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

In the current literature, the linear cross-polarization term, denoted as $\left\langle {{{\left| {{S_{HV}}} \right|}^2}} \right\rangle $, 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 $\left\langle {{{\left| {{S_{HV}}} \right|}^2}} \right\rangle $, 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 $\left\langle {{{\left| {{S_{HV}}} \right|}^2}} \right\rangle $. Accordingly, we have derived a mathematical relationship under the reflection symmetry condition that provides a closed-form solution for calculating $\left\langle {{{\left| {{S_{HV}}} \right|}^2}} \right\rangle $ from hybrid-pol SAR datasets. This has been validated through both theoretical analysis and practical assessments using ALOS PALSAR L-band data