Closed-Form Solution For Accurate Estimation of ⟨|SHV|2⟩ In Hybrid-Polarimetry SAR For Oil Spill Monitoring

In the existing literature, the linear cross-polarization term, i.e. $\left\langle\left|S_{H V}\right|^{2}\right\rangle$, is often considered a lost parameter in hybrid-polarimetry (hybrid-pol) SAR. This hypothesis arose from the recognition that, even when taking into account the reflection-symmetry condition (which is nearly valid for all types of natural surfaces), there are five parameters required to compute $\left\langle\left|S_{H V}\right|^{2}\right\rangle$, whereas Hybrid-pol SAR can only acquire four parameters, resulting in an underdetermined solution. We respectfully hold a different perspective from the earlier statements and would like to clarify that utilizing four parameters, instead of five, is indeed adequate for the precise calculation of $\left\langle\left|S_{H V}\right|^{2}\right\rangle$. Consequently, we have established a mathematical relationship under the reflection symmetry condition that provides a closed-form solution for calculating $\left\langle\left|S_{H V}\right|^{2}\right\rangle$ from hybrid-pol SAR datasets. For validation, both theoretical and practical assessments have been conducted, with the implementation of compound scattering matrices based analysis and the real Satellite ALOS PALSAR L-band dataset.