Dynamical image analysis and some applications to inverse problems

In this talk we present tracking and registration methods for data analysis of image sequences and movies. These techniques are applied to analyze common movies, microbiological cell data and elastography movies, respectively.
A common approach, which is applicable to these different applications, is regularization. This approach is flexible enough to be adoptable to the different needs of various applications outlined in this talk. The different realizations are implemented by different regularization energies in the optimization energies.
Tracking and registration is an interesting topic for its own, but can also serve as a preprocessing tool for solving inverse problems, such as for instance in elastography. Also this aspect is highlighted.
Analytical questions related to regularization are existence and uniqueness of minimizers, and stability properties, which are discussed in detail.
This talk is based on joint works with Clemens Kirisits, Lukas Lang, Aniello Patrone and Thomas Widlak (University of Vienna).