Deblurring an Image using inverse filtering

 I am trying to deblur an image using inverse filtering that was blurred using a 25x25 gaussian blur function with sigma = 15. I am extracting the blurred image from a .mat file, displaying it which works correctly.

 

Next I define my gaussian filter and then compute frequency reponse of the filter. To deblur the image, I divide blurred image by frequency response of the filter and take ifft.

 

The blurred image displays correctly in figure 1, but figure 2 which should display deblurred image displays all purple. I am trying to keep my code as simple and minimal as possible.

 

What I am doing wrong here? I will appreciate any hints or inputs

 

images = load('project_images.mat');   % Load the mat file containing images

m_blur = images.mandrill_blurred;  % Extract the first image 
imagesc(m_blur);                   % display the blurred image

h = fspecial('gaussian',[25 25],15);   % 25x25 Gaussian blur function with sigma = 15
hf = fft2(h,size(m_blur,1),size(m_blur,2));      


m_deblur = real(ifft2(m_blur)./hf);      %inverse filter 

figure(2)
imagesc(m_deblur)                        % Display deblurred image

 

 

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A bit of data exploration shows that you have quite an outlier in your image:

 

figure(3),clf(3)
histogram(m_deblur)
set(gca,'YScale','log')
axis([-10 140 0.1 max(ylim)])

Once you replace that with a 0, the automatic scaling should work as expected again. In the code below I went a bit further and set the caxis value manually to something that felt about right.

figure(2)
imagesc(m_deblur)                        % Display deblurred image
caxis([-0.15 0.15])

So in conlusion: this image is not ready yet.

The reason for this is that you didn't put the blurred image in the Fourier domain yet, so the division doesn't make a lot of sense.

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