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Inverse Problems

Final Theses

Topics for theses are found individually. In any case, please follow these instructions [German].
If interested: frank.werner@mathematik.uni-wuerzburg.de

 

Bachelor Theses

Cover of a Bachelor Thesis

As a rule, the basis for a Bachelor's thesis is at least attendance of Numerical Mathematics I and, if applicable, also of Numerical Mathematics II. Initial knowledge of functional analysis and/or modelling and scientific computing is also advantageous. Alternatively, topics in the intersection of numerics and stochastics/statistics are also assigned.

The list of supervised theses below gives an overview of possible topics, although of course no topic can be assigned identically a second time.

You do not have to think of a topic yourself. Based on your prior knowledge and your interests, possible topics can be discussed at an initial meeting.

Master Theses

Cover of a Master Thesis

The basis of a Master's thesis is usually the lectures on functional analysis, inverse problems, specialisation lectures (AGs) and seminars. As a rule, you should have attended at least one course on inverse problems. Basic knowledge of statistics/stochastics is also helpful.

The list of supervised theses below gives an overview of possible topics. Of course, no topic is assigned identically a second time.

You do not have to think about the topic yourself, but you are welcome to suggest your own ideas. Based on your prior knowledge and your interests, possible topics can be discussed at an initial meeting.

Of course, admission essays in the teaching degree programs are also assigned upon request. Formal criteria can be found on the institute's page on study organization:
Degree theses

Supervised doctoral, master's and bachelor's theses (by F. Werner)

  • On minimax detection of localized signals from indirect or correlated data (Göttingen, 2022)
  • Multiscale Scanning in Higher Dimensions: Limit theory, statistical consequences and an application in STED microscopy (Göttingen, 2018)

  • Comparison of trace estimating algorithms in filter-based regularization of statistical inverse problems (Würzburg, 2022)
  • Tikhonov-based Hypothesis Testing for Statistical Inverse Problems (Würzburg, 2022)
  • A convergence analysis for solving inverse problems with a trained neural network as a regularizer (Würzburg, 2022)
  • Finding Fluorescent Markers using Neural Networks: Mathematical Theory and Practical Implementations (Würzburg, 2021)
  • Statistical Inverse Problems in the discretized white noise model (Göttingen, 2021)
  • Modellbildung und Trendschätzung bei Sterbetafeln (Göttingen, 2020)
  • Multiscale quantile regression in multiple dimensions (Göttingen, 2020)
  • Minimax optimality of a Lepski-based parameter choice rule in statistical inverse problems (Göttingen, 2020)

  • Identifikation eines PDE-Parameters mittels der IRGNM (2023)
  • The CG Method for Solving Tikhonov Equations (Würzburg, 2022)
  • Alternatives Abbruchkriterium des CG-Verfahrens zur Lösung der Tikhonov-Gleichung (Würzburg, 2022)
  • Numerischer Vergleich verschiedener Parameterwahlen für diskrete inverse Probleme (Würzburg, 2021)
  • Runge-Kutta-Verfahren als Regularisierungsmethode für Inverse Probleme (Würzburg, 2021)
  • Numerische Untersuchung des modifizierten Lepskiĭ-Verfahrens (Würzburg, 2021)
  • Wie optimal ist das Quasi-Optimalitätsprinzip? (Würzburg, 2021)
  • Implementation of variational Poisson denoising (Würzburg, 2021)
  • Der Wiener Filter und Regularisierung (Würzburg, 2021)
  • Solving an Inverse Transmission Scattering Problem via the Iteratively Regularized Gauss-Newton Method (Göttingen, 2014)