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I was just wondering if anyone could explain to me the approach one would take to removing striped noise from the fourier domain of an image. I was reading an article about MRI image from 1 just giving a general outline of the location of spatial frequencies, and it had a slide (displayed below) which got me thinking in how I would attempt to remove the striped noise.

My original thought was to just block the given frequency with a mask but if I set the mask to 0 then I would have to be pretty accurate with the mask so I dont block out any other components that may be necessary for the image.

My second idea which I am not sure on is as each point the frequency domain is represented by phase and a modulus could I somehow use that to remove the striped noise?

enter image description here

1 http://mriquestions.com/locations-in-k-space.html

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I have solved a similar problem using an Ideal low-pass filter. The idea of the process is rather simple: eliminate all frequencies above a certain threshold, while passing the ones below it. If you plot the Power spectrum of the noisy image, you will spot two dots which correspond to the stripes (one in the top-left quadrant, one in the bottom-right quadrant). Therefore, you should aim to set the threshold as close to those dots as possible but strictly below them. Here is a plot that visualizes the process of applying an Ideal low-pass filter to a noisy version of the trui.png.

enter image description here

The reason why the filtered image is slightly blurrier than the original one is because the low frequencies are around the centre of the Power spectrum and we cut off all frequencies higher than the threshold.

Note: I have modified the stripes in a way such that they result in convenient dots in the frequency domain. This makes it easier to filter them out using the Ideal low-pass filter. Keep in mind that in reality, the dots might be way closer to the centre of the Power spectrum, thus hindering the Ideal low-pass filter's performance.

Hopefully, I was able to point you in the right direction. You can refer to C. Gonzalez, E. Woods if you are interested in the theory behind the filter. Moreover, you might be able to find a better solution to this problem in the book.

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    $\begingroup$ So you just zeroed DFT bins? There should be a disclaimer on this generally worst implementation of "ideal low-pass". I figure it works here per the would-be smooth transition band being low energy. $\endgroup$
    – OverLordGoldDragon
    Apr 17 at 9:11
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    $\begingroup$ Thanks for linking this thread. The approach definitely has its flaws and I did elaborate a bit on them. $\endgroup$
    – Hristo Georgiev
    Apr 17 at 9:54

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