Ok, that can be reversed, but the problem is that it is a "composite" effect, it is more than just a "twirl", it is 2 or more twirls together.
It probably possible in photoshop somehow to use actions/automate to produce say, 100 different slight counter twirls to produce 100 images, and then on each of them produce another 100 twirls, that would produce 10,000 images but it would be pretty easy to visually see which ones are the clearest. The main problem is that the original mapping would have damaged the quality of the picture so it may be fuzzy when it is finally untwirled, if that is even possible.
EDIT : My estimation for the picture is... a car.