Dokumente Fakultät für Mathematik und Informatik (inkl. GAUSS) nach Gutachter "Plonka-Hoch, Gerlind Prof. Dr."
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A Wasserstein-like Distance on Vector Fields
(2023-10-06)We introduce a new distance on the space of vector fields over a Riemannian manifold that is motivated by the construction and properties of the Wasserstein distance. The construction relies on a particular metric on the ... -
On minimax detection of localized signals from indirect or correlated data
(2022-05-05)This is a cumulative thesis consisting of two papers, in which we treat two problems related to the detectability of local anomalies within certain types of data. In the first paper, we suppose that a segment of a Gaussian ... -
Optimal Hankel Structured Rank-1 Approximation
(2022-03-10)Hankel matrices are closely related to linear time-invariant (LTI) models, which are widely used in areas like system theory, signal processing, computer algebra, or machine learning. The complexity of such a model is ... -
Modifications of Prony's Method for the Reconstruction of Structured Functions
(2021-12-20)The reconstruction and analysis of sparse signals is a common and widely studied problem in signal processing, for example in wireless telecommunication or power system theory. Hereby, most recovery methods exploit structures ... -
Adaptive Sparsification Mechanisms in Signal Recovery
(2021-04-06)This thesis considers two different adaptive recovery concepts. The first concept is concerned with proximity operators intertwined between an injective linear operator with bounded range and its pseudoinverse. A prominent ... -
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 ... -
Cartoon-Residual Image Decompositions with Application in Fingerprint Recognition
(2019-12-11)Image decompositions into a piecewise smooth part - called a cartoon - and a residual part containing oscillating patterns and/or noise, proved to be very useful in automated image processing, for example in applications ... -
Sparse Fast Trigonometric Transforms
(2019-07-22)Trigonometric transforms like the Fourier transform or the discrete cosine transform (DCT) are of immense importance in signal and image processing, physics, engineering, and data processing. The research of past decades ... -
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 ... -
The Generalized Operator Based Prony Method
(2019-05-10)The well known Prony method was introduced to reconstruct finite linear combinations of complex exponentials. A first approach towards generalizing this method to more arbitrary expansions was made by Peter & Plonka in ... -
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 ... -
Adaptive Multiscale Methods for Sparse Image Representation and Dictionary Learning
(2019-01-16)In this thesis we are interested in the topic of sparse digital image representation through adaptive multiscale basis. We develop for this two numerical methods: the Region Based Easy Path Wavelet Transform and the Haardict. ... -
Application of AAK theory for sparse approximation
(2017-10-27)Sparse approximation of structured signals is a common problem in signal processing and system theory. In particular, approximation by exponential sums often arises in natural sciences for the analysis of decay processes. ... -
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 ... -
Deterministic Sparse FFT Algorithms
(2016-09-30)The discrete Fourier transform (DFT) is a well-known transform with many applications in various fields. By fast Fourier transform (FFT) algorithms, the DFT of a vector can be efficiently computed. Using these algorithms, ... -
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, ... -
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 ... -
Ambiguities in one-dimensional phase retrieval from Fourier magnitudes
(2016-01-13)In many scientific areas, such as astronomy, electron microscopy, and crystallography, one is faced with the problem to recover an unknown signal from the magnitudes of its Fourier transform. Unfortunately, this phase ... -
Application of Persistent Homology in Signal and Image Denoising
(2015-07-29)Motivated by recent developments in topological persistence for assessment of the importance of features in data sets, we study the ideas of persistence homology for one-dimensional digital signals and its application in ... -
Reconstruction of Structured Functions From Sparse Fourier Data
(2015-01-19)In several scientific areas, such as radio astronomy, computed tomography, and magnetic resonance imaging, the reconstruction of structured functions from the knowledge of samples of their Fourier transform is a common ...