Gimp doesn't have this because in addition to the image, you need explicit knowledge of where the image came from.
Suppose you have an image which you already know is a cartoon. Compressed sensing can clean it up, but uses explicit knowledge of what cartoons look like. Similarly, if you know the image is scanned text, a different compressed sensing algorithm based on scanned text can clean it up.
But if you don't know where the image comes from to begin with, compressed sensing won't work.
