The use of multidimensional copulas to describe amplitude distribution of polarimetric SAR data

The paper focuses on a flexible model of multidimensional probability density function (pdf) dedicated to describe amplitude distribution of polarimetric SAR data. The model is based on the copula theory for characterizing the dependency between polarimetric channels (HH, VV, HV/VH or the target vector components). The benefit in using copula theory is to extend correlation concept to a wider dependence one, which may not be linear. From this point of view, the model is more flexible than the classical Wishart distribution. But it may include it. The other benefit in using the copula model is to separate the dependence concept from the shape of the marginal pdfs. Hence, this multidimensional characterization may be linked to classical 1D gamma pdf, or to a more flexible Pearson system of distributions. In the case of high resolution data, pdf shapes are becoming of heavy tailed and the Fisher system of distributions seems to be an interesting alternative for such a model. Any parametric 1D model may be used. The paper mainly focuses on the model itself and more precisely on the technique required to construct such multidimensional dependence function. The difficulties arise for copula on 3D in which the dependency is not homogeneous between the components (the link between HH and VV may not be of the same behavior as the one between HH and HV). Illustrations are given on classification and despeckling. Classification will be performed by a stochastic estimation maximisation (SEM). Despeckling will be achieved by a maximum A posteriori technique.