Hypothesis Testing, Separability, and Classification of Polarimetric SAR Intensity Data With Nonparametric U-Statistics

Polarimetric synthetic aperture radar (PolSAR) sensors have emerged as a groundbreaking remote sensing technology. They enable the acquisition of the amplitude, phase, and orientation of electromagnetic waves across multiple polarizations. This capability provides enhanced potential for detailed environmental analysis. However, challenges such as complex data structures, non-Gaussian noise properties, and low signal-to-noise ratios pose significant barriers to the effective use of PolSAR data. Existing methods for modeling and analyzing PolSAR data are predominantly parametric and rely on assumptions that may fail under certain conditions. Aware of these limitations, this study introduces the use of U-statistics for PolSAR data analysis. Using information from the diagonal intensities of the covariance matrix, we propose a hypothesis testing mechanism to assess sample homogeneity, a top-down hierarchical separability analysis, and a U-statistics-based classification approach. The proposed procedures are validated using an ALOS-PALSAR image of the Amazonian region. The results show the robustness and effectiveness of the proposed methods, offering a reliable framework for analyzing and classifying PolSAR data under nonparametric assumptions.