I have an interferometric image which shows fringes at a certain frequency, basically a dominantly periodic signal overlaying the information that I want to extracthere are the fringes that I want to remove. The size of the image is 1024x4067 pixels. So using matlab I performed fft2(im,n) with n = size of image, giving me this fft-imageenter image description here, with maximum values given at (9,24) and it's symetric (1017,4045). I am totally confused now as of how to interprete this result. Does that mean I have a frequency of 9 in y and 24 in x direction making it some sort of Acos(2pi/9y+2pi/24x)+Bisin(2pi/9y+2pi/24x) wave!? I'm guessing this it totally wrong and stupid, but I'm really confused.. :-/ thanks for your help!

here is the shifted FFT image!

  • $\begingroup$ It doesn't look like you have used 'fftshift' on this spectrum (please see: uk.mathworks.com/help/matlab/ref/fftshift.html ). Can you please obtain the 2D FFT of a number of your fringe patterns (2-3) and post it along? From the attached image, it doesn't look like your fringe pattern is periodic but maybe you can still filter its effect. $\endgroup$ – A_A Apr 8 '15 at 7:42
  • $\begingroup$ I added the shiftet image to the original question. I dont understand what you mean with "Can you please obtain the 2D FFT of a number of your fringe patterns (2-3)"... $\endgroup$ – uetli Apr 8 '15 at 8:33
  • $\begingroup$ Thank you. What I am trying to say is, is the fringe pattern consistent across different acquisitions? If not, can you obtain 2-3 different fringe patterns and their spectra? $\endgroup$ – A_A Apr 8 '15 at 13:38
  • $\begingroup$ I just have this one acquisition unfortuntely... :-( $\endgroup$ – uetli Apr 9 '15 at 6:33
  1. Remove the mean from the image you linked before analysing it with fft2.
  2. Use fftshift to get a more readable image.
  3. Use a logarithmic scale on the 2d spectrum if you don't see anything.
  4. Please label the x and y axis with normalized frequency.
  5. Using the insight on the noise spectrum you got from the fft2, design the filters you need to remove the periodic noise.
  6. You noise isn't stationary withing the image, so your filters won't work awesome.

You could also try the following : Consider your columns as realization of a random vector of size approx 1000 (number of rows). Take your first 100 columns, apply PCA with covariance matric proportional to V*V' with V of size [100*1000], the vertical periodic pattern will be your most powerfull eigen vector. Project your data on the 99 remaining vector. Repeat this process on others 100 columns batches, be carefull with energy normalization.


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