This Topic is pretty complicated.
First, about still Images :
Of course the Original Image can not be restored in full Quality,
because the Mosaic Effect causes loss of Information.
A possible way to make it look better...
Did you notice that Thumbnails of censored Hentai often looks uncensored ?
Thats the Key.
I'm not good at Image Manipulation, but the following should work :
- measure the size of one Mosaic Block, example : 4 pixels
- select the Mosaic Area
- create a Layer from Selection
- scale it down by the Size of a Mosaic Block, in my example by 4
- scale it up to Original Size, use the best possible Interpolation
The Result will be very blurry, but it may be less ugly than Mosaic
For a perfect result, use Paint Tools and retouch the Image.
Now about Video... things get interesting
The Method described above works on Video, too -
but doing it frame by frame will take 100 years,
and there might be a better Solution.
It should be possible to detect the Mosaic Area using a custom Program
and convert all the Mosaic to a blurry Mess.
IMHO, this is still better than the Flickering Mosaic, because it looks more natural.
But there is more - a Video is not just a Stack of many Images,
there is Movement of Camera, zoom and Movement of Actors and Objects.
This could be used to extract more Information - dont forget the Mosaic is Flickering.
I'm still learning about this Topic, there is some interesting Stuff on the Web.
A few Links :
http://www.thedeemon.com/VideoEnhancer/
http://www.psi.toronto.edu/~vincent/videoepitome.html
http://users.soe.ucsc.edu/~milanfar/software/superresolution.html
Sure, there is no ready-to-use Solution, but it can be done. Not perfect, but less ugly.