A Monte-Carlo study of classical spectral estimation of the backscatter in k-distributed images

Some estimators for the spectral density of the return in synthetic aperture radar (SAR) images are studied using Monte Carlo experiences. The spectral density is an important quantifier of the texture that, in turn, can be related to biophysical magnitudes and it can be used to establish the kind of target being observed. These images are contaminated by a particular kind of noise, called speckle, that departs from the classical hypothesis of obeying the Gaussian law and of entering the signal in an additive manner requiring, thus, a careful treatment. The departure from the Gaussian law will be modeled by means of the k distribution. This law arises from certain (very realistic) hypothesis for the relationship between signal and noise. The empirical observation of structured data is modeled by the use of spatial correlation. There are two approaches to the problem of the presence of speckle noise, one being the use of techniques for its reduction (usually specially devised filters) and the other the proposal of methodologies that take its presence into account. These approaches are compared, to the problem of estimating the spatial correlation structure of the ground truth. The performance of these estimators are assessed using Monte Carlo experiences, since the problem is analytically intractable.