Browsing Fakultät für Mathematik und Informatik (inkl. GAUSS) by Advisor "Munk, Axel Prof. Dr."
Now showing items 120 of 31

A Statistical Model of Microscope Resolution
(20200710)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 ... 
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 ... 
Confidence bands for structural relationship models
(20070129)The goal of the thesis is to construct the simultaneous confidence bands for structural relationship models introduced by Freitag (2000), Freitag and Munk (2005). Consider the twosample ... 
Contributions to the Theory of Statistical Optimal Transport
(20220701)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 ... 
Datadriven goodnessoffit tests
(20070822)The thesis consists of the two main parts.In the first part, we consider testing statistical hypotheses about densities of signals in deconvolution models. A new approach to this problem is proposed. ... 
Empirical Optimal Transport on Discrete Spaces: Limit Theorems, Distributional Bounds and Applications
(20190109)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 ... 
Estimating rigid motion in sparse sequential dynamic imaging: with application to nanoscale fluorescence microscopy
(20170405)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 Multilevel Judgment Aggregation
(20110106)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
(20180104)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
(20150522)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 ... 
Heterogeneous Multiscale ChangePoint Inference and its Application to Ion Channel Recordings
(20180209)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
(20090323)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 ... 
Inference in inhomogeneous hidden Markov models with application to ion channel data
(20171218)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
(20060918)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 ... 
Limit Laws for Empirical Optimal Transport
(20220217)Optimal Transport (OT) has recently gained increasing attention in various fields ranging from biology to machine learning and mathematics. Especially OT based dissimilarity measures can be designed to respect the underlying ... 
Maximum Likelihood Theory for Retention of Effect NonInferiority Trials
(20100528)This work deals with the methodical issues of noninferiority trials whose aim is to demonstrate that a new test treatment is noninferior to a wellestablished reference treatment. In the ... 
Modelling and Analysing Orientation Fields of Fingerprints
(20070921)Global features of fingerprints, the most useful of which are orientation fields, are deployed for classification, image enhancement, and to define intrinsic coordinates. We thus strive for ... 
Multiscale Changepoint Segmentation: Beyond Step Functions
(20170308)Many multiscale segmentation methods have been proven to work successfully for detecting multiple changepoints, mainly because they provide faithful statistical statements, while at the same time allowing for efficient ... 
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 ... 
Nonparametric Methods in Spot Volatility Estimation
(20110106)This work is devoted to study a model, where we observe a stochastic process X under additional measurement noise. The main objective is to estimate a ``fluctuation measure``, called the volatility/intermittency of ...