When calculating interferometric coherence, why can't you do so on a pixel by pixel basis? I know the equation for estimating coherence = (|S1∙S2* |)/√(S1∙S1*∙S2∙S2*) where S1 and S2 are the two single look complexes. And I know this calculation uses a maximum likelihood estimator but why do you need to specify an estimation window and why cant the estimation window size be 1?
Thank you.
Because its basically a phase correlation of scatter cells (mostly named as pixels) which needs a minimum number of values to correlate. This might be the answer for both questions. If you want 'pixel wise' comparison try to utilize polarimetry and treat different as 'bands' like in optical remote sensing. Keep always in mind that scattering has to be always considered.
Cheers, Chris
Christian Rogaß thank you for your reply.
Do you need this minimum number of pixels to correlate over because each pixel is influenced to some degree by neighboring pixels? So the signal from one individual pixel isn't completely representative of the signal from that region? And so you need this estimation window to account for this as well as small changes between the acquisitions (like small differences in perpendicular baseline, etc) in order to get a more complete estimation of the coherence of the signal? Or am I thinking about that wrong
You are absolutely right. Compared to optical remote sensing where 'adjacency' is a high order effect the signal impact of 'neighbors' is much higher here. A perfect coherence estimator would include dipol distribution, local 3D geometry for ray tracing and radiosity estimation and a gaussian shaped weighting window to 'reflect' the mixing and superimposition of the representing physical process. I was often thinking to compile a paper about all this in connection with a multi stage, alternative phase unwrapping.... Hope it helps. If not you can send me an email: [email protected]
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