You can downsample (and gain some noise reduction), if you're oversampled for:
Downsamplling? Why would you want to lower the sampling. Won't that lower the resolution and lose detail. Do you do any NR, or just downsample?
How would you downsample? Is that done in PI?
Increasing sampling cannot increase resolution if something else is impacting resolution. It's much like using "digital zoom" on a terrestrial camera. An overly magnified image just magnifies blur from other sources.
Read the Startools webpage I cited above. They show an actual two image comparison showing how, in certain circumstances, you can trade "resolution" for a better to signal to noise ratio. It's serious proof. I've used their Binning tool (a form of downsampling) successfully. The gain was modest, but noticeable.
Is it an ideal case to make their point? No doubt. But is it a realistic case? Also, no doubt.
Actually, this isn't quite true. Increasing sampling can improve resolution, even if seeing is your single worst blur factor. Total blur is an RMS. It isn't just seeing, it isn't just image scale, it isn't just diffraction nor aberrations, it isn't just guiding and tracking error. It is all of them combined:
TotalBlur = SQRT(Seeing^2 + Diffraction^2 + Aberrations^2 + FilterBlur^2 + GuidingError^2 + TrackingError^2 + WindBlur^2 + PixelScale^2)
If you have an 80mm f/6 scope, your dawes limit is 1.44". If you have a 4 micron pixel size, your image scale is 1.72". Let's say your seeing is 2". Let's say you are using no filters, your lens is truly diffraction limited, you have no wind and your guide RMS is 0.8". Your total system blur would then be:
TotalBlur = SQRT(2^2 + 1.44^2 + 1.72^2 + 0.8^2) = 3.1" RMS
So what happens if you reduce your pixel size by a factor of 2? Your image scale is now 0.86":
TotalBlur = SQRT(2^2 + 1.44^2 + 0.86^2 + 0.8^2) = 2.7" RMS
That right there is a 13% increase in resolution. What if your seeing was a little better than you thought it was? Say 1.8"? This is often what you find as you start better sampling your stars...the pixels themselves add their own blur, so your measurements of what your seeing likely is are going to be skewed (and on top of that, few people account for the diffraction blurring or guide RMS when they try to use FWHM to figure out what their seeing is...most just assume that FWHM === seeing! That's false!!)
TotalBlur = SQRT(1.8^2 + 1.44^2 + 0.86^2 + 0.8^2) = 2.6" RMS
Well, that's a 4% increase...but, your gains are limited. By seeing? Well, not really, seeing just got better. Your scope is still limiting you to 1.44". What if you used a larger aperture? Say a 101mm?
TotalBlur = SQRT(1.8^2 + 1.13^2 + 0.68^2 + 0.8^2) = 2.37" RMS
That is another 9% increase in resolution. Relative to the original 3.1", it's a 24% improvement in resolution. Seeing has hardly changed here...you thought it was 2", turned out it was really 1.8" once you were sampling the stars more accurately and getting more accurate measaurements...that is only a difference of 0.2". Guiding didn't change either, since seeing really didn't change, so your guide RMS is still 0.8". What really changed was the sampling ratio...better sampling leads to better resolution most of the time. Given this is an RMS, the larger terms do dominate. If you have PARTICULARLY bad seeing, which I consider to be around 3" or worse (sadly, farily common in more northern latitudes, i.e. northern Canada, Netherlands, Alaska, etc. where you might be stuck under the polar vortex), then seeing will certainly limit your results and diminish the returns on better sampling. However I believe true 3" seeing is pretty rare...3" FWHMs are not...but FWHM is the TotalBlur...which includes many other factors.