401-4521-70L  Geometric Tomography - Uniqueness, Statistical Reconstruction and Algorithms

SemesterHerbstsemester 2020
DozierendeJ. Hörrmann
Periodizitäteinmalige Veranstaltung

KurzbeschreibungSelf-contained course on the theoretical aspects of the reconstruction of geometric objects from tomographic projection and section data.
LernzielIntroduction to geometric tomography and understanding of various theoretical aspects of reconstruction problems.
InhaltThe problem of reconstruction of an object from geometric information like X-ray data is a classical inverse problem on the overlap between applied mathematics, statistics, computer science and electrical engineering. We focus on various aspects of the problem in the case of prior shape information on the reconstruction object. We will answer questions on uniqueness of the reconstruction and also cover statistical and algorithmic aspects.
LiteraturR. Gardner: Geometric Tomography
F. Natterer: The Mathematics of Computerized Tomography
A. Rieder: Keine Probleme mit inversen Problemen
Voraussetzungen / BesonderesA sound mathematical background in geometry, analysis and probability is required though a repetition of relevant material will be included. The ability to understand and write mathematical proofs is mandatory.