Computer Tomography

Winter Semester 2021/22

Note: The course on computer tomography takes places in the first 7 weeks of the semester and is the first part of the course about inverse problems which takes place the whole sememster! You can either participate at the CT course or at the inverse problems course.

The course will treat computer tomography, i.e. we will discuss the mathematical model (Radon transformation), theoretical foundations and how to reconstruct from given noisy data. Since the reconstruction problem is a typical example of an ill-posed inverse problem, we will study also general concepts of solving inverse problems. In particular the following topics are discussed:

Expertimental setup and medical application
The Radon transformation
The filtered back projection
Iterative reconstruction methods
Background: Solving inverse problems (only introduction into the topic).

At the moment, it is difficult to plan the teaching in winter term. I hope that we can have normal lectures in the Geomatikum, but if this is not possible, I will provide live BBB lectures. You will find actual information on Moodle.

Exercises:

One exercises sheet every week;
You need to mark at least 60% of the overall exercises.
The exercises consits of both theoretical and pratical (Matlab) exercises.

Actual exercise sheet: See Moodle course page

Exams: The exam (first round) will take place in December 2021 (only for the participants of the CT course).

Literature:

T. G. Feeman, The Mathematics of Medical Imaging, Springer, 2010
F. Natterer, The Mathematics of Computerized Tomography, Classics in Applied Mathematics 32, SIAM, 2001
F. Natterer and F. Wübbeling, Mathematical Methods in Image Reconstruction, SIAM, Philadelphia, 2001
T. Buzug, Computer Tomography
Engl, Hanke, Neubauer, Regularization of Inverse Problems
Rieder, Keine Probleme mit inversen Problemen

Other useful material

Nice introduction to computer tomography CT (including videos) by Samuli Siltanen