what is wrong with ifft process on this image?

I want to apply some processing and changes on my 2D signal and then take it back to time/spatial domain by using ifft, but I dont know why the ifft gave me something weird. So I simplified it to a simple image and then applied fft and then ifft as the code below:

I expect the inverse fft gave me the image again but why this happens?

clear all;
img = imread("cameraman.tif");
figure, imshow(img);

[m, n]=size(img);
img_fft = fftshift(abs(fft2(img)));
img_fft_shifted = ifftshift(img_fft);
img_fft_mag = abs(img_fft_shifted);
img_back = abs(ifft2(ifftshift(img_fft_mag))/(m));
figure, imshow(img_back);

[Walter Roberson]

When you take the abs() of the fft2(), you are getting rid of all of the phase information and exaggerating the magnitudes.

Note that the result of abs() is not going to depend on whether you have shifted version or the original version, so doing the fft shift then abs then ifftshift is the same as just taking abs

Also note that the original data is uint8 but the processed data will not be.

format long g
img = imread("cameraman.tif");
figure, imshow(img);

processed = ifft2(abs(fft2(img)));
[min(processed(:)), max(processed(:))]

ans = 1×2

1.0e+00 * 32.5469475250268 4834.65318990045

surf(processed)

rs = uint8(min(processed, 255));
imshow(rs)

[Walter Roberson]

You can see that because of the abs(), the range of values you get returned is fairly high; if you imagesc() or imshow(img, []) to show the range scaled linearly, then you get an all-black output. You have to clip the values to get back something -- and that something will not look like the original because you lost the phase information.

[William Rose]

@Walter Roberson, thank you for your comments. I always learn a lot from them.

[2NOR_Kh]

I got what you mentioned. Thanks for that!

so, I cant reconstruct my signal again. However, in the RF ultrasound we apply hilbert transform and abs:

env = abs(hilbert(RF_Signal));

RF_Signal is the time domain signal and it is a complex value signal and we dont need the phase of it and will get rid of it in the time domain. Also, when working with the signal in the frequency domin, again we just need to do our processing on the spectrum and not need the phase. That is why I need that abs and fftshift in the frequency domain.

in this case, is there any solution to reconstruct the signal by its spectrum only?

[Walter Roberson]

Sorry, I do not know how to use hilbert transform.

[William Rose]

@2NOR_Kh,

RF_Signal is a complex function of time. You do not need the phase part of this complex signal. YOu want to apply a filter to the magnitude spectrum of the signal and reconstruct the filtered signal from its spectrum, without its phase.

I do not think this is possible. This discussion is made more complicated by the fact that the complex signal has a phase in the time domain and a hase (which is different) in the frequency domain. You do not need the time domain phase informaiton. But you do need the phase info in the frequency domain in order to recontruct the original time domain signal. Throw away the time-domain phase info atthe very end, after you have done the frequency domain filtering and have done the inverse transform.

I could be wrong since I am not experienced with complex time domain signals.

One interesting feature of the HIlbert transform which may or may no be relevant is that it can filnd the minimum phase associated with an amplitude spectrum of the response of a causal system.

Answer 1

[William Rose]

@2NOR_Kh,

img = imread("cameraman.tif");
figure, subplot(121); imshow(img); title('Original');
[m, n]=size(img);
%img_fft = fftshift(abs(fft2(img)));
%img_fft_shifted = ifftshift(img_fft);
%img_fft_mag = abs(img_fft_shifted);
%img_back = abs(ifft2(ifftshift(img_fft_mag))/(m));
img_fft=fft2(img);
img_back=abs(ifft2(img_fft))/m;
subplot(122); imshow(img_back); title('Returned Image')

Try it.

[2NOR_Kh]

I have to also apply fftshift and abs on my signal then apply some changes on the spectrum and agter those changes taking the signal back to time domain.

So, I need to reconstruct my time domain signal from the:

FE=fftshift(abs(fft(liver_padd(:,1))));

which liver padd is a RF ultrasound scan of liver and liver_padd(:,1) is the first line of this data.

[William Rose]

@2NOR_Kh,

Your original question was why your script using fft2() and ifft2() did not return the original image. @Walter Roberson explained why the script failed: you lost the phase info by using abs() on the FFT of the image. I gave an example of how to use fft2() and ifft2() to get back the original image.

It seems to me like you are now asking a different question: how to filter and reconstruct a 1D time domain signal which is embedded as column 1 of a 2D RF ultrasound scan. That is a good quesiton but it is quite different. Do I understand correctly? If so, I suggest you attach a sample liver_padd image which includes the time domain signal as column 1.

What is the sampling rate of the 1-D time-domain signal? Is the time domain signal the position of a vessel edge as a function of time?

Answer 2

[Mehri Mehrnia]

what is that division by m??

[2NOR_Kh]

to normalize the pixel values. but if you use a different function than imshow, you maght not need it.