Inverse problems - numerical and statistical aspects
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
- 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 6 sheets).