Image and Geometry Processing III:

Computer Tomography

Winter term 2015/16
Lecture
Tuesdays, 10:15 - 11:55, MN 68
Fridays, 10:15 - 11:55, MN 68
First Lecture: October 26, 2015

Exercises
Time and location will be fixed later.

Participants:
The lecture is suitable for students in mathematics, physics and computer science.

Assumptions to finish the lecture successfully:
There will be oral examinations (20 minutes) in February/March 2016.

Assumptions to get admission for the examination:
Attendance of the exercises, oral presentation of two exercise solutions, and 50 percent of the achievable points for homework.
With this lecture + exercises you can obtain 9 ECTS points.

Content:
This Lecture Image and Geometry Processing III is concerned with mathematical analysis and numerical methods of computerized tomography. In particular we will focus on the following topics:

1. Introduction

Mathematical foundations:
2. Repetition: Fourier-Transformation
3. The Radon transform and inversion formulas
4. The inversion formula of Cormack
5. Uniqueness of the inverse Radon transform
6. Singular value decomposition of the Radon transform

Numerical Algorithms:
7. Repetition: The Shannon sampling theorem
8. Filtered backprojection
9. Fourier reconstruction
10. Kaczmarz's method
11. Application of Kaczmarz' method to inverse Radon transform
12. Direct algebraic methods
13. The inverse Radon problem for incomplete data

Literature:
R. Kress: Computertomographie, Vorlesungsskript 2005, Universität Göttingen.
F. Natterer: The Mathematics of Computerized Tomography, Teubner, Stuttgart, 1986.
F. Natterer und F. Wübbeling: Mathematical Methods in Image Reconstruction, SIAM, Philadelphia, 2001.