technically, you can derive entropy and alpha, yes. But the results are not very useful, especially for cross polarization. It just doesn’t give all the information needed for polarimetry:
Thus, HH-VV SAR is a suitable alternative to full-polarization SAR in certain cases. Meanwhile, the extraction performance of the other two dual-polarization SARs is badly degraded due to the lack of co-polarization. Therefore, HH-HV and HV-VV SARs cannot effectively extract the scattering mechanisms in the H-α plane.
As you can see, HH-VV works quite fine, but the identification of
- Z3 = low entropy multiple (dark red)
- Z4 = mdium entropy surface (cyan)
- Z5 = medium entropy dipole (blue)
- Z8 = High entropy dipole (green)
just goes miserably wrong in cross-polarized (HV or VH) modes. You just have to consider that polarimetry needs the information of all four polarizations in order to correctly decompose the different scattering mechanisms within the matrix.
All the parameters you name are found on an empirical base. You can search for dual-pol publications specifically which try to find a way around but as for entropy/alpha decomposition on cross-pol data you have to be careful.