TABLE OF CONTENTS In order to derive the Gaussian model, the central limit theorem is applied to estimate the effect resulting from the vector sum of basic effects of each basic scatterer inside the resolution cell, assuming they are numerous. To make this application possible, several conditions have to be met: we particularly need to have a fully developed speckle on a homogenous (untextured) stationary scene. The components of 
[1] are then complex Gaussian random variables with 0 mean:
, with the dimension d, follows a centered Gaussian distribution:
where 
is the conjugate transpose of 
, C is the determinant of C (covariance matrix of 
; see equation [1.19]) and d is the dimension of 
, leading to 3 or 4.
Therefore, the distribution is fully characterized by covariance matrix C [2], from which all higher order moments are deduced. In particular, odd-order moments are zero and the non-zero moments of order 4 are given by:
because by assuming an independent backscattering of the various backscatterers inside the resolution cell, we have E(S i.S j) = 0 (uniformly distributed phase of the backscattering elements).
According to equation [5.16], we obtain in particular: 
.
Finally, note that for L-look multi-look data, the observed covariance matrix ? follows a complex Wishart distribution law (equation [5.8]) [GOO 76a]:
The Gaussian model is by far the most widely used. Theoretically, however,...
