It was introduced – I actually knew the history of this a little bit more thoroughly, and I cannot recall it now. It was certainly not introduced in the context of X-ray tomography or anything else. It was introduced for purely mathematical reasons, for interesting geometric reasons. The idea was to sort of study the geometry of a region by knowing integrals of sections through it just as a purely mathematical question. I don’t think there were any practical implications that were anticipated or attempted certainly at the time it was introduced. So our question is – so you know all these values. All right? You know all these values, and the question is can you invert the transform? Can you find mu, given that you know all the values of its transform? ...

See the whole transcript at The Fourier Transform and its Applications - Lecture 30