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Numerical Simulation - Variational Methods and Inverse Problems in Imaging

Lecturer: Prof. Dr. Martin Rumpf

The lecture course will discuss numerical methods and efficient algorithms in the context of modern image processing approaches. A particular emphasize will be on convex relaxation methods in the space of functions of bounded variations with applications to object labeling in images or object reconstruction from stereo. The numerical approximation will rely on duality techniques in constraint optimization and a rigorous error control will be developed. Furthermore, the course will investigate compressed sensing for inverse problems in imaging, e.g. in computer tomography. Finally, numerical methods in optimal transportation and applications to image matching will be presented.

Practical lab P5E1 will complement the lecture course. In this practical lab efficient algorithms for depth computation for stereo images, image reconstruction via sparse sampling and image matching using an optimal transportation approach will be developed by the participants in teams of 2-3 students.

Schedule