain classes. The probability density function was derived as a product of a gamma distributed complex speckle variable and the generalized inverse Gaussian distribution for terrain backscatter. The latter is the outcome of a compound Poisson process which describes statistically the underlying physical scattering process. A particular case of the G-distribution is the K-distribution. Another limiting case is the called here G⁰-distribution, which is able to model extremely heterogeneous clutter, such as that of urban areas, that cannot be properly modeled with K-distribution. As the G-distribution is scaleable it can be standardized by normalizing the SAR data with the mean intensity. The other two parameters, which are responsible for shape and spread of the distribution, are estimated by the method of moments where the negative moments are generated by inverse transformation of the normalized SAR data