Radon between the lines

Inverting the Radon transform is used in image reconstruction in  CT scanners. Professor B Osgood provides a lecture on this topic here. This post essentially reproduces the argument and notation of this lecture.

Radon transform concept slide

In Mathematica,  Radon[] and InverseRadon[] can be used for image files as the following illustrate. The Radon transform of an image then its inverse is shown.