Wei-Hao Wang:
First, if one wants to claim drizzle improves the resolution, one really should compare before/after images with the same pixel scale. I do agree that Kay's drizzle result is very impressive from a Cat51. But to really claim that's due to drizzle, a fair and controlled comparison is necessary.
At the same time, measuring FWHM in an image after BXT is scientifically meaningless. But it is indeed a good measure of visual impact. Even if the smaller FWHM doesn't tell the intrinsic resolution of the data, it tells about visual sharpness (along with a potential risk of processing artifact, i.e., sharp features that do not really exist). But again, if you want to claim the small FWHM is caused by drizzle, then you really should measure it before you apply BXT. On the other hand, if one wants to claim the small FWHM is caused by BXT, the he/she should measure the FWHM after BXT on an undrizzled image. If you don't do this controlled comparison, you may attribute the good result to a wrong reason.
All that being said, many people find that BXT works better on images with finer pixel scales (whether it's achieved by drizzle or not). So what Kay saw here may be a combined effect of drizzle+BXT (and excellent processing!).
Yes, the result is clearly a combination of drizzle + whatever the processing is. But it is clear that you achieve results that you can not achieve without drizzling. This is quite obvious on the globular clusters. Without drizzling, stars do not just look like a square, but you also can not resolve the close pairs. I have seen 3x revealed some very close stars compared to 2x where I was not able to see-- it is not as significant as without drizzling to 2x though. I'll take time to show some results. But again, I have to make the distinction that this is not in terms of scientific results or data analysis, it is the visual impact.