"The pixelation destroys fundamental information from the image. Even knowing the algorithm used to perform pixelation will not allow full recovery or even ensure significant recovery."
Indeed. The only thing proved by recovering a pixelated image is that it wasn't pixelated enough in the first place. I suppose it's vaguely interesting if a computer can identify an image that's messed up enough that a human can't, but since we're dealing with a process that destroys information it's utterly trivial to do so in a way that guarantees nothing can ever recover enough information to identify anything.