How to vertically stretch an image according to a varying function

I have an image that has a changing magnification as I go from one side to the next. I would like to stretch the image to compensate for the magnification in the y direction using the equation I have for magnification with respect to location.

Is there anyway I can do this?

I believe that I can create a Piece-Wise Transform using a grid without the magnification and one with and attempt to transform it but I feel like there must be a more direct way to do it.