MATLAB: Inverse fourier transform Imginary Components

complex numbersfourier domain

When I take an image and do fft on it in Matlab it produces a complex matrix. If I take the ifft of that image, it produces a double array. When doing the ifft, does matlab discard the imaginary component of the image, if any?

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When you have a set of fourier coefficients that are in complex conjugates pairs, then the result of the inverse fourier is always real-valued; see here for one

It is not a matter of discarding any complex part: it is that the result of the inverse transformation you did had only 0's for the complex part, and MATLAB automatically leaves out an all-0 complex part.

If you had done an inverse fft of coefficients that did not have the complex-conjugate symmetries then the result would have been something that had non-zero complex parts.

Related Solutions

MATLAB: Deblurring an Image using inverse filtering

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.

images = load('mandrill_blurred.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(fft2(m_blur)./hf));      %inverse filter 
%                     ^^^^^      ^    ^
%                      you forgot this
figure(2)
imagesc(m_deblur)                        % Display deblurred image

MATLAB: How to take the FFT and then the IFFT of an image

The FFT function will return a complex double array. If you read in a .JPG or a .TIF file, you will notice that they are UINT8 arrays. So, you will have to take the real part of the IFFT and then convert it back into UINT8. Try the example below:

IM=imread('flowers.tif');  % Read in a image
whos
image(IM);                     % Display image
FF = fft(IM);                   % Take FFT
whos
IFF = ifft(FF);                 % take IFFT
whos
FINAL_IM = uint8(real(IFF));      % Take real part and convert back to UINT8
whos
figure
imshow(FINAL_IM)       % Get back original image.

The WHOS calls in the above code will output the stored variable information so you can see where the conversion to UINT8 is taking place.

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Related Solutions

MATLAB: Deblurring an Image using inverse filtering

MATLAB: How to take the FFT and then the IFFT of an image

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