I have a image that I need to shift with less than a pixel.
My plan was to do a Fourier transform and multiply the signal with $e^{-aiu-biv}$ where $a, b$ are the shifts in x and y direction. This might make sense in theory but in practice I don't really know how to represent $e^{-aiu-biv}$.
I am using numpy to do a 2d FFT of the image which, ofcourse, is represented as a matrix of complex values. From this point of I'm kinda lost, how do I multiply this with $e^{-aiu-biv}$?
It seems like fundamentally something is wrong as I need to temporarily represent the image in a higher resolution, shift is slightly and then collapse it back to the original resolution.