Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Referee "Munk, Axel Prof. Dr."
Now showing items 1-20 of 39
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A Bayesian approach to initial model inference in cryo-electron microscopy
(2016-03-18)Single-particle cryo-electron microscopy (cryo-EM) is widely used to study the structure of macromolecular assemblies. Tens of thousands of noisy two-dimensional images of the macromolecular assembly viewed from different ... -
A Statistical Model of Microscope Resolution
(2020-07-10)A general rule of thumb in imaging is that the resolution of a light microscope depends linearly on the full width at half maximum (FWHM) of its point spread function (psf). In the present work we carefully define a ... -
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 ... -
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 ... -
Computational methods for random tomography with applications to cryo-EM data
(2022-08-01)Over the last decade, Cryo Electron Microscopy (cryo-EM) has emerged as a powerful and reliable technique to determine the three-dimensional (3D) structure of large macro-molecular assemblies at near atomic resolution. ... -
Contributions to the Theory of Statistical Optimal Transport
(2022-07-01)The application of optimal transport based methodologies for statistical purposes has experienced a surge of interest and activity in recent years. This doctoral thesis collects the work of four research articles on the ... -
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 ... -
Cryptanalysis of the Fuzzy Vault for Fingerprints: Vulnerabilities and Countermeasures
(2013-07-08)The fuzzy fingerprint vault is a popular approach to protect a fingerprint's minutiae as a building block of a security application. In this thesis simulations of several attack scenarios are conducted against implementations ... -
Empirical Optimal Transport on Discrete Spaces: Limit Theorems, Distributional Bounds and Applications
(2019-01-09)Optimal Transport and especially distances based on optimal transport are a widely applied tool in different mathematical disciplines. Among others it is used in probability theory to study for example limit laws or derive ... -
Equivariant Functional Shape Analysis in SO(3) with Applications to Gait Analysis
(2016-11-04)In gait analysis of the knee joint the data is given by curves in the group of $3\times3$ rotation matrices. We introduce $\mathcal{S}$-equivariant functional models (viz., Gaussian perturbations of a center curve) and ... -
Estimating rigid motion in sparse sequential dynamic imaging: with application to nanoscale fluorescence microscopy
(2017-04-05)In this work, we deal with sequences of pixel images (frames) which are noisy shifted, rotated, and scaled versions of some unknown image f. Moreover, those frames are sparse in the sense that they do not show the whole ... -
Fingerprint Growth Prediction, Image Preprocessing and Multi-level Judgment Aggregation
(2011-01-06)Finger growth is studied in the first part of the thesis and a method for growth prediction is presented. The effectiveness of the method is validated in several tests. Fingerprint image ... -
Finite Alphabet Blind Separation
(2018-01-04)This thesis considers a particular blind source separation problem, where the sources are assumed to only take values in a known finite set, denoted as the alphabet. More precisely, one observes M linear mixtures of m ... -
Fourier and Variational Based Approaches for Fingerprint Segmentation
(2015-05-22)Fingerprint recognition plays an important role in many commercial applications and is used by millions of people every day, e.g. for unlocking mobile phones. Fingerprint image segmentation is typically the first processing ... -
Geometric convergence of slice sampling
(2021-10-19)In Bayesian statistics sampling w.r.t. a posterior distribution, which is given through a prior and a likelihood function, is a challenging task. The generation of exact samples is in general quite difficult, since the ... -
Heterogeneous Multiscale Change-Point Inference and its Application to Ion Channel Recordings
(2018-02-09)Ion channel recordings by the patch clamp technique are a major tool to quantify the electrophysiological dynamics of ion channels in the cell membrane, which is for instance important in medicine for the development of ... -
Hierarchically linked extended features for fingerprint processing
(2009-03-23)This thesis discusses a novel approach for fingerprint feature extraction. A new fingerprint structure has been proposed as a basis for the extraction of extended features. These new features ... -
Identifying dependencies among delays
(2008-02-29)The treatment of disturbances in case of capacity restrictions in the Delay management problem has been theoretically and numerically examined. A new formulation of these secondary conditions for the macromodel of the ... -
Inference in inhomogeneous hidden Markov models with application to ion channel data
(2017-12-18)Ion channel recordings under a changing environment are hardly analyzed and are the main cause for the new model class we introduce. This thesis mainly concerns hidden Markov models with a homogeneous hidden Markov chain ... -
Jump estimation for noisy blurred step functions
(2006-09-18)We consider the estimation of a step function $f$ from noisy observations of $Kf$, where $K$ is some integral operator with bounded integral Kernel. We use a penalized least squares estimator ...