Accurate Estimation of ⟨|SHV|2⟩ in Hybrid-polarimetry SAR: A closed-form solution

In the current literature, the linear cross-polarization term, denoted as <vertical bar S-HV vertical bar(2)>, is often considered a lost parameter in hybrid-polarimetry (hybrid-pol) SAR. This assumption is based on the belief that even with the reflection-symmetry condition (which holds for most natural surfaces), five parameters are needed to compute <vertical bar S-HV vertical bar(2)>, whereas hybrid-pol can only measure four parameters, leading to an underdetermined solution. We respectfully disagree with this viewpoint and assert that four parameters are indeed sufficient for accurately calculating <vertical bar S-HV vertical bar(2)>. Accordingly, we have derived a mathematical relationship under the reflection symmetry condition that provides a closed-form solution for calculating <vertical bar S-HV vertical bar(2)> from hybrid-pol SAR datasets. This has been validated through both theoretical analysis and practical assessments using ALOS PALSAR L-band data