Covariance Matrix Estimation via Geometric Median in Highly Heterogeneous PolSAR Images

The Wishart distribution is a well-established statistical model for characterizing the density of random variables in polarimetric synthetic aperture radar (PolSAR) data, particularly within homogeneous regions where Gaussian assumptions hold. However, as PolSAR applications expand into heterogeneous environments, alternative statistical models have been developed to better capture the complexity of such areas, playing an important role in tasks such as classification. In this study, we examine the effectiveness of covariance matrix estimation using the median matrix, a technique grounded in optimal transport theory and validated in prior research for its effectiveness. Building on this foundation, we propose the application of a statistical model tailored for heterogeneous regions, i.e., following the $\mathcal {G}^{0}_{P}$ distribution, addressing the limitations of traditional assumptions. This method is particularly suitable for high-resolution PolSAR datasets, where the homogeneity hypothesis often does not hold. The experimental results obtained using L-band PolSAR images acquired over Foulum in Denmark demonstrate the robustness of our proposed variant.