1
$\begingroup$

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 POW! Magically the image is crystal clear!!!

Does anyone have any insite into this? Are there any statistical approaches that can be used to test a hypothesis that these 'hot points' are in fact interference? Are there other interesting approaches to analyzing these transforms statistically??

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. And to anyone who is NOT familiar with this topic... HOW AWESOME IS THIS?!?!?

$\endgroup$
1
  • $\begingroup$ You might want to ask this question on mathematica.stackexchange.com for a possible set of code to do this. $\endgroup$
    – JimB
    Commented Apr 1, 2021 at 17:07

1 Answer 1

1
$\begingroup$

Random noise tends to turn into high frequency Fourier coefficients. FFT. Clip the high frequencies off. IFT. Cleaner picture...unless what you are seeking resides in the noise. This is true for 1D and 2D.

Old, standard technique...too often forgotten about in favor of smoothers and wavelets.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.