Unfortunately, I can't post the article as it requires a subscription. I will paraphrase the concept though. The basic idea is to use shape changing mirrors and adaptive optics to correct for the atmospheric distortion. Incident light hits an adaptive mirror which then passes the light through a beam splitter. Part of the beam is focused to produce the high resolution image while the other part is passed to image sensor which perform the DSP to adjust the shape changing mirrors resulting in the optimal deformation removing the atmoshperic distortion.
If you are particularly interested in the subject, drop me a pm and I will see if I can turn up some more info. You may also enjoy poking around this site; although I haven't actually looked at it myself.
Adaptive Optics Lectures