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IRTG Modern Inverse Problems (MIP)

Kategorie: ‘Research Topics’

Computational Tools for Chemical Imaging

09. Oktober 2018 | von

Prof. Benjamin Berkels

The project will advance the state of the art in segmentation and unximing of data from chemical imaging, which is an umbrella term for image acquisition techniques that record a full spectral band of data at each pixel. A major challenge for the analysis of hyperspectral data is its huge size and high dimensionality.

Segmentation of hyperspectral data is the task of partitioning the image domain into disjoint sub-regions based on a suitable notion of spectral homogeneity, i.e. assigning a class label to each pixel based on its spectral vector data. For instance, for hyperspectral satellite images, such classes could be soil, water, grass, street, etc. A more general task than segmentation is called unmixing. Instead of belonging to just one class, unmixing considers each pixel to be a mixture of a number of constituents. Unmixing then needs to determine both the mixture ratios and the constituents. Nowadays, numerous hyperspectral image modalities are available, which makes this research relevant for a wide range of applications. One considered application will be cancer treatment, where Fourier transform infrared spectroscopy data of human tissue samples needs to be classified into classes like “highly cancerous”, “mildly cancerous” or “normal”.

The main aims of this project are:
• Robust segmentation of hyperspectral data with large intra-class variation;
• Unmixing of mixture of  mixtures data using hierarchical matrix factorization.

Novel Stabilized Finite-Element Methods for Microstructured and Complex Fluids

08. Oktober 2018 | von

Prof. Marek Behr, Ph.D.

The project will advance the state of the art in the computational treatment of viscoelastic (VE) constitutive equations and similar model equations arising elsewhere. The applications of this research range from production engineering and melt-based forming processes (die swell of VE fluid shown in figure), to biomedical device design, to aerospace technology.

Low-order stabilized finite elements (FEM) are the workhorse of computational engineering, but are sensi- tive to element quality and stabilization parameters. Discontinuous Petrov-Galerkin (DPG) methods have a solid mathematical foundation and robustness, but are not yet used in industrial contexts. By merging the properties of FEM and DPG, robust method for microstructured fluids in industrial settings will be obtained.

The research goals of this project are:

  • Understanding of the stability and accuracy properties of two alternate finite element dis- cretization approaches;

  • Transfer of Discontinuous Petrov-Galerkin stability and accuracy advantages to low-order industrial FE formulations;

  • Insight into numerical behavior of sensitivities and adjoints required for design tasks in both approaches.