Inverse Problems
Summer Semester 2020
The course will treat the classical as well as the statistical 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
- Ill-posed operator equations
- Regularization of linear inverse problems
- Iterative reconstruction methods
- Tikhonov - regularization
- Optimal convergence rates for statistical inverse problems
- Adaptive methods
- Nonparametric Bayes methods
Online course:
- Organization of the course (exercises and course material etc) via Moodle
- The passwort for the course is sent via STiNE.
- Lectures are planed to take place on BigBlueButton (it is recommended to open the link with google chrome).
Exercises:
- One exercises sheet every week
- The exercises consist of both theoretical and computer exercises.
- You need to mark at least 50 % of the overall exercises (50 % of the first 6 and 50 % of the second 5 sheets).
- Actual exercise sheet: –
Literature:
- Engl, Hanke, Neubauer, Regularization of Inverse Problems
- Rieder, Keine Probleme mit inversen Problemen
- Hansen, Discrete Inverse Problems
- Cavalier, Inverse Problems in Statistics
- Stuart, Inverse Problems: A Bayesian Perspective
Other useful material
- Nice introduction to inverse problems by Samuli Siltanen
- and to computer tomography CT (including videos)