The following concept is a direct transfer to the amateur astronomy context of a piece of research titled,
Sensing Increased Image Resolution Using Aperture Masks (Northwestern University & MIT Media Lab circa 2008) to which I place a couple of links at the bottom of this post (1).
It should be possible to achieve sub-pixel image movements using a simple mask mechansism which is akin to moving the scope sub-pixel distances and therefore drizzle/dither and achieve higher sampling rates. HST has achieved the same by deploying sub-pixel movement of the entire platform (which was needed because the WFP2 was well undersampled with the HST). (2)
It should be emphasised that sub-pixel dithering is only of value if you started of undersamped in the first place. For example you had a well matched setup and then you added a focal reducer.
Consider an aperture mask that only allows light from a sub-region of the full aperture to reach the focal plane.
Consider a perfectly focused setup.
If one moves the position of the restricted (ie stopped down) aperture the image at the focal plane remains in the same position.
Now consider a very slightly out-of-focus image.
Move the restricted aperture to a different location and the image moves very slightly. If this is not immediately obvious think of what happens with a Hartmann mask. If we are very close to focus - but not at focus - we have sub-pixel movement.
Okay some apparent draw backs will glare out.
A ) Restricted aperture means that the diffraction limited resolution comes down so aren't we losing detail in the first place?
The resolution that we can attain is generally limited by seeing conditions and the FWHM probably wont change due to reduced aperture.
If we consider typical seeing of FWHM = 3" then what is the smallest aperture before we degrade this further?
A = (58.4 x w)/(FWHM)
For w=656nm (red) and FWHM = 3" we get A = 46mm.
With a little exercise on a drawing package I can see that one could get a 3x3 mask matrix (round apertures) on an 8" full aperture area. I chose 3x3 to echo what was done by the researchers. I see no reason why a 2x2 matrix would not work and if used would allow a larger restricted aperture.
B ) We're losing light due to smaller aperture.
This is a huge downside. A 46mm aperture only captures 5% of the light of a full aperture 8" scope. This would require twenty times longer exposure and is probably a show-stopper for astronomical application of this technique. However, if the restricted apertures could be large and allowed to overlap then this downside could be mitigated somewhat. Experiments in this area may be worth while.
C ) The blur (we need a slight defocus) destroys information and then we are sampling that blur.
This isn't as bad as it first sounds. I believe that we can blur up (increase FWHM) to the point where our dithered sampling is at Nyquest (ie two - or whatever number you choose - dithered pixels to one very slightly bloated FWHM) - but no further. (I'm not sure if my idea of blur concurrs with the researchers' view).
If anyone wishes to pursue feel free. Its too much bother for me personally but thought it would be remiss of me not to pass it on in case it could be of use somewhere.
Mark
(1) Original material:
web.media.mit.edu/~ankit/superres/
and
web.media.mit.edu/~ankit/superres/superres_supp_cvpr08.pdf
(2) Why dither:
www.stsci.edu/~stefano/newcal97/pdf/fruchtera.pdf
  