Browsing Naturwissenschaften, Mathematik und Informatik by Advisor "Hohage, Thorsten Prof. Dr."
Now showing items 1-10 of 10
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Variational regularization theory for sparsity promoting wavelet regularization
(2022-01-31)In many scientific and industrial applications, the quantity of interest is not what is directly observed, but is instead a parameter which has a causal effect on experimental measurements. To obtain the desired unknown ... -
Analysis of an Inverse Source Problem with Correlation Data in Experimental Aeroacoustics
(2021-08-19)In aeroacoustic testing one seeks to localize and reconstruct the power of an aeroacoustic source, given correlation estimates of pressure fluctuations in the frequency domain. This inverse problem with operator-valued ... -
Convergence rates for variational regularization of inverse problems in exponential families
(2020-07-16)We consider statistical inverse problems with statistical noise. By using regularization methods one can approximate the true solution of the inverse problem by a regularized solution. The previous investigation of convergence ... -
Convergence rates for variational regularization of statistical inverse problems
(2020-05-13)We consider inverse problems with statistical (noisy) data. By applying regularization methods one can approximate the true solution of the inverse problem by a regularized solution. In this thesis we show convergence rates ... -
Bending energy regularization on shape spaces: a class of iterative methods on manifolds and applications to inverse obstacle problems
(2019-12-13)In applications such as nondestructive testing, geophysical exploration or medical imaging one often aims to reconstruct the boundary curve of a smooth bounded domain from indirect measurements. As a typical example we ... -
Inverse Problems in Propagation-based X-ray Phase Contrast Imaging and Tomography: Stability Analysis and Reconstruction Methods
(2019-06-12)Propagation-based X-ray phase contrast imaging (XPCI) and -tomography (XPCT) extend the capabilities of classical X-ray radiography and computed tomography (CT) to imaging of microscopic specimens with nanometer-sized ... -
New Algorithms for Local and Global Fiber Tractography in Diffusion-Weighted Magnetic Resonance Imaging
(2017-11-28)Fiber tractography based on diffusion-weighted magnetic resonance imaging is to date the only method for the three-dimensional visualization of nerve fiber bundles in the living human brain noninvasively. However, various ... -
Spatial Coherence Enhancing Reconstructions for High Angular Resolution Diffusion MRI
(2016-01-21)A main step in processing and analyzing data obtained from High Angular Resolution Diffusion MRI is the reconstruction of some measure of diffusion per spatial location and per direction in the volume under examination. ... -
Nonlinear Reconstruction Methods for Parallel Magnetic Resonance Imaging
(2009-10-14)Parallel acquisition techniques have been proposed to reduce the measurement times for magnetic resonance imaging. These techniques rely on the simultaneous acquisition of an undersampled ... -
Preconditioned Newton methods for ill-posed problems
(2007-09-05)We consider preconditioned regularized Newton methods tailored to the efficient solution of nonlinear large-scale exponentially ill-posed problems.In the first part of this thesis we investigate ...