Module ME4030-KP04, ME4030

Duration

1 Semester

Turnus of offer

each summer semester

Credit points

4

Course of studies, specific fields and terms:

• Master Auditory Technology 2022, optional subject, Auditory Technology
• Master MES 2020, optional subject, medical engineering science
• Master Medical Informatics 2019, optional subject, medical image processing
• Master Auditory Technology 2017, optional subject, Auditory Technology
• Master MES 2014, optional subject, medical engineering science
• Master MES 2011, optional subject, mathematics
• Master Computer Science 2012, optional subject, advanced curriculum signal and image processing
• Master Computer Science 2012, optional subject, specialization field robotics and automation
• Master Computer Science 2012, optional subject, specialization field medical informatics
• Master Computer Science 2012, optional subject, advanced curriculum imaging systems
• Master MES 2011, advanced curriculum, imaging systems, signal and image processing
• Master CLS 2010, optional subject, mathematics

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, acoustic)
• 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:

• Prof. Dr. rer. nat. Thorsten Buzug

Teacher:

• Institute of Medical Engineering
• Prof. Dr. rer. nat. Thorsten Buzug

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:

Last Updated:

05.09.2021