We consider the problem of classifying a pair of Synthetic Aperture Radar (SAR) images by proposing an explainable and frugal algorithm that integrates a set of divergences. The approach relies on a statistical framework that takes standard probability distributions into account for modelling SAR data. Then, by learning a combination of parameterized Renyi divergences and their parameters from the data, we are able to classify the pair of images with fewer parameters than regular machine learning approaches while also allowing an interpretation of the results related to the priors used. Experiments on real multi-class data demonstrate the virtues of the suggested method when compared to both Random Forest and Convolutional Neural Networks (CNN) classifiers, showing its resilience to disturbances such as polluted labels and variations in the percentage of training data.