T-I-3draft

Radon transform and X-ray tomography

The goal of this homework is to introduce the Radon transform of a two-dimensional function. We will show that this transform is invertible, and that its inverse involves the Fourier transform in two dimensions. From a practical point of view, the Radon transform is the basis of X-ray tomography (as well as X-ray scanning), applied in the medical context in order to obtain cross-section images of different organs. The second part of the homework consists of a documentation work to be conducted in pairs: each pair of students should prepare a blackboard presentation of approximately five minutes on this part.