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Computer tomography (Winter term 2017)

The course will treat computer tomography, i.e. will 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 (ART etc.)
• Background: Solving inverse problems (only introduction into the topic).

Exercises:

• One exercises sheet every 2 weeks;
• It is recommended to solve the exercises regularly in order to pass the final exam.
• The exercises consits of both theoretical and pratical (Matlab) exercises.

Actual exercise sheet: Exercises

Data for the last exercise: XrayData set and small XrayData set

Exams:

Please make an appointment for the oral exam (senging a mail to Ms Kopp). Possible days are 8./9.2.18 and 26./27.3.18.

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

Reider, Keine Probleme mit inversen Problemen

Other useful material

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