Adaptive optics generally apply slight changes to mirrors to account for atmospheric turbulence. These generally require either a mirror to be broken up into smaller mirrors, each with their own actuator, or for a single large mirror to be slightly deformed by many different actuators.
Is it possible to do much of this digitally?
Couldn't software slightly attenuate or amplify each pixel at each time-slice collected from a passive mirror? These changes would depend on the distortions measured by a guide star or laser (this digital system would still require a guiding light)? I suspect this would probably be less accurate than true adaptive optics, but it would also be far less expensive (as you wouldn't need so many actuators).
Has this approach been studied and dropped? Is it ridiculous and not even theoretically possible? I'm curious if anything has researched this idea.