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Computer tomography (Winter term 2018)

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!

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).

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: Exercises

Exams:

The exam will take place in December 2019.

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 by Samuli Siltanen: CT (including videos)