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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.

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  • $\begingroup$ 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
    Commented Feb 26, 2016 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? $\endgroup$
    – jojeck ♦
    Commented Feb 26, 2016 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
    Commented Feb 26, 2016 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
    Commented Feb 26, 2016 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
    Commented Feb 29, 2016 at 23:08

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This is image processing: many times, you see authors discussing an algorithm to process a given distorted / noisy image, and converting it into an (unbelievably) perfected form, without providing any code or input-output images (in files). Then it becomes quite impossible to replicate what they propose to achieve.

In your example, basic LSI spatial filtering is demonstrated. The original image is so much degraded that visually it seems very hard to recover. Yet, looking into its spectrum reveals that there are some components unlikely to come from an original undistorted image. In addition, it's quite nice that those components are all distributed around a circular ring of frequencies. So, a circular 2D filter, narrow enough to suppress all those circular band of spurious components while leaving all the rest of spectrum untouched, will do the magic for this image at hand.

That being said, however, in practice such a structured distortion is less likely to be observed. Imho, it was added there just for the purpose of the demonstration, yet I can't confirm it. You should better ask NASA, for a credit of the original image, and for the mechanism of its distortion...

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