Winter Semester 2021/22
The course will treat the classical theory for linear inverse problems. Inverse problems occur in many applications in physics, engineering, biology and imaging. Loosely speaking, solving the forward problem consists of computing the outcome of a known model given the model parameters. The inverse problem consists of computation of the unknown parameter of interest given the physical model and noisy measurements of the outcome. Typical examples are parameter identification problems such as computer tomography, deconvolution problems, denoising of images etc. In particular the following topics are discussed:
- Examples of ill-posed inverse problems
- Reconstruction in Computer tomography
- Ill-posed operator equations
- Regularization of linear inverse problems
- Iterative reconstruction methods
- Outlook: nonlinear inverse problems and variational regularization methods
Note: The first part of the course will take place together with the course about computer tomography. At the moment, it is difficult to plan the teaching in winter term. I hope that we can have normal lectures in the Geomatikum, but if this is not possible, I will provide live BBB lectures. You will find actual information on Moodle.
- One exercises sheet every week;
- The exercises consits of both theoretical and computer (Matlab) exercises.
- You need to mark at least 60% of the overall exercises and 50% of the computer exercises.
Actual exercise sheet: See Moodle course
Exams: Exam will take place in February 2022.
- Engl, Hanke, Neubauer, Regularization of inverse problems
- Rieder, Keine Probleme mit inversen Problemen
- Hansen, Discrete inverse problems
- Louis, Inverse und schlecht gestellte Probleme
- Mueller, Siltanen, Linear and nonlinear inverse problems with practical applications
- T. G. Feeman, The mathematics of medical imaging, Springer, 2010
- F. Natterer, The Mathematics of Computerized Tomography, Classics in Applied Mathematics 32,SIAM, 2001
Other useful material