How to apply Mean Filter on a FT Image in the Frequency Domain?

Hey everyone,

I am trying to write a script to denoise an image after applying FT on the image to convert it into the frequency domain. Is it possible to apply the filtering techniques used on the spatial domain such as Mean Filtering, Median Filtering and Gaussian Filtering on the frequecy domain instead? If it is possible how do i do that. Thnak you!

Answer 1

[Nagasai Bharat]

Hi,

There are no specific functions for the spatial filters counterpart in frequency domains. But you could create one using using the convolution theorem which suggests that filters which convolve in spatial domain, multiply in frequency domain.

Hence here you could apply fourier transform for both image and filter and dot multiply them and then apply inverse fourier transform to the output.

One main thing to be cautious is about applying fourier transform on filter is to consider padding so to make their sizes equal to eliminate aliasing/wraparound.