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Notch Filter

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crisubeda edited this page May 13, 2021 · 12 revisions

Notch Filter

The Notch filter is characterized by rejecting a given frequency, between the upper and lower cutting frequencies. When we talk about the filtration of periodic noise by a Notch filter in image processing, we mean that is necessary to apply the following steps:

  1. Take the FFT of the input image. F = fft2(I).
  2. Display the log power spectrum of the fftshift-ed F.
  3. Find the locations, xi, of the spikes that correspond to the periodic distortion.
  4. Create a 1-band image, M, of class double the same size as I.
  5. Set all M’s pixels to 1.0.
  6. Let N(xi) be a neighborhood of xi with area sufficient to cover the spike at xi.
  7. For each xi do: for each yj ϵ N(xi), set M(yj) = 0.
  8. Take the ifftshift of M.
  9. For each band, k, of the image let Gk = Fk .*M.
  10. Then the noise-reduced image is: J = real(ifft2(G)).

This app is going to do all those things and manages to filter out the noise. The Notch filter will then be applied to these two images. These images are noisy, and the goal is to remove it using that filter.

During the execution of the app, it is important to understand several things:

  • The section where a numeric value is requested for “Area” refers to how many points in the image will be taken around the selected points of the Fourier Transform of the noisy image.
  • The application allows you to choose certain points in the Fourier Transform, and therefore in the frequency domain. Those points that will be marked to filter, can be seen very clearly in the following images. Those points are going to be frequencies and they are going to be selected in the following way:

It is not going to be necessary to take all the points of the whole image. With taking the points that belong to one half of the image is enough. This is because the application will select the complementary ones (look the selected points in the previous images)

Below are three videos of how these two images that were previously discussed are filtered. Two of those are from the same image but applying different values for the area with the goal of compare the finally filtration.

For Clown image:

With Area = 5:

With Area = 1:

For Moon landing image:

With Area = 20:

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