802676S Introduction to Inverse Problems (5 cr)
Cooperation network course
Network: Education network on Inverse Problems
This course is offered through the Network for Inverse Problems. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master’s Degree Programme in Mathematics
- Master's degree Programme in Mathematics (Subject Teacher)
- Doctoral Degree Programme in Mathematics and Statistics
Description
Theory of ill-posed inverse problems, singular value decomposition, Generalized-Inverse and Normal equations, Landweber iterations and Tikhonov regularization, Morozov discrepancy principle. Examples include convolutions, Fourier and Radon transform, corresponding to applications in image processing, X-ray and Magnetic Resonance Tomography. Use of Matlab/Python for implementation.
Learning outcomes
After successful completion of the course the student can identify linear ill-posed inverse problems and their severity. Furthermore, the students will be able to analyze and solve such problems with direct and indirect solution methods, identify necessary regularization, is able to implement such methods and work with basic simulated and experimental data.
Additional information
Language of instruction English Timing 3rd/last year during B.Sc. studies, 1st or 2nd year of Master, 3rd period. Target group Students having mathematics, applied mathematics, or statistics as the major or a minor subject.
Description of prerequisites
Prerequisites and co-requisites Core courses in the B.Sc curriculum of mathematical sciences, especially linear algebra; Numerical Analysis, Fourier analysis (beneficial, but not necessary), Functional analysis (beneficial, but not necessary).