From Gaussian to inverse Gaussian statistics in SAR imagery

Among the family of exponential distributions the normal or Gaussian distribution plays a fundamental role in natural environments-above all-due to its symmetrical properties. In distributed terrain the size, position and orientation of scatterers within the ground resolution cell of a SAR system is Gaussian distributed as well as their backscatter over a series of radar pulses; particularly when the size of scatterers is of similar magnitude as the radar wavelength and their number is greater then 10. Now, the motion of the SAR system influences the statistics of backscatter in such a way that its symmetrical properties are lost to asymmetry. The more the structure of terrain changes from homogeneous to heterogeneous (from pasture to forest) and from heterogeneous to extremely heterogeneous (from forest to urban) the more the statistics of SAR backscatter deviates from Gaussian. Hence, another distribution, the inverse Gaussian, arises most naturally for backscatter of distributed targets under the assumption that the single scatter cell keeps its Gaussian behavior. (The term inverse refers to the cumulant generating function of this distribution being the inverse of the Gaussian one.).