Website
Module guide

Modul ME4030 T

Module Part: Inverse Problems in Image Processing (InversProa)

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
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
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
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.
Grading through:
  • Written or oral exam as announced by the examiner
Responsible for this module:
  • Siehe Hauptmodul
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
Language:
  • offered only in German
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