Fourier transform of Image to identify sinusoidal sources of interference
Alright. This is image processing. Sometimes its results might seem indeed magical. And quite some other times, in some books or papers, you see they discuss an algorithm or method to process a given distorted/noisy image and convert it into an unbelievably perfected form. Yet they don't provide any actual code, neither are the input and output images made available. It's therefore quite impossible to replicate what they propose to have achieved. 

In this example a ridiculously simple idea is provoked. In fact it is the most basic idea of all signal procesing: Filtering! There is an original degraded image so much degraded that it might seem impossible to recover, but when it's analysed via DFT it's been seen that there're some spurious frequency components which are not to be expected from the original undistorted image. In addition it's quite interesting that those spurious frequencies are all distributed inside a circular ring of frequencies! So this is the easiest of all signal processing. Just design a circular 2D filter narrow enough to suppress all those circular band of spurious components, and leave all the rest untuoched. The result is that magic. 

That being said, however, It is very unlikely that in your everyday life you would encounter such a highly structured "noise" or "distortion". It seems as if almost this distortion was just added there for the purpose of a filtering demonstration. And indeed due to poor fact checking and documentation this kind of demonstration tricks seem to exist. What you basicly do is this: You have an original clear image. You add some artificially generated noise to it and you apply a noise recovery algorithm to remove it! Aaaand ta daaaa perfect recovery is possible, in real life or just for an artifically generated noise?