I would like to apply a Pauli Decomposition to my Dual-Pol SAR Data (HH; VV). As a result, I need the complex values from Pauli Basis HH+VV and HH-VV and I will not use it for a RGB picture generation. I know that the R, (G), B bands produced by the following intensities: R = 0.5*|Shh - Svv|²; B = 0.5*|Shh + Svv|² My question is now how can I convert the intensities R and B to their complex forms?
It sounds like your HH and VV data are "detected" amplitudes/intensities rather than SLC data (single look complex). In this case, you can use them directly and compute R = HH-VV and B = HH+VV. You could convert them back to complex numbers, but that would be meaningless without the phase information. Note that this is not truly a Pauli decomposition in the absence of the HV data.
EDIT, in light of OP comment:
If the data are truly SLC complex data, then you evaluate them as you wrote. In numpy this would be
0.5*numpy.abs(HH+VV)**2, or using no temporary arrays:
HH += VV del VV numpy.abs(HH, out=HH) HH **= 2 HH *= 0.5
where HH and VV are the original complex values. The output is a real number, so you can save HH.real to a Float32 file for further analysis.