Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Referee "Luke, Russell Prof. Dr."
Now showing items 1-18 of 18
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A unified framework for spline estimators
(2013-07-09)This dissertation develops a uni ed framework to study the (asymptotic) properties of all (periodic) spline based estimators, that is of regression, penalized and smoothing splines. The explicit form of the periodic ... -
Benjamini-Schramm Convergence of Normalized Characteristic Numbers of Riemannian Manifolds
(2020-04-30)We study a weak form of Gromov-Hausdorff convergence of Riemannian manifolds, also known as Benjamini-Schramm convergence. This concept is also applicable to other areas and has widely been studied in the context of ... -
Compressed Sensing and ΣΔ-Quantization
(2019-02-11)The main issue of my thesis is to bound the error while recovering signals from their compressed and quantized form. Especially my central contribution is that, together with my co-authors, we provide the first analysis ... -
Diophantine Representation in Thin Sequences
(2016-08-24)In this work we investigate conditions under which forms of arbitrary degree represent almost all elements of thin sequences (especially the set of squares). Stronger results are given for forms of degree 3 and 4. -
Empirical Bayesian Smoothing Splines for Signals with Correlated Errors: Methods and Applications
(2016-08-12)Smoothing splines is a well stablished method in non-parametric statistics, although the selection of the smoothness degree of the regression function is rarely addressed and, instead, a two times differentiable function, ... -
Fixed Point Algorithms for Nonconvex Feasibility with Applications
(2014-07-31)Projection algorithms for solving (nonconvex) feasibility problems provide powerful and computationally efficient schemes for a wide variety of applications. Algorithms as Alternating Projections (AP) and Douglas-Rachford ... -
Increasing the robustness of active upper limb prostheses
(2017-02-02)This thesis is based on my work done at the Institute for Neurorehabilitation Systems at the University Medical Center Goettingen. My work has been partially founded by German Ministry for Education and Research (BMBF) via ... -
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 ... -
Multiscale Change-point Segmentation: Beyond Step Functions
(2017-03-08)Many multiscale segmentation methods have been proven to work successfully for detecting multiple change-points, mainly because they provide faithful statistical statements, while at the same time allowing for efficient ... -
Neural Networks for MRI Reconstruction
(2024-06-10)MRI is arguably the most versatile imaging modality for clinical use available today. In recent years, the development of advanced deep-learning-based reconstruction methods has significantly accelerated data acquisition ... -
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 ... -
On two Random Models in Data Analysis
(2017-03-02)In this thesis, we study two random models with various applications in data analysis. For our first model, we investigate subspaces spanned by biased random vectors. The underlying random model is motivated by applications ... -
Phase Retrieval with Sparsity Constraints
(2016-06-29)The two-dimensional phase retrieval problem arises in many areas of experimental physics, e.g. in x-ray microscopy. The central theme of this thesis is the application of sparsity constraints in the two-dimensional ... -
Projection Methods in Sparse and Low Rank Feasibility
(2015-07-07)In this thesis, we give an analysis of fixed point algorithms involving projections onto closed, not necessarily convex, subsets of finite dimensional vector spaces. These methods are used in applications such as imaging ... -
Random Function Iterations for Stochastic Feasibility Problems
(2019-03-21)The aim of this thesis is to develop a theory that describes errors in fixed point iterations stochastically, treating the iterations as a Markov chain and analyzing them for convergence in distribution. These particular ... -
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 ... -
Variational Convergence and Discrete Minimal Surfaces
(2015-11-05)This work is concerned with the convergence behavior of the solutions to parametric variational problems. An emphasis is put on sequences of variational problems that arise as discretizations of either infinite-dimensional ... -
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 ...