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Model-based scattering decomposition [1-4] is an effective and popular tool for analyzing polarimetric SAR (PolSAR) data due to its clear physical explanation, convenient implementation, and easy visual interpretation. This technique aims to express the measured PolSAR data as the combination of different scattering mechanisms. However, the original three-component model proposed by Freeman and Durden  assumes azimuthal reflection symmetry and consequently does not use the complete information of the covariance or coherency matrix. Recent advances focused on increasing component numbers (e.g., the four-component model ) or reducing the number of knowns (e.g., by matrix rotation ), with the purpose to account for more elements in the matrix data. Nevertheless, it is to the best knowledge of the authors that finding a physically meaningful matrix expansion (i.e., model-based) that exactly (but not approximately) matches the measured data remains an unresolved task.