Lehrende: Dr. Matthias Beckmann
Veranstaltungsart: Vorlesung
Anzeige im Stundenplan: M-VMMOA-V
Semesterwochenstunden: 2
Unterrichtssprache: Englisch
Min. | Max. Teilnehmerzahl: - | -
Kommentare/ Inhalte: This course gives an introduction to the mathematics of computer(ized) tomography (CT). We will dicuss the principle of X-ray tomography, the mathematical model for the measurement process, the underlying mathematical reconstruction problem and some classical reconstruction techniques. Since CT is a typical example of an inverse problem, we will also discuss the ill-posedness of the CT reconstruction problem. The following topics will be addressed: * Imaging principle of X-ray tomography * Radon transform and its properties * Filtered back projection * Ill-posedness of CT reconstruction problem * Reconstruction techniques
Lernziel: * Acquisition of sound knowledge of mathematical theory and basic algorithms of CT
Vorgehen: The course, comprising 2+1 hours per week, is split into a lecture series (2h each week) and accompanying exercise classes (2h every other week). It is necessary to attend the lectures and to actively participate in the exercise classes. Exercises will be assigned every second week, and the students are required to present their solutions during the exercise classes.
Literatur: * F. Natterer: The Mathematics of Computerized Tomography. SIAM, Philadelphia, 2001. * F. Natterer, F. Wübbeling: Mathematical Methods in Image Reconstruction. SIAM, Philadelphia, 2001. * T. Feeman: The Mathematics of Medical Imaging. A Beginner's Guide. Second Edition. Springer, New York, 2015. * C. Epstein: Introduction to the Mathematics of Medical Imaging. Second Edition. SIAM, Philadelphia, 2008. * T. Buzug: Computed Tomography. Springer, Berlin, 2008. * A. Iske: Approximation Theory and Algorithms for Data Analysis. Springer, Cham, 2018.
Zusätzliche Hinweise zu Prüfungen: Information on the exams will be provided at the beginning of the course.
