Duration:
1 Semester | Turnus of offer:
each summer semester | Credit points:
4 |
Course of studies, specific field and terms: - Master Computer Science 2014 (module part), Module part, Arbitrary semester
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Classes and lectures: - Tomographische Verfahren II: Inverse Probleme bei der Bildgebung (exercise, 1 SWS)
- Tomographische Verfahren II: Inverse Probleme bei der Bildgebung (lecture, 2 SWS)
| Workload: - 55 Hours private studies
- 45 Hours in-classroom work
- 20 Hours exam preparation
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Contents of teaching: | - Introduction to inverse and ill-posed problems on the basis of selected examples (including seismology, impedance tomography, heat conduction, computed tomography, acoustics)
- Concept of ill-posedness of the inverse problem (Hadamard)
- Singular value decomposition and generalized inverse
- Regularization methods (eg Tikhonov, Phillips, Ivanov)
- Deconvolution
- Image restoration (deblurring, defocusing)
- Statistical methods (Bayes, maximum likelihood)
- Computed Tomography, Magnetic Particle Imaging
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Qualification-goals/Competencies: - Students are able to explain the concept of ill-posedness of the inverse problem and distinguish given inverse problems regarding good or bad posedness.
- They are able to formulate inverse problems of mathematical imaging and solve (approximate) with suitable numerical methods.
- They can assess the condition of a problem and the stability of a method.
- They master different regularization methods and are able to apply them to practical problems.
- They know methods to determine a suitable regularization.
- They can use methods of image reconstruction and restoration on real measurement data.
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Grading through: - Written or oral exam as announced by the examiner
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Responsible for this module: Teachers: |
Literature: - Kak and Slaney: Principles of Computerized Tomographic Imaging - SIAM Series 33, New York, 2001
- Natterer and Wübbeling: Mathematical Methods in Image Reconstruction - SIAM Monographs, New York 2001
- Bertero and Boccacci: Inverse Problems in Imaging - IoP Press, London, 2002
- Andreas Rieder: Keine Probleme mit inversen Problemen - Vieweg, Wiesbaden, 2003
- Buzug: Computed Tomography - Springer, Berlin, 2008
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Language: |
Notes:Prerequisites for attending the module: - None Prerequisites for the exam: - Preliminary examinations can be determined at the beginning of the semester. If preliminary work has been defined, it must have been completed and positively assessed before the initial examination. |
Letzte Änderung: 5.9.2021 |
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