Sentinel 1 - GRD - How to properly calculate the VH/VV ratio

Hello,

I am currently trying to calculate the ratio VH/VV (and VV/VH) from some Sentinel in GRD. I already calculated it, but I was wondering at which step should I do the ratio.

I tried before and after converting VH and VV to decibel (using Linear to/from dB), and i got different results, and also when I converted the ratio in decibel after calculating it from VV and VH without conversion.

Also I was wondering if it is relevant to use both VV/VH and VH/VV in an analysis, especially because both look like negative of each other.

And eventually I asked myself if I should calculate the ratio before or after applying the speckle filtering, because of the loss of information ?

Here are my results for the VH/VV ratio :

And i applied the following steps to my image :
Subset>Thermal Noise Removal>Apply-Orbit-File>Calibration>Terrain Correction>Speckle Filter (Lee Sigma)

Thanks in advance (And sorry for my poor english, iā€™m french)

if you want to highlight the role of polarization (how strong is VH compared to VV or vice versa) the ratio is a suitable measure, but if you convert to dB scale, you have to consider the laws of logarithms:

VH/VV becomes VHdb-VVdb

VV/VH becomes VVdb-VHdb

explanation: https://people.richland.edu/james/lecture/m116/logs/properties.html

Regarding the other question: I would first speckle filter and then convert the ratio, but this is a rather personal preference because it makes more sense to me.

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Thanks a lot for your help ! Then i think that I am going to use the dB version, from what I have read, it seems more appropriate to show the medium values ?

Also, when you say to apply speckle filter and then convert the ratio, you mean that you would apply the speckle to VH and VV, calculate the ratio and only then convert it to dB ?

I would speckle filter both bands (VV and VH), convert them to db and finally calculate the ratios (difference in dB)

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Ok, thanks again for your help