Radon transform

Summary

The Radon transform sends a function $f$ on $\R^n$ to the function that gives the integral of $f$ over each hyperplane. In the plane the hyperplanes are lines. There the Radon transform records what an X-ray scanner measures: the total absorption along each line through a body. The projection-slice theorem links it to the Fourier transform, and the Radon inversion formula recovers $f$ from its Radon transform. It is the mathematical basis of computed tomography and a central object of integral geometry.