Blättern Fakultät für Mathematik und Informatik (inkl. GAUSS) nach "Plonka-Hoch, Gerlind Prof. Dr." Betreuer
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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. ... -
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 ... -
Adaptive Waveletmethoden zur Approximation von Bildern
(2011-07-15)This thesis is concerned with adaptive wavelet methods for the approximation of images. First, the Easy-Path-Wavelet-Transform (EPWT) is introduced. The EPWT works as follows. We determine ... -
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 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. ... -
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 ... -
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, ... -
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 ... -
Numerische Methoden zur Analyse hochdimensionaler Daten
(2014-09-10)This thesis is concerned with two of the major tasks in processing huge data sets, dimensionality reduction and data denoising. The first part of the thesis yields a summary on dimensionality reduction. Dimensionality ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ...