On this page, I keep track of the talks I gave and keep slides for at least a similar talk. Some might even include a recording of the talk or links to external further sources.
Organizer
 Workshop on Optimization on Manifolds, August 9, 2019, Technische Universität Chemnitz, Germany (together with Glaydston de Carvalho Bento, Roland Herzog, José VidalNuñéz)
 Young Researchers Minisymposium “YR3 Local and nonlocal methods for processing manifold and point cloud data” at the Jahrestagung der Gesellschaft für angewandte Mathematik und Mechanik 2017, March 6—10, Weimar, Germany (together with Daniel Tenbrinck).
 Workshop on manifoldvalued image processing, December 1st, 2016, Technische Universität Kaiserslautern, Germany (together with Gabriele Steidl).
Selected Talks

Fenchel Duality Theory and a PrimalDual Algorithm on Riemannian Manifolds
Optimization and Numerical Analysis Seminar, School of Mathematics, University of Birmingham,
February 26, 2020,
Birmingham, United Kingdom

A Variational Model for Data Fitting on Manifolds by Minimizing the Acceleration of a Bézier Curve
Institutsseminar, Institut für Numerische Mathematik, TU Dresden,
November 27, 2018,
Dresden, Germany
Fitting a smooth curve to data points $d_0,\dots,d_n$ lying on a Riemannian manifold $\mathcal M$ and associated with realvalued parameters $t_0,\dots,t_n$ is a common problem in applications like wind field approximation, rigid body motion interpolation, or spherevalued data analysis. The resulting curve should strike a balance between data proximity and a smoothing regularization constraint.
In this talk we present a variational model to fit a composite Bézier curve to the set of data points $d_0,\dots,d_n$ on a Riemannian manifold $\mathcal M$. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the data points. We approximate the acceleration by discretizing the squared second order derivative along the curve. We derive a closedform, numerically stable and efficient algorithm to compute the gradient of a Bézier curve on manifolds with respect to its control points. This gradient can be expressed as a concatenation of so called adjoint Jacobi fields. Several examples illustrate the capabilities of this approach both for interpolation and approximation. 
A Graph Framework for Manifoldvalued Data
87^{th}Annual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für angewandte Mathematik und Mechanik, GAMM),
March 6—10, 2017
Weimar & Ilmenau
A talk within the Session 21 on Image processing
Talks
2020

Fenchel Duality Theory and a PrimalDual Algorithm on Riemannian Manifolds
Optimization and Numerical Analysis Seminar, School of Mathematics, University of Birmingham,
February 26, 2020,
Birmingham, United Kingdom
2019

Fenchel Duality Theory and a PrimalDual Algorithm on Riemannian Manifolds
Oberseminar Applied Algebra und Analysis, Institut für Analysis und Algebra,
December 10, 2019,
Braunschweig, Germany

A PrimalDual Algorithm for Convex Nonsmooth Optimization on Riemannian Manifolds
European Numerical Mathematics and Advanced Applications Conference 2019,
September 30—4, 2019
Egmond aan Zee, The Netherlands

Fenchel Duality Theory and a PrimalDual Algorithm on Riemannian Manifolds
Modeling, interpolation, and approximation for waves and signals,
August 19—September 23, 2019
Lübeck, Germany
Invited Plenary Talk

A PrimalDual Algorithm for Convex Nonsmooth Optimization on Riemannian Manifolds
6^{th} International Conference on Continuous Optimization,
August 4—8, 2019
Berlin, Germany
Based on a Fenchel dual notion on Riemannian manifolds we investigate the saddle point problem related to a nonsmooth convex optimization problem. We derive a primaldual hybrid gradient algorithm to compute the saddle point using either an exact or a linearized approach for the involved nonlinear operator. We investigate a sufficient condition for convergence of the linearized algorithm on Hadamard manifolds. Numerical examples illustrate, that on Hadamard manifolds we are on par with state of the art algorithms and on general manifolds we outperform existing approaches.

A Variational Model for Data Fitting on Manifolds by Minimizing the Acceleration of a Bézier Curve
International Congress on Industrial and Applied Mathematics,
July 19—16, 2019
Valencia, Spain
We present a variational model to fit a composite Bézier curve to data points on a Riemannian manifold. The resulting curve has a minimal mean squared acceleration while also remaining close the data. We discretize the acceleration of the curve and derive an efficient algorithm to compute the gradient w.r.t. its control points, expressed as a concatenation of adjoint Jacobi fields. Several examples illustrate the capabilities of this approach both for interpolation and approximation.

A Variational Model for Data Fitting on Manifolds by Minimizing the Acceleration of a Bézier Curve
30th European Conference on Operational Research,
June 23—26, 2019
Dublin, Ireland
Fitting a smooth curve to a set of n data points lying on a Riemannian manifold and associated with realvalued time points is a common problem in applications like wind field approximation, rigid body motion interpolation, or spherevalued data analysis. The resulting curve should strike a balance between data proximity and a smoothing regularization constraint.
In this talk we present a variational model to fit a composite Bézier curve to the set of data points on a Riemannian manifold. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the data points. We approximate the acceleration by discretizing the squared second order derivative along the curve. We derive a closedform, numerically stable and efficient algorithm to compute the gradient of a Bézier curve on manifolds with respect to its control points. This gradient can be expressed as a concatenation of so called adjoint Jacobi fields. Several examples illustrate the capabilities of this approach both for interpolation and approximation. 
Optimization on Manifolds for Models using Second Order Differences
Kolloquium des Instituts für Mathematik, Universität zu Lübeck,
June 6, 2019,
Lübeck, Germany
In many real life scenarios, measured data appears as values on a Riemannian manifold. For example in interferometric Synthetic Aperture Radar (InSAR) data is given as a phase, in electron backscattered diffraction (EBSD) as data items being from a quotient of the orientation group SO(3), and in diffusion tensor magnetic resonance imaging (DTMRI) the measured data are symmetric positive definite matrices. These data items are often measured on an equispaced grid like usual signals and image but they also suffer from the same measurement errors like presence of noise or incompleteness. Hence there is a need to perform data processing tasks like denoising, inpainting or interpolation on these manifoldvalued data.
In this talk we present variational models for these tasks involving discrete second order differences for manifoldvalued data. To compute a minimizer of such a the model, we obtain a highdimensional, possibly nonsmooth, optimization problem defined on a Riemannian manifold. We present algorithms to efficiently solve these problems and illustrate their performance. 
Optimization on Manifolds for Models using Second Order Differences
Kolloquium über Angewandte Mathematik, Institut für Numerische und Angewandte Mathematik, GeorgAugustUniversität Göttingen,
May 28, 2019,
Göttingen, Germany
In many real life scenarios, measured data appears as values on a Riemannian manifold. For example in interferometric Synthetic Aperture Radar (InSAR) data is given as a phase, in electron backscattered diffraction (EBSD) as data items being from a quotient of the orientation group SO(3), and in diffusion tensor magnetic resonance imaging (DTMRI) the measured data are symmetric positive definite matrices. These data items are often measured on an equispaced grid like usual signals and image but they also suffer from the same measurement errors like presence of noise or incompleteness. Hence there is a need to perform data processing tasks like denoising, inpainting or interpolation on these manifoldvalued data.
In this talk we present variational models for these tasks involving discrete second order differences for manifoldvalued data. To compute a minimizer of such a the model, we obtain a highdimensional, possibly nonsmooth, optimization problem defined on a Riemannian manifold. We present algorithms to efficiently solve these problems and illustrate their performance. 
Nonsmooth Optimization on Riemannian Manifolds and ManifoldValued Data Processing
Geometry and Learning from Data in 3D and Beyond, Workshop I: Geometric Processing,
April 1—5, 2019
Los Angeles, CA, USA
In many real life scenarios measured data appears as values from a Riemannian manifold. For example in interferometric Synthetic Aperture Radar (InSAR) data is given as a phase, in electron backscattered diffraction (EBSD) as data items being from a quotient of the orientation group SO(3), and in diffusion tensor magnetic resonance imaging (DTMRI) the measured data are symmetric positive definite matrices. These data items are often measured on a equispaced grid like usual signals and image but they also suffer from the same measurement errors like presence of noise or incompleteness. Hence there is a need to perform data processing tasks like denoising, inpainting or even interpolation on these manifoldvalued data.
In this talk we present variational methods and nonsmooth optimization algorithms for processing manifoldvalued data. For the first, we present first and second order difference based priors and their application to the tasks from image processing. To compute minimizers of the variational methods, we present algorithms to efficiently solve nonsmooth optimization tasks on manifolds. 
Intrinsic Formulation of KKT Conditions and Constraint Qualifications on Smooth Manifolds
90^{th}Annual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für angewandte Mathematik und Mechanik, GAMM),
February 22—20, 2019
Vienna, Austria
We formulate KarushKuhnTucker (KKT) conditions for equality and inequality con strained optimization problems on smooth manifolds. Under the Guignard constraint qualification, local minimizers are shown to admit Lagrange multipliers. We also investigate other constraint qualifications and provide results parallel to those in Euclidean space. Illustrating numerical examples will be presented.
2018

A Variational Model for Data Fitting on Manifolds by Minimizing the Acceleration of a Bézier Curve
Kolloquium, Department Mathematik, FAU ErlangenNürnberg,
December 10—14, 2018
Erlangen, Germany
Fitting a smooth curve to data points $d_0,\dots,d_n$ lying on a Riemannian manifold $\mathcal M$ and associated with realvalued parameters $t_0,\dots,t_n$ is a common problem in applications like wind field approximation, rigid body motion interpolation, or spherevalued data analysis. The resulting curve should strike a balance between data proximity and a smoothing regularization constraint.
In this talk we present a variational model to fit a composite Bézier curve to the set of data points $d_0,\dots,d_n$ on a Riemannian manifold $\mathcal M$. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the data points. We approximate the acceleration by discretizing the squared second order derivative along the curve. We derive a closedform, numerically stable and efficient algorithm to compute the gradient of a Bézier curve on manifolds with respect to its control points. This gradient can be expressed as a concatenation of so called adjoint Jacobi fields. Several examples illustrate the capabilities of this approach both for interpolation and approximation. 
A Variational Model for Data Fitting on Manifolds by Minimizing the Acceleration of a Bézier Curve
Institutsseminar, Institut für Numerische Mathematik, TU Dresden,
November 27, 2018,
Dresden, Germany
Fitting a smooth curve to data points $d_0,\dots,d_n$ lying on a Riemannian manifold $\mathcal M$ and associated with realvalued parameters $t_0,\dots,t_n$ is a common problem in applications like wind field approximation, rigid body motion interpolation, or spherevalued data analysis. The resulting curve should strike a balance between data proximity and a smoothing regularization constraint.
In this talk we present a variational model to fit a composite Bézier curve to the set of data points $d_0,\dots,d_n$ on a Riemannian manifold $\mathcal M$. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the data points. We approximate the acceleration by discretizing the squared second order derivative along the curve. We derive a closedform, numerically stable and efficient algorithm to compute the gradient of a Bézier curve on manifolds with respect to its control points. This gradient can be expressed as a concatenation of so called adjoint Jacobi fields. Several examples illustrate the capabilities of this approach both for interpolation and approximation. 
A Variational Model for Data Fitting on Manifolds by Minimizing the Acceleration of a Bézier Curve
Mecklenburg Workshop – Approximation Methods and Fast Algorithms,
September 10—14, 2018
Hasenwinkel, Germany
Fitting a smooth curve to data points $d_0,\dots,d_n$ lying on a Riemannian manifold $\mathcal M$ and associated with realvalued parameters $t_0,\dots,t_n$ is a common problem in applications like wind field approximation, rigid body motion interpolation, or spherevalued data analysis. The resulting curve should strike a balance between data proximity and a smoothing regularization constraint.
In this talk we present a variational model to fit a composite Bézier curve to the set of data points $d_0,\dots,d_n$ on a Riemannian manifold $\mathcal M$. The resulting curve is obtained in such a way that its mean squared acceleration is minimal in addition to remaining close the data points. We approximate the acceleration by discretizing the squared second order derivative along the curve. We derive a closedform, numerically stable and efficient algorithm to compute the gradient of a Bézier curve on manifolds with respect to its control points. This gradient can be expressed as a concatenation of so called adjoint Jacobi fields. Several examples illustrate the capabilities of this approach both for interpolation and approximation. 
Variational Methods for Manifoldvalued image Processing
Seminar “Theory and Algorithms in Data Science” at the Alan Turing Institute,
September 3, 2018,
London, United Kingdom
Invited talk and a week of research stay with M. Cucuringu and Hemant Tyagi.
In many real life scenarios measured data appears as values from a Riemannian manifold. For example in interferometric Synthetic Aperture Radar (InSAR) data is given as a phase, in electron backscattered diffraction (EBSD) as data items being from a quotient of the orientation group SO(3), and in diffusion tensor magnetic resonance imaging (DTMRI) the measured data are symmetric positive definite matrices. These data items are often measured on a pixel grid like usual images and they also suffer from the same measurement errors like noisy or incompleteness.Hence there is a need to perform image processing tasks like denoising, inpainting or segmentation on these manifoldvalued images. Recently the ROFModel for TV regularization has been transferred to the setting of manifoldvalued images to perform such image processing tasks.
In this talk we present methods and algorithms to compute the TV regularization for manifoldvalued images efficiently using variational methods. We present generalizations to second order models, and to the case, where the data is not given on a pixel grid, for example when dealing with nonlocal methods. 
A parallel DouglasRachford Algorithm for Data on Hadamard Manifolds
23rd International Symposium on Mathematical Programming,
July 1—6, 2018
Bordeaux, France
Invited talk within the Session “Riemannian Geometry in Optimization for Learning” organized by N. Boumal.
In many applications like DTMRI or a data set of multivariate Gaussian distributions. Since these measurements suffer from errors or even loss of data, we aim to transfer image processing methods to manifoldvalued data. In this talk we present a parallel DouglasRachford algorithm for manifoldvalued data and proof its convergence to a minimizer for Hadamard manifolds of constant curvature. We illustrate the algorithm using the total variation regularization or ROF model and demonstrate the performance within the ManifoldValued Image Restoration Toolbox (MVIRT).

Nonlocal Inpainting of Manifoldvalued Data on Finite Weighted Graphs
SIAM Conference of Imaging Science 2018,
June 5—8, 2018
Bologna, Italy
Invited talk within the Session Minisymposium #31 “Variational Approaches for Regularizing Nonlinear Geometric Data”
When dealing with manifoldvalued data one faces the same challenging processing tasks as, e.g., in classical imaging. In this talk we consider image inpainting for manifoldvalued data in which missing information have to be filled in suitably. We present a generalization of the graph infinityLaplacian to manifoldvalued data based on the minmax characterization of the local discrete Lipschitz constant. We derive a numerical scheme to solve the obtained manifoldvalued infinityLaplace equation and inpaint missing data.

The GraphInfinity Laplacian for Manifoldvalued Data
89^{th}Annual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für angewandte Mathematik und Mechanik, GAMM),
March 19—23, 2018
Munich, Germany
Due to recent technological advances in the development of modern sensors new imaging modalities have emerged for which the acquired data values are given on a Riemannian manifold, e.g., in phase values in InSAR imaging or when dealing with diffusion tensors in DTMRI. Furthermore, to process not only rectangular domains and regular grids, graphs can be employed to model both data on arbitrary (sampled) manifolds as well as nonlocal vicinity.
In this talk we extend a framework for processing discrete manifoldvalued data to the task of inpainting missing values, such that the inpainted area nonlocally incorporates data into the reconstruction. We discuss a generalization of the graph infinityLaplacian to manifoldvalued data based on the minmax characterization of the local discrete Lipschitz constant. Finally, we present a numerical scheme to solve the obtained manifoldvalued infinityLaplace equation.
2017

Nonlocal Inpainting of Manifoldvalued Data on Finite Weighted Graphs
3^{rd} Conference on Geometric Science of Information,
November 7—9, 2017
Paris, France
Contributed talk within the session “Optimization on Manifolds” organized by P.A. Absil and R. Sepulchre.
Recently, there has been a strong ambition to translate models and algorithms from traditional image processing to nonEuclidean domains, e.g., to manifoldvalued data. While the task of denoising has been extensively studied in the last years, there was rarely an attempt to perform image inpainting on manifoldvalued data. In this paper we present a nonlocal inpainting method for manifoldvalued data given on a finite weighted graph. We introduce a new graph infinityLaplace operator based on the idea of discrete minimizing Lipschitz extensions, which we use to formulate the inpainting problem as PDE on the graph. Furthermore, we derive an explicit numerical solving scheme, which we evaluate on two classes of synthetic manifoldvalued images.

MVIRT – A Toolbox for Manifoldvalued Image Restoration
IEEE International Conference on Image Processing (ICIP) 2017,
September 17—20, 2017
Bejing, China
Invited talk within the Special Session “Trends in Statistical Analysis of ManifoldValued Data – Theory and Applications to Imaging”, supported by a DAAD conference travel grant
In many real life application measured data takes its values on Riemannian manifolds. For the special case of the Euclidean space this setting includes the classical grayscale and color images. Like these classical images, manifoldvalued data might suffer from measurement errors in form of noise or missing data. In this talk we present the manifoldvalued image restoration toolbox (MVIRT) that provides implementations of classical image processing tasks. Based on recent developments in variational methods for manifoldvalued image processing methods, like total variation regularization, the toolbox provides easy access to work with these algorithms. The toolbox is implemented in Matlab, open source, and easily extendible, e.g. with own manifolds, noise models or further algorithms. This paper introduces the main mathematical methods as well as numerical examples.

A Graph Framework for Manifoldvalued Data
Kolloquium angewandte Mathematik at the Institute of Computational and Applied Mathematics, WWU Münster.,
June 26, 2017,
Münster, Germany
Invited talk and research stay within the research group of B. Wirth.
In many realworld applications measured data are not in a Euclidean vector space but rather are given on a Riemannian manifold. This is the case, e.g., when dealing with Interferometric Synthetic Aperture Radar (InSAR) data consisting of phase values or data obtained in Diffusion Tensor Magnetic Resonance Imaging (DTMRI). In this talk we present a framework for processing discrete manifoldvalued data, for which the underlying (sampling) topology is modeled by a graph. We introduce the notion of a manifoldvalued differences on a graph and based on this deduce a family of manifoldvalued graph operators. In particular, we introduce the graph pLaplacian and graph infinityLaplacian for manifoldvalued data. We discuss a numerical scheme to compute a solution to the corresponding parabolic PDEs and apply this algorithm to different manifoldvalued data, illustrating the diversity and flexibility of the proposed framework in denoising and inpainting applications. This is joint work with Daniel Tenbrinck (WWU Münster)

Infimal Convolution Coupling of First and Second Order Differences on ManifoldValued Images
6^{th} Internvational Conference on Scale Space and Variational Methods in Computer Vision,
June 4—8, 2017
Kolding, Denmark

Variational Models for Manifoldvalued Image Processing
Seminars in Mathematical Engineering of the ICTEAM at Université catolique de Louvain,
March 21, 2017,
LouvainlaNeuve, Belgium
Invited talk and a week of research stay with the group of P.A. Absil.

A Graph Framework for Manifoldvalued Data
87^{th}Annual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für angewandte Mathematik und Mechanik, GAMM),
March 6—10, 2017
Weimar & Ilmenau
A talk within the Session 21 on Image processing
2016
 A Second Order Nonsmooth Variational Model for Restoring Manifoldvalued Image Mecklenburg Workshop – Approximation Methods and Data Analysis, September 5—9, 2016 Hasenwinkel, Germany

Second Order TVType Regularization Methods for ManifoldValued Images
SIAM Conference of Imaging Sciences 2016,
May 23—26, 2016
Albuquerque, NM, USA
Invited talk within the Minisymposium I on “Inversion on Nonlinear Image Formation Models”, supported by a DAAD conference travel grant.
In many real world situations, measured data is noisy and nonlinear, i.e., the data is given as values in a certain manifold. Examples are Interferometric Synthetic Aperture Radar (InSAR) images or the hue channel of HSV, where the entries are phasevalued, directions in \(\mathbb R^n\), which are data given on \(\mathbb S^{n1}\), and diffusion tensor magnetic resonance imaging (DTMRI), where the obtained pixel of the image are symmetric positive definite matrices.
In this talk we extend the recently introduced total variation model on manifolds by a second order TV type model. We first introduce second order differences on manifolds in a sound way using the induced metric on Riemannian manifolds. By avoiding a definition involving tangent bundles, this definition allows for a minimization employing the inexact cyclic proximal point algorithm, where the proximal maps can be computed using Jacobian fields. The algorithm is then applied to several examples on the aforementioned manifolds to illustrate the efficiency of the algorithm.
This is joint work with M. Bačák, J. Persch, G. Steidl, and A. Weinmann. 
A Second Order Nonsmooth Variational Model for Restoring Manifoldvalued Image
Seminar AG Imaging at the Imaging Workgroup, Institute of Computational and Applied Mathematics,
May 11, 2016,
Münster, Germany
Invited talk and a week research stay with D. Tenbrinck.
In many real world situations, measured data is noisy and nonlinear, i.e., the data is given as values in a certain manifold or on a submanifold of the euclidean space the measurements are taken in. Examples are InSAR images and the hue channel of HSV, where the entries are phasevalued, directions in \(\mathbb R n\), which are data given on sphere \(\mathbb S^{n−1}\), and diffusion tensor magnetic resonance imaging, where the obtained data items are symmetric positive definite \(3\times 3\) matrices. In this talk we extend the recently introduced total variation model on manifolds by a second order TV type model. We first introduce second order differences on manifolds in a sound way using the induced metric on Riemannian manifolds. By avoiding a definition involving tangent bundles, this definition allows for a minimization employing the inexact cyclic proximal point algorithm, where the proximal maps can be computed using Jacobian fields. The algorithm is then applied to several examples on the aforementioned manifolds to illustrate the efficiency of the algorithm.

A Second Order Nonsmooth Variational Model for Restoring Manifoldvalued images
37^{th} Northern German Colloquium on Applied Analysis and Numerical Mathematics,
April 22—23, 2016
Lübeck, Germany

A Second Order Nonsmooth Variational Model for Restoring Manifoldvalued images
86^{th}Annual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für angewandte Mathematik und Mechanik, GAMM),
March 7—11, 2016
Braunschweig, Germany
Invited talk within the Young Researchers Minisymposium YR 3 “Dedicated regularization for variational image processing”
2015

A Second Order Nonsmooth Variational Model for Restoring Manifoldvalued images
Variational Methods for Dynamic Inverse Problems and imaging,
September 28—30, 2015
Münster, Germany

A Second Order Nonsmooth Variational Model for Restoring Manifoldvalued images
25th RheinMain Arbeitskreis – Mathematics of Computation,
July 10, 2015,
Darmstadt, Germany
Invited talk
In many real world situations, measured data is noisy and nonlinear, i.e., the data is given as values in a certain manifold. Examples are InSAR images and the hue channel of HSV, where the entries are phasevalued, directions in \(R^n\), which are data given on \(S^{n1}\), and diffusion tensor magnetic resonance imaging, where the obtained data items are symmetric positive definite matrices.

The anisotropic StrangFix conditions
Mecklenburger Workshop – Approximation Methods and Function Spaces,
March 16—20, 2015
Hasenwinkel, Germany

Second Order Differences for Combined Cyclic and Vector Space Data and their Application to Denoising and Inpainting
Cambridge Image Analysis seminars,
March 4, 2015,
Cambridge, United Kingdom
Invited talk and a week research stay with J. Lellmann
 Inpainting and Denoising of Cyclic Data Using First and Second Order Differences Seminar of the Institute of Computational Biology, Helmholtzzentrum München, February 18, 2015, Munich, Germany Invited talk and research stay with M. Bačák and A. Weinmann

Inpainting of Cyclic Data using First and Second Order Differences
10th International Conference on Energy Minimizing Methods in Computer Vision and Pattern Recognition,
January 13—16, 2015
Hong Kong, China
Cyclic data arise in various image and signal processing applications such as interferometric synthetic aperture radar, electroencephalogram data analysis, and color image restoration in HSV or LCh spaces. In this paper we introduce a variational inpainting model for cyclic data which utilizes our definition of absolute cyclic second order differences. Based on analytical expressions for the proximal mappings of these differences we propose a cyclic proximal point algorithm (CPPA) for minimizing the corresponding functional. We choose appropriate cycles to implement this algorithm in an efficient way. We further introduce a simple strategy to initialize the unknown inpainting region. Numerical results both for synthetic and realworld data demonstrate the performance of our algorithm.
2014

Second Order Differences of Cyclic Data and Applications in Variational Denoising
Deutschfranzösischer Workshop Mathematische Bildverarbeitung,
October 6—8, 2014
Fraunhofer ITWM, Kaiserslautern, Germany

Second Order Differences of Cyclic Data and Applications in Variational Denoising
Mathematical Image Processing and Phase Retrieval,
September 1—3, 2014
Göttingen, Germany

Second Order Differences of Cyclic Data and Application to Variational Denoising
Seminar of the Institute of Computational Biology, Helmholtzzentrum München,
May 14, 2014,
Munich, Germany
Invited talk and research stay with A. Weinmann

Multivariate anisotrope Interpolation auf dem Torus
Mecklenburger Workshop – Approximationsmethoden und schnelle Algorithmen,
March 17—20, 2014
Hasenwinkel, Germany

Multivariate Anisotropic periodic Wavelets
85^{th}Annual Meeting of the International Association of Applied Mathematics and Mechanics (Gesellschaft für angewandte Mathematik und Mechanik, GAMM),
March 10—14, 2014
Erlangen, Germany
2013

Multivariate Anisotropic Wavelets on the Torus
Workshop on Advances in Image Processing,
September 30—October 2, 2013
Anweiler am Trifels, Germany

Multivariate anisotrope Wavelets auf dem Torus
Mecklenburger Workshop — Approximationsmethoden und schnelle Algorithmen,
June 20—23, 2013
Hasenwinkel, Germany

Multivariate anisotrope Wavelets auf dem Torus
32. Norddeutsches Kolloquium über angewandte Analysis und Numerische Mathematik,
May 3—4, 2013
Clausthal, Germany

Die multivariate anisotropen WaveletTransformation auf dem Torus
Kolloquiumsvortrag, Image Processing and Data Analysis Group,
April 8, 2013,
Kaiserslautern, Germany
2012

The multivariate anisotropic Wavelet Transform on the Torus
Workshop on Mathematics for Life Sciences,
September 3—14, 2012
Kiev, Ukraine
2011

Die multivariate periodische WaveletTransformation
32. Norddeutsches Kolloquium über angewandte Analysis und Numerische Mathematik,
May 27—28, 2011
Institut für Mathematik, Universität Osnabrück, Osnabrück
Für periodische Wavelets im eindimensionalen Fall ist seit Mitte der 1990er Jahre eine umfassende Theorie bekannt. Dieser Vortrag stellt die multivariate Verallgemeinerung vor. Ausgehend von anisotropen gleichmäßigen Mustern auf dem $d$dimensionalen Torus wird eine diskrete FourierTransformation definiert. Dies führt zu diskreten Frequenzmengen – die erzeugende Gruppe –, die bestimmte Richtungen bevorzugen und trotzdem schnelle Algorithmen ermöglichen. Dazu ist es notwendig, eine bestimmte Anordnung der Musterpunkte, sowie der erzeugenden Gruppe, zu finden. Die darauf aufbauende WaveletZerlegung wird für den Spezialfall einer dyadischen Zerlegung präsentiert. Sie zerlegt einen Raum von Translaten in zwei zueinander orthogonale Unterräume mit jeweils halber Dimension des Ursprungsraumes. Auch hier ist eine schnelle Implementierung möglich, wenn man für die Elemente der erzeugenden Gruppe eine entsprechende Anordnung wählt.

Multivariate translationsinvariante Räume
21. RheinRuhr Workshop,
February 11, 2011,
Königswinter, Germany

Multivariate Periodic Function Spaces
Sparse Representations and Efficitent Sensing of Data,
February 3, 2011,
Dagstuhl Seminar, Dagstuhl, Germany
2009

Drawing Hypergraphs using NURBS curves
Presentation of my diploma thesis,
September 16, 2009,
TU Bergakademie Freiberg, Freiberg, Germany
Other Conferences
 7^{th} International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2019),
 June 30—July 4, 2019, Hofgeismar.
 Chemnitz Symposium on Inverse Problems 2018 (CSIP18),
 September 27—28, 2018, Chemnitz.
 Chemnitz Finite Element Symposium 2018 (CFEM18),
 September 24—26, 2018, Chemnitz.
 Mathematics and Image Analysis 2018 (MIA 2018),
 January 15—17, 2018, Berlin, Germany.
 RheinMainArbeitskreis Mathematics of Computation,
 July 7, 2017, Mannheim, Germany.
 Workshop: Shape, Images and Optimization,
 February 28—March 3, 2017, Münster, Germany.
 Project Meeting of the Marie Curie Inital Training Network Scheme: INTREPID Forensics,
 February 5, 2016, Leicester, United Kingdom.
 Summer School on Applied Analysis 2015,
 September 21—25, 2015, Chemnitz, Germany.
 5^{th} International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2013),
 May 30—June 4, 2015, Bordeaux, France.
 Workshop “Optimisation Géométrique sur les Variétés”,
 November 21, 2014, Paris, France.
 Colloquium Commemorating Bernd Fischer,
 October 10, 2014, Lübeck, Gemany.
 Summer School on Applied Analysis 2014,
 September 22—26, 2014, Chemnitz, Germany.
 Mathematik in Medizin und Lebenswissenschaften,
 May 1, 2014, Lübeck, Germany, Meeting on occasion of the 20^{th} birthday of the Institute of Mathematics at the University of Lübeck..
 RheinMainArbeitskreis Mathematics of Computation,
 February 7, 2014, Marburg, Germany.
 Summer School on Applied Analysis 2013,
 September 23—27, 2013, Chemnitz, Germany.
 Summer School on Applied Analysis 2012,
 September 24—28, 2012, Chemnitz, Germany.
 33. Norddeutsches Kolloquium über Angewandte Analysis und Numerische Mathematik,
 May 4—5, 2012, Rostock, Germany.
 22. RheinRhuhrWorkshop,
 February 3—4, 2012, Bestwig, Germany.
 28th GAMMSeminar Leipzig on Analysis and Numerical Methods in Higher Dimension,
 January 16—18, 2012, Leipzig, Germany.
 Summer School on Applied Analysis 2011,
 September 26—30, 2011, Chemnitz, Germany.
 1^{st} Workshop: A Computational Approach to Harmonic Analysis,
 August 22—26, 2011, Marburg, Germany.
 From Abstract to Computational Harmonic Analysis,
 June 13—19, 2011, Strobl, Austria.
 Summer School on Applied Analysis 2010,
 October 4—8, 2010, Chemnitz, Germany.
 20. RheinRhuhrWorkshop,
 February 12—13, 2010, Burg Gemen, Germany.