how can i enhance image by Fourier transform?

hi i wanna create a matlab function to do such work:

actually i have picture a and c. i dont know how to denoise it with ftt functions.

Answer 1

[Image Analyst]

See my fft filtering demo below. Feel free to adapt it to your images.

[Afsaneh]

tanx for your guidance. but the result doesn't seem to improve my image. but added more and more noises! here is the result:

[Afsaneh]

sorry. i will read it more carefully and will report its result. tanx

[Afsaneh]

pardon me to my misundrestand! i will describ my undrestanding:

• first i read my noisy image. in this case there is no need to add cosine noises to it, so the code is like this:

% Read in a standard MATLAB gray scale demo image.

grayImage=imread('Fig0240(a)(apollo 17_boulder_noisy).tif');
subplot(2, 3, 1);
imshow(grayImage, [0 255]);
title('noisy Image', 'FontSize', fontSize);

• Then i must compute Fourier transform and centralizes it:

% Compute the 2D fft.
frequencyImage = fftshift(fft2(grayImage));
% Take log magnitude so we can see it better in the display.
amplitudeImage = log(abs(frequencyImage));
minValue = min(min(amplitudeImage))
maxValue = max(max(amplitudeImage))
subplot(2, 3, 2);
imshow(amplitudeImage, []);
caption = sprintf('Notice the two spikes\nperpendicular to the periodic frequency');
title(caption, 'FontSize', fontSize);
axis on;
% zoom(10)

• Here is my Question: How to identify amplitude threshold? i changed it. some more and some less. but it didn't reach a specific value! whats more, i see additional spikes in filtered image that by increasing or decreasing amplitude value, wont remove and i couldn't find image (b).

% Find the location of the big spikes.
amplitudeThreshold = 10.9;
brightSpikes = amplitudeImage > amplitudeThreshold; % Binary image.
subplot(2, 3, 3);
imshow(brightSpikes);
axis on;
title('Bright Spikes', 'FontSize', fontSize);

• in executing the big central spike, how can i get that interval?

% Exclude the central DC spike.  Everything from row 115 to 143.
brightSpikes(115:143, :) = 0;
subplot(2, 3, 4);
imshow(brightSpikes);
title('Bright spikes other than central spike', 'FontSize', fontSize);

• here is my last question. but in my case which i have the mask's image(image(c)), how can i apply it? because u used of spike information to create a mask and then omitted the noises.

[Image Analyst]

Try changing the 10.9 to other values and see what selects the spikes. You should also change the(115:143,:) to indexes that get rid of the central spike for you image - they will be different because you have a different size image than I used.

[Athanasios Margiolakis]

Thank you for sharing the code. It is very helpful and easy to read.