Speckle filtering with Lee filters

Could you please elaborate what you mean by that?

I am so confused when some literature as (Lee 1994) mentioned that speckles were granular noise resulted from interference. and (Engdahl, 2013) said it’s “noise-like” appearance.

Also, how come single light source cause such effect, is it because of interference emerged from diffraction?

Well, whether it is “noise” is practise depends on the application - in intensity-based applications it is usually a nuisance. It is “noise-like” in the sense that it is random but fully reproducible if coherence has been preserved.

It can be viewed as the end-result of the coherent summation of reflections from many “elementary scatterers” that are much smaller than the resolution-cell.

So, can the doppler shift contradict the frequency coherence that causes speckle effect? As if the observed frequency of echoes change between multiple scatterers, so the signals won’t completely interfere and speckle won’t appear?

I’m not sure if I understand your question but speckle is present in fully focused images where the doppler-history difference has been used to focus the image. And in any case the elemental scatterers are much smaller than the resolution-cell and cannot be resolved.