How to reconstruct the image from the absolute gradients rather than the directional gradients?

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To put It more clearly, I have a gradient image (sqrt(Ix.^2+Iy.^2)) which was recorded using my image acquisition system. I need to reconstruct the image from this gradient image and I don't have any direction determined by which i can find the gradients (Ix,Iy) because of which I am unable to do so. Please suggest a suitable Image reconstruction scheme or algorithms if Possible.

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