Inverse problems (Winter term 2021)

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
• Tikhonov - regularization
• Outlook: nonlinear inverse problems and variational regularization methods

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.

Update 1.10.21: The course will take place in presence and not as in Stine stated as online course! However, check Stine for concrete days and times.

Update 4.10.21: Lectures: Monday, 12-14, H1 and Wednesday, 14-16, H2; Exercise Monday, 14-16, room 1240

Previous knowledge: Basics from Bsc courses (calculus, linear algebra, numerical mathematics) and basic programming skills. Prior knowledge from functional analysis is an advantage but fundamental theorems will be stated in the course.

Exercises:

• One exercises sheet every week;
• The exercises consist of both theoretical and computer (Matlab) exercises.
• You need to mark at least 60% of the overall exercises and 50% of the computer exercises.
• Exercises are taught by Dr. Do