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# DFT: Filtering of Coherent Noise

[Laboratory]

The original image and its magnitude spectrum (size 256x256) is shown below

a)Original image; b)Its Spectrum
a) | b)

Observe that in the magnitude spectrum we can identify coherent noise, "stars" of different sizes. Our objective is to eliminate this noisy pattern by making the "stars" zero. Shown below is a pattern that we can use to multiply in the frequency domain and cancel the noisy pattern. Pass the mouse over the magnitude spectrum of the image to determine the coordinates of the spikes and use this information to create your frequency mask. After multiplying the frequency filter with the DFT of the original image we get the spectrum of the image with the noise removed.

a)Frequency mask to cancel "stars"; b)Product Spectrum
a) | b)

Taking the inverse DFT of the filtered DFT we get the original image with most of the coherent noise removed. We can take the absolute difference between the original image and the filtered image to see the noise that was removed (its maximum amplitude is approx. 6 in a scale of 0-255)

a)Filtered image; b)Difference between the original image and the filtered image
a) | b)

- Lab: DFT: Filtering of Coherent Noise