Projects
This list of selected projects offers an overview over the current research carried out within the group.
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Optimal control of reaction-diffusion systems in cardiac electrophysiology
Chamakuri Nagaiah and Karl Kunisch
The development and implementation of an accurate and efficient numerical method} for the numerical solution of optimal control of bidomain equations as well as the determination of the control response of an electrical impulse which can be able to drive the system from arrhythmia pattern to a uniform pattern is the focus of this project.
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Inverse problems with L¹ data fitting
Christian Clason, Bangti Jin, and Karl Kunisch
For non-Gaussian noise models such as impulsive noise, e.g. salt-and-pepper or random-valued noise, L¹ data fitting is more robust than standard L² terms, but leads to non-differentiable functionals to be minimized. The goal is to develop superlinearly convergent numerical methods for such inverse problems, including the automatic choice of regularization parameters.
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Duality-based splitting for fast ℓ¹-TV image restoration
Christian Clason, Bangti Jin, and Karl Kunisch
We consider the problem of restoring images degraded by blurring and impulsive noise (e.g. salt-and-pepper noise). For such noise models, an ℓ¹ data-fitting term is more robust than standard ℓ² terms, while edges in the image are better preserved by a total variation penalty. The aim is to develop fast methods for solving the resulting non-smooth minimization problem, which can be implemented on graphics processing units (GPUs).
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Optimal control of quantum systems
Greg von Winckel
The control of quantum electronic states in physical systems has a host of applications such as quantum computers, control of photochemical processes, and semiconductor lasers.
The aim of this work is to compute a time-dependent control which appears as a variable coefficient in the Schrödinger equation, such that a particle in a given initial state will have maximal probability of being in a target state at a specified time.
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Optimal control of partial differential equations with measures
Christian Clason and Karl Kunisch
Optimal control problems for partial differential equations with controls in the space L¹ are known to lead to sparse controls, which have applications in the optimal placement of discrete sensors or actuators. The natural functional-analytic framework for such problems is the space of bounded Borel measures. The goal is to develop efficient numerical methods for the solution of optimal control problems with measures.
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Elastic/hyperelastic image registration as a multidimensional control problem
Marcus Wagner
This problem has been widely formulated as a multidimensional variational problem, which is solved by indirect methods. Our goal is to improve the variational model by incorporation of constraints and to solve the resulting optimal control problem by direct methods instead of indirect ones.
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Total Generalized Variation
Kristian Bredies, Karl Kunisch, and Thomas Pock
Total variation regularization is based on the assumption that the underlying image consists of piecewise constant regions. For natural images, this assumption is no longer valid causing the solutions to suffer from undesired staircasing artifacts. Such limitations can be overcome by considering the total generalized variation.
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Active contour models for yeast cell segmentation
Kristian Bredies and Heimo Wolinski
The goal is to obtain cell-based quantitative information about the lipid droplets from the fluorescence images. However, the necessary information about the cell boundaries is only present in the 2D transmission images which exhibit a strongly heterogeneous structure. This causes standard thresholding-based methods to fail. The objective is to develop a cell segmentation strategy which is suitable for this class of images.
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Image reconstruction for parallel imaging
S.L. Keeling, C. Clason, M. Hintermüller, F. Knoll, A. Laurain, G. von Winckel
The goal of parallel imaging is to accelerate image acquisition. The available data are not only modulated and aliased, but because of the higher temporal resolution required, the correspondingly reduced acquisition time per image results in a relatively high noise level. The objective is to overcome the modulations, aliasing and noise in each surface coil measurement, and to combine these data to reconstruct an underlying uncorrupted image.
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Registration and segmentation of modulated image sequences
Stephen Keeling
The goal of this work is to remove the motion in a DCE-MRI sequence so that pure temporal changes in a chosen tissue can be investigated to detect potential pathology. To remove the motion, all images in the sequence must be registered to a template of some kind. The task is complicated by intensity modulations.
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