Coming back from gradient using circshift for image processing

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Hello everyone,
I would like to ask your help.
This is the question:
If I use circhshift for getting the Gradient between neighboring pixels in Y direction, can I calculate image back, having this gradient information?
Afer using the fourier transform and implementing other functions I got a complex field of an image.
Then the code calculates the shift of my image along the y-direction. In the end it operates the ratio of the first image on the shifted image for getting the phase angle:
C = complex field of the image
C2 = circshift(C, [0,4]);
ph = angle(C./C2);
The question is: how can I come back from circshift (gradient) to a quantitative information?
Hope that my question was clear enough.
Thank you very much.

Accepted Answer

Matt J
Matt J on 3 Oct 2022
Edited: Matt J on 3 Oct 2022
No, you cannot. Any constant image, for example, has the same "gradient", so the process cannot be invertible.

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