Characterization of radar clutter by gamma induced distributions

In the weak scattering regime the statistical properties of terrain backscatter data observed with satellite and airborne synthetic aperture radars differ from Gaussian statistics the higher the resolution, the lower the looknumber and the stronger the texture are. The recently presented and discussed G-distribution is a most suitable candidate to cover up the wide range of homogeneous, heterogeneous and extremely heterogeneous radar clutter, which under limiting conditions converges to Gaussian. The G-distribution contains as particular cases the isotropic (=zero mean) KO-distribution and the GO-distribution, the last of which is able to model very heavy backscatter such as that of urban areas. In this paper are given reasons that the multilook G-distribution is based on three joint distributions from the Gamma family. The gamma-distributed complex speckle is conditionally multiplied with the gamma-distributed regular part of radar returns and the widely dispersed part of returns, which is inverse-gamma-distributed. The mixing of gamma and inverted gamma generates the generalized inverse Gaussian distribution. If the radar data are normalized the G-distribution is completely determined by the shape parameter α and the concentration parameter ω. Both parameters can be estimated by the method of moments in an unbiased way