I'm a statistics grad student, and I just started getting into Digital-Image-Processing (an analogy for processing super-large contingency tables). In the book "Digital Image Processing" by Gonzalez and Woods, I was reading chapter 2, page 94 of the third edition, and found the following image that is MAGIC to me...

Removing Sinusoidal interference - DIP Gonzalez Woods

They begin with a noisy image, identify some 'hot points' surrounding the center of the Fourier transform, then simply remove them, reverse the transform, and I can't help vocally demonstrate an emotional reaction while assessing that the image is now crystal clear.

Does anyone have any insight into this? I'd like to know what are the underlying notions and methods used to filter this image.

Additionally, if any of the StackExchange users a familiar with this topic and can suggest some articles/books that I might read, I would be very grateful.

  • $\begingroup$ Those points on fig (b) displayed in a circle are the Fourier's transform of the sinusoidal parasitic components. The mask fig (c) aim to remove them, therefore, the final image fig (d) is fig (a) minus the sinusoidal noise. it works exactly like 1D signal processing but ... in 2D $\endgroup$ – MaximGi Feb 26 '16 at 8:25
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    $\begingroup$ I don't think that "HOW AWESOME" and "POW!" is an example of scientific language... Any way to refine the question? $\endgroup$ – jojek Feb 26 '16 at 8:50
  • $\begingroup$ I believe that the question deserves some improvement time since it triggers interesting questions on the magic of image or signal processing, and the choice of stunning examples $\endgroup$ – Laurent Duval Feb 26 '16 at 10:16
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    $\begingroup$ on hold ?? I was in the middle of an answer. He is asking for a deeper explanation of this example (not opinion based), and, additionally some references (can be opinion based, but usually done in the comments). $\endgroup$ – MaximGi Feb 26 '16 at 13:25
  • $\begingroup$ @jojek sorry if my use of language is overly casual... I was just trying to convey my enthusiasm (and hopeful stir up some enthusiasm from any young readers that came across my post). $\endgroup$ – Lewkrr Feb 29 '16 at 23:08

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?

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