The goal of this experiment is to introduce the field of medical imaging and to implement basic techniques of iterative reconstruction. After doing this experiment, you should have an idea about inverse problems arising in medical tomography and about numerical optimization methods that can be used in order to solve these problems.

The first part of the experiment introduces computational tomography (particularly, the notion of projection and Radon transform) and basics of optimization – a theory which tells how to algorithmically minimize a given convex function of many variables. We will implement a simple iterative algorithm for reconstruction of an object from its projection.

The second part is dedicated to the relation between the Radon and the Fourier transforms and the frequency-domain reconstruction techniques arising from this relation. We will implement an iterative inverse non-uniform Fourier transform (NUFT) and use it for tomographic reconstruction.