Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Advisor & Referee "Hohage, Thorsten Prof. Dr."
Now showing items 1-20 of 20
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Energy-based geometric regularization in three-dimensional inverse obstacle scattering
(2024-12-13)The classic "inverse obstacle scattering problem" in three-dimensions names the challenge of reconstructing 3D-objects from (noisy) far-fied measurements of scattered waves. Like any interesting inverse problem, this ... -
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 ... -
Learned infinite elements for helioseismology
(2021-12-16)This thesis presents efficient techniques for integrating the information contained in the Dirichlet-to-Neumann (DtN) map of time-harmonic waves propagating in a stratified medium into finite element discretizations. This ... -
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 ... -
Multiscale Total Variation Estimators for Regression and Inverse Problems
(2019-06-28)In the context of nonparametric regression and inverse problems, variational multiscale methods combine multiscale dictionaries with regularization functionals in a variational framework. In recent years, these methods ... -
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 ... -
Algorithms for structured nonconvex optimization: theory and practice
(2018-07-24)We first synthesize and unify notions of regularity, both of individual functions/sets and of families of functions/sets, as they appear in the convergence theory of fixed point iterations. Several new primal and dual ... -
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 ... -
Variational Regularization Strategy for Atmospheric Tomography
(2016-07-22)The main focus of this dissertation is to establish the necessary theory with numerical illustrations for solving an atmospheric tomography problem. The inverse problem is the reconstruction of some volume data ... -
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. ... -
Stabilisierte Lagrange Finite-Elemente im Elektromagnetismus und in der inkompressiblen Magnetohydrodynamik
(2015-11-05)This thesis deals with the usage of nodal-based finite element methods in electromagnetism and incompressible magnetohydrodynamics. At first, we start to investigate the induction equation from Maxwell's equation. We give ... -
On a Two Dimensional Inverse Scattering Problem for a Dielectric
(2012-03-05)The inverse problem under consideration is to reconstruct the shape of an infinitely long homogeneous dielectric cylinder from the far field (or near field) pattern for scattering of a ... -
Change point estimation in noisy Hammerstein integral equations
(2011-01-17)We consider the inverse regression model Y = Hf (X) + ε for several classes of non- linear Hammerstein integral operators H. In particular identifiability depending on the integral kernel ... -
Statistische Multiresolutions-Schätzer in linearen inversen Problemen - Grundlagen und algorithmische Aspekte
(2010-12-15)Applications of statistical multiresolution techniques in regression problems have attracted a lot of attention recently. The main reason for this is that the resulting statistical ... -
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 ... -
Identification of model and grid parameters for incompressible turbulent flows
(2007-10-24)The present thesis studies the behavior of turbulence models for incompressible flows based on the DLR-THETA-code and calibrates relevant model and grid parameters arising in the numerical ... -
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 ...