Syllabus
1. Inverse problems, their basic properties, examples.
2. Construction of the naive solution, need for regularization, influence of noise.
3. Basic direct and iterative regularization methods. Hybrid methods.
4. Regularization parameter selection approaches.
5. Propagation of noise in iterative regularization methods, noise level estimation without apriori information.
6. Special problems.
Annotation
In a variety of applications (computerized tomography, geology, image processing etc.) there is a need to solve inverse problems, where the goal is to extract information about the studied phenomena from the measured data corrupted by errors (noise). Since these problems are sensitive on perturbations in the data, it is necessary to solve them using special approaches, so called regularization methods.
The lectures give an insight into the properties of inverse problems, and summarize modern regularization approaches including parameter choice methods.