Unsupervised segmentation of PolSAR data with complex Wishart and 𝒢^0_m distributions and Shannon entropy

Polarimetric synthetic aperture radar (PolSAR) systems are powerful remote sensing instruments. Despite their ability to acquire images in all weather conditions, day and night, and to detect dielectric properties and structures, PolSAR images are corrupted by multidimensional speckle. Such contamination, resulting from the use of coherent illumination, does not obey the classical hypothesis of additive Gaussian noise and therefore require special treatment. Moreover, the data are structured as positive-definite Hermitian matrices. The Wishart and 𝒢^0_m laws, both defined on the set of all positive definite Hermitian matrices, successfully describe fully PolSAR returns. The Shannon entropy is a scalar that measures the contrast between two PolSAR observations in this context. We obtain the Shannon entropy of these models and, using the h - ϕ entropy formalism, its asymptotic distribution. With these two elements, and using the Stochastic Expectation-Maximisation algorithm, we obtain better segmentations than those provided by the k-means and k-medoids with nine-dimensional inputs. We show applications to actual PolSAR data. Our results show that 𝒢^0_m entropy-based segmentation is better suited for images where the class features are not well separated, while its Wishart counterpart gives the best results in scenarios with more separable regions.