#### Inverse Problems

# Computational and Statistical Inverse Problems

##### Aims & Contents

Many practical questions fall into the category of inverse problems, for example parameter estimation in the analysis of measurements, image processing, data reconstruction or optimization of a system of partial differential equations. On the mathematical side, the main challenge of inverse problems is that the solution of such a problem is ill-posed, in the sense that the solution is not stable with respect to parameter variations. Functional analysis provides an understanding of why this is the case.

Therefore, one needs to impose additional constraints on the problem. In the first part of this lecture, we deal with classical methods, such as regularization terms, or truncated SVD. A very recent idea to put information into the problem comes from the Bayesian approach to Statistics. This approach, which we describe in the second part of the lecture, is a general modeling tool to extract information from inverse problems.

The lecture will develop theoretical foundations, but also give students experience through hands-on Matlab exercises.

##### Dates

Tuesday, 08:30 - 10:00 in 1090|328

Thursday, 10:15 - 11:45 in 1090|328

The exact schedule of lectures/exercises will be published in L2P. First lecture on Thursday, April 9.

The lecture is in English. Course materials and further information will be found in L2P. There are 5CP to earn with an oral examination. The oral exams of this course and the course on Uncertainty Quantification can be combined.

##### Literature

Mueller, Siltanen: Linear and Nonlinear Inverse problems with Practical Applications, SIAM, 2012

Kaipio, Somersalo: Statistical and Computational Inverse Problems, Springer-Verlag, 2005.