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Seminar Consistency Conditions in Computed Tomography [SemCCCT]

Projection data for tomographic reconstruction is highly over-determined. For example, a computed tomography (CT) scan acquires hundreds of views of the same object, merely from different directions. Assuming the object itself remains unchanged, geometry and physics of such acquisitions impose constraints on the projection data. These constraints can be expressed mathematically in various ways to formulate consistency conditions. This seminar discusses derivations, properties and applications of several such consistency conditions applied to fan- and cone-beam CT. The goal of this seminar is to provide a review of various formulations of consistency conditions, their underlying assumptions, completeness and possibly applications, such as artifacts that can be compensated for. In the beginning of the term, there will be an introductory class to set the goals for individual topics. Each participant may choose one sub-topic and receive a scientific paper as a basis for further literature research. Most topics require an in-depth understanding of the mathematics of computed tomography, geometry or physics. Your goal is to present your research to the other participants of the seminar on a level of abstraction that can be understood by master-level students of computer science and/or mathematics without prior domain-specific knowledge. The final presentations will be weekly on Mondays 8-10am from beginning of May through the end of the semester. The grade is composed to 70% of a final presentation and 30% of a 5 pages seminar paper (IEEE style). There will be two introductory lectures. The first addresses organization and provides an overview of possible topics. The second class addresses presentation style and answers your questions. We assign topics on a first-come-first-serve basis.

Dates & Rooms:
Monday, 8:00 - 10:00; Room:


Presentations: Mondays 08:00-10:00, KH 1.021 (Universitätsstraße 15).

Seminar Paper: Due at the end of the lecture period. Extension to the end of the semester possible under special circumstances.

Introductory Meeting on April 11th 8am in seminar room of Helmstraße 1, Erlangen


Recommended Literature

  • F. John, "The ultrahyperbolic differential equation with four independent variables." Duke Mathematical Journal 4(2): 300-322. 1938
  • P. R. Edholm, R. M. Lewitt, and B. Lindholm. "Novel properties of the Fourier decomposition of the sinogram." Physics and Engineering of Computerized Multidimensional Imaging and Processing. International Society for Optics and Photonics, 1986.

  • S. K. Patch, "Consistency conditions upon 3D CT data and the wave equation." Physics in medicine and biology 47.15: 2637, 2002.

  • M. S. Levine, E. Y. Sidky, and X. Pan, “Consistency conditions for cone-beam ct data acquired with a straight-line source trajectory,” Tsinghua Sci Technol., vol. 15, no. 1, Feb 2010.

  • R. Clackdoyle "Necessary and sufficient consistency conditions for fanbeam projections along a line." Nuclear Science, IEEE Transactions on 60.3: 1560-1569, 2013.

  • A. Aichert, M. Berger, J. Wang, N. Maass, A. Doerfler, J. Hornegger, and A. Maier, “Epipolar consistency in transmission imaging,” Medical Imaging, IEEE Transactions on, vol. 34, no. 11, pp. 2205–2219, Nov 2015.