Formalism of Compact Polarimetric Descriptors and Extension of the $\Delta\alpha_{\text{B}}/\alpha_{\text{B}}$ Method for General Compact-Pol SAR

Abstract

Compact polarimetry is a dual-polarization hybrid imaging mode and provides partially backscatter characteristics of scatterers. The compact polarimetric (CP) synthetic aperture radar (SAR) measures the combinations of fully polarimetric (FP) scattering coefficients, which is dependent on the transmit-wave polarization state. The backscattered wave is fully described by a 2-D complex scattering vector, in which the dual-channel polarization ratio represents the vector nature for describing target polarimetric properties. However, due to the dependence of CP measurements on the transmit wave, the complex channel ratio is explained differently for the same scatterers under different observation modes, e.g., the channel ratio $\rho =\pm j$ under the left circular mode and $\rho =\pm 1$ under the linear $\pi /4$ mode for the canonical trihedral and dihedral scatterers. The explanation diversity is inconvenient for the use of CP data, resulting in nonunified target decomposition algorithms. In this study, first, we propose a new formalism method for the general CP SAR mode, such that all CP mode observables are described based on the same standard for target scattering characterization. This provides potential for developing unified CP decomposition algorithms. Then, based on this formalism, a polarization ratio-based scattering characterization method is proposed, which is mathematically equal to the FP $\Delta \alpha _{\text {B}}/\alpha _{\text {B}}$ method but without any scattering assumption. Theoretical analyses and discussions are provided. Experiments show that the proposed method is efficient for compact polarimetric scattering interpretation.