Ok the above equations didn’t worked as well as I would have liked. I finally choose a simple deconvolution scheme with total variation regularization, and without the band pass filter.
Example with https://discuss.pixls.us/t/playraw-view-on-the-mosel/15099/2:
Before:
After:
Notice how the background has not been deblurred while the foreground is much sharper. Also the transition is very progressive.