Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Referee "Hohage, Thorsten Prof. Dr."
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Algorithms for structured nonconvex optimization: theory and practice
(20180724)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 ... 
Analysis of an Inverse Source Problem with Correlation Data in Experimental Aeroacoustics
(20210819)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 operatorvalued ... 
Bending energy regularization on shape spaces: a class of iterative methods on manifolds and applications to inverse obstacle problems
(20191213)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 ... 
Change point estimation in noisy Hammerstein integral equations
(20110117)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 ... 
Convergence rates for variational regularization of inverse problems in exponential families
(20200716)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
(20200513)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 ... 
Identification of model and grid parameters for incompressible turbulent flows
(20071024)The present thesis studies the behavior of turbulence models for incompressible flows based on the DLRTHETAcode and calibrates relevant model and grid parameters arising in the numerical ... 
Inverse Problems in Propagationbased Xray Phase Contrast Imaging and Tomography: Stability Analysis and Reconstruction Methods
(20190612)Propagationbased Xray phase contrast imaging (XPCI) and tomography (XPCT) extend the capabilities of classical Xray radiography and computed tomography (CT) to imaging of microscopic specimens with nanometersized ... 
Learned infinite elements for helioseismology
(20211216)This thesis presents efficient techniques for integrating the information contained in the DirichlettoNeumann (DtN) map of timeharmonic waves propagating in a stratified medium into finite element discretizations. This ... 
Multiscale Total Variation Estimators for Regression and Inverse Problems
(20190628)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 ... 
New Algorithms for Local and Global Fiber Tractography in DiffusionWeighted Magnetic Resonance Imaging
(20171128)Fiber tractography based on diffusionweighted magnetic resonance imaging is to date the only method for the threedimensional visualization of nerve fiber bundles in the living human brain noninvasively. However, various ... 
On a Two Dimensional Inverse Scattering Problem for a Dielectric
(20120305)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 ... 
Preconditioned Newton methods for illposed problems
(20070905)We consider preconditioned regularized Newton methods tailored to the efficient solution of nonlinear largescale exponentially illposed problems.In the first part of this thesis we investigate ... 
Spatial Coherence Enhancing Reconstructions for High Angular Resolution Diffusion MRI
(20160121)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 FiniteElemente im Elektromagnetismus und in der inkompressiblen Magnetohydrodynamik
(20151105)This thesis deals with the usage of nodalbased finite element methods in electromagnetism and incompressible magnetohydrodynamics. At first, we start to investigate the induction equation from Maxwell's equation. We give ... 
Statistische MultiresolutionsSchätzer in linearen inversen Problemen  Grundlagen und algorithmische Aspekte
(20101215)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 ... 
Variational Regularization Strategy for Atmospheric Tomography
(20160722)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 ... 
Variational regularization theory for sparsity promoting wavelet regularization
(20220131)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 ...