Topics in Mathematics Münster

Research Interests

$\bullet$ Mathematical image processing.
$\bullet$ Inverse problems.
$\bullet$ Topology and shape optimisation.
$\bullet$ Approximation and optimisation methods in nonlinear spaces.
$\bullet$ Calculus of variations.

Selected Publications of Prof. Dr. Benedikt Wirth

$\bullet$ B. Heeren, M. Rumpf, and B. Wirth. Variational time discretization of Riemannian splines. IMA J. Numer. Anal. (in press), drx077, 2018. doi.org/10.1093/imanum/drx077

$\bullet$ A. Brancolini, C. Rossmanith, and B. Wirth. Optimal micropatterns in 2D transport networks and their relation to image inpainting. Arch. for Ration. Mech. Anal., 228(1):279–308, 2018.

$\bullet$ R. V. Kohn and B. Wirth. Optimal fine-scale structures in compliance minimization for a shear load. Comm. Pure Appl. Math., 69(8):1572–1610, 2016.

$\bullet$ P.-A. Absil, P.-Y. Gousenbourger, P. Striewski, and B. Wirth. Differentiable piecewise- Bézier surfaces on Riemannian manifolds. SIAM J. Imaging Sci., 9(4):1788–1828, 2016.

$\bullet$ M. Elsey and B. Wirth. Redistancing dynamics for vector-valued multilabel segmentation with costly fidelity: grain identification in polycrystal images. J. Sci. Comput., 63(1):279–306, 2015.

$\bullet$ K. Bredies, T. Pock, and B. Wirth. A convex, lower semicontinuous approximation of Euler's elastica energy. SIAM J. Math. Anal., 47(1):566–613, 2015.

$\bullet$ R. V. Kohn and B. Wirth. Optimal fine-scale structures in compliance minimization for a uniaxial load. Proc. R. Soc. A, 470(2170), 2014.

$\bullet$ W. Ring and B. Wirth. Optimization methods on Riemannian manifolds and their application to shape space. SIAM J. Optim., 22(2):596–627, 2012.

$\bullet$ P. Penzler, M. Rumpf, and B. Wirth. A phase-field model for compliance shape optimization in nonlinear elasticity. ESAIM Control Optim. Calc. Var., 18(1):229–258, 2012.

$\bullet$ B. Wirth, J. Gerhard, and W. Marquardt. Robust optimisation with normal vectors on critical manifolds of disturbance-induced stability loss. J. Nonlinear Sci., 21(1):57–92, 2011.

Current Cluster Publications of Prof. Dr. Benedikt Wirth

$\bullet $ David P. Bourne, Bernhard Schmitzer, and Benedikt Wirth. Semi-discrete unbalanced optimal transport and quantization. arXiv e-prints, July 2024. arXiv:1808.01962v2.

$\bullet $ Martin Holler and Benedikt Wirth. Exact reconstruction and reconstruction from noisy data with anisotropic total variation. SIAM Journal on Mathematical Analysis, 56(3):2938–2967, May 2024. doi:10.1137/22m1508571.

$\bullet $ M. Holler, A. Schlüter, and B. Wirth. Dimension reduction, exact recovery, and error estimates for sparse reconstruction in phase space. Applied and Computational Harmonic Analysis, 70:101631, May 2024. doi:10.1016/j.acha.2024.101631.

$\bullet $ Juliane Braunsmann, Marko Rajković, Martin Rumpf, and Benedikt Wirth. Convergent autoencoder approximation of low bending and low distortion manifold embeddings. ESAIM: Mathematical Modelling and Numerical Analysis, 58(1):335–361, January 2024. doi:10.1051/m2an/2023088.

$\bullet $ Manuel Kunisch, Sascha Beutler, Christian Pilger, Friedemann Kiefer, Thomas Huser, and Benedikt Wirth. Active axial motion compensation in multiphoton-excited fluorescence microscopy. arXiv e-prints, January 2024. arXiv:2401.10598.

$\bullet $ Marco Mauritz, Bernhard Schmitzer, and Benedikt Wirth. A bayesian model for dynamic mass reconstruction from pet listmode data. arXiv e-prints, November 2023. arXiv:2311.17784.

$\bullet $ Bernadette Hahn and Benedikt Wirth. Convex reconstruction of moving particles with inexact motion model. PAMM, September 2023. doi:10.1002/pamm.202300054.

$\bullet $ Mara Guastini, Marko Rajković, Martin Rumpf, and Benedikt Wirth. The variational approach to the flow of Sobolev-diffeomorphisms model. In Luca Calatroni, Marco Donatelli, Serena Morigi, Marco Prato, and Matteo Santacesaria, editors, Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, 551–564. Springer International Publishing, May 2023. doi:10.1007/978-3-031-31975-4_42.

$\bullet $ Josua Sassen, Klaus Hildebrandt, Martin Rumpf, and Benedikt Wirth. Parametrizing product shape manifolds by composite networks. arXiv e-prints, February 2023. arXiv:2302.14665.

$\bullet $ Hanne Hardering and Benedikt Wirth. Quartic $L^p$-convergence of cubic Riemannian splines. IMA J. Numer. Anal., 42(4):3360–3385, October 2022. doi:10.1093/imanum/drab077.

$\bullet $ Julius Lohmann, Bernhard Schmitzer, and Benedikt Wirth. Duality in branched transport and urban planning. Appl. Math. Opt., 86(3):Paper No. 45, 32, October 2022. doi:10.1007/s00245-022-09927-3.

$\bullet $ Juliane Braunsmann, Marko Rajković, Martin Rumpf, and Benedikt Wirth. Convergent autoencoder approximation of low bending and low distortion manifold embeddings. arXiv e-prints, August 2022. arXiv:2208.10193.

$\bullet $ Julius Lohmann, Bernhard Schmitzer, and Benedikt Wirth. Formulation of branched transport as geometry optimization. J. Math. Pures Appl., 163:739–779, July 2022. doi:10.1016/j.matpur.2022.05.021.

$\bullet $ Martin Holler and Benedikt Wirth. Exact reconstruction and reconstruction from noisy data with anisotropic total variation. arXiv e-prints, July 2022. arXiv:2207.04757.

$\bullet $ Georgios Papanikos and Benedikt Wirth. A non-convex variational model for joint polyenergetic CT reconstruction, sensor denoising and material decomposition. arXiv e-prints, June 2022. arXiv:2206.02908.

$\bullet $ Paul Striewski and Benedikt Wirth. Elastic 3D–2D image registration. J. Math. Imaging Vis., 64(5):443–462, June 2022. doi:10.1007/s10851-022-01083-1.

$\bullet $ Jonas Potthoff and Benedikt Wirth. Optimal fine-scale structures in compliance minimization for a uniaxial load in three space dimensions. ESAIM: Control Optim. Calc. Var., 28:27, May 2022. doi:10.1051/cocv/2022023.

$\bullet $ Carolin Dirks and Benedikt Wirth. An adaptive finite element approach for lifted branched transport problems. In Optimization and control for partial differential equations—uncertainty quantification, open and closed-loop control, and shape optimization, volume 29 of Radon Ser. Comput. Appl. Math., pages 189–236. March 2022. doi:10.1515/9783110695984-009.

$\bullet $ Alexander Effland, Behrend Heeren, Martin Rumpf, and Benedikt Wirth. Consistent curvature approximation on Riemannian shape spaces. IMA J. Numer. Anal., 42(1):78–106, January 2022. doi:10.1093/imanum/draa092.

$\bullet $ Martin Holler, Alexander Schlüter, and Benedikt Wirth. Dimension reduction, exact recovery, and error estimates for sparse reconstruction in phase space. arXiv e-prints, December 2021. arXiv:2112.09743.

$\bullet $ Christian Clason, Carla Tameling, and Benedikt Wirth. Convex relaxation of discrete vector-valued optimization problems. SIAM Rev., 63(4):783–821, November 2021. doi:10.1137/21M1426237.

$\bullet $ Juliane Braunsmann, Marko Rajković, Martin Rumpf, and Benedikt Wirth. Learning low bending and low distortion manifold embeddings. In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), 4411–4419. June 2021. doi:10.1109/CVPRW53098.2021.00498.

$\bullet $ Carolin Dirks, Paul Striewski, Benedikt Wirth, Anne Aalto, and Adan Olguin-Olguin. A mathematical model for bleb regulation in zebrafish primordial germ cells. Mathematical Medicine and Biology: A Journal of the IMA, February 2021. doi:10.1093/imammb/dqab002.

$\bullet $ Christian Clason, Dirk A. Lorenz, Hinrich Mahler, and Benedikt Wirth. Entropic regularization of continuous optimal transport problems. J. Math. Anal. Appl., 494(1):124432, 22, February 2021. doi:10.1016/j.jmaa.2020.124432.

$\bullet $ Benedikt Wirth. Green’s function for the Neumann–Poisson problem on $n$-dimensional balls. Am. Math. Mon., 127(8):737–743, September 2020. doi:10.1080/00029890.2020.1790910.

$\bullet $ Behrend Heeren, Stefan Paulus, Heiner Goldbach, Heiner Kuhlmann, Anne-Katrin Mahlein, Martin Rumpf, and Benedikt Wirth. Statistical shape analysis of tap roots: a methodological case study on laser scanned sugar beets. BMC Bioinf., 21(1):335, July 2020. doi:10.1186/s12859-020-03654-8.

$\bullet $ Bernhard Schmitzer, Klaus P. Schäfers, and Benedikt Wirth. Dynamic cell imaging in PET with optimal transport regularization. IEEE Trans. Med. Imaging, 39(5):1626–1635, May 2020. doi:10.1109/TMI.2019.2953773.

$\bullet $ Ulrich Böttcher and Benedikt Wirth. Convex lifting-type methods for curvature regularization. In Philipp Grohs, Martin Holler, and Andreas Weinmann, editors, Handbook of Variational Methods for Nonlinear Geometric Data, chapter 7, pages 207–233. April 2020. doi:10.1007/978-3-030-31351-7_7.

$\bullet $ Luca Ferrari, Carolin Dirks, and Benedikt Wirth. Phase field approximations of branched transportation problems. Calc. Var. Partial Differential Equations, 59(1):Paper No. 37, 34, January 2020. doi:10.1007/s00526-019-1680-3.

$\bullet $ Behrend Heeren, Martin Rumpf, Max Wardetzky, and Benedikt Wirth. Discrete Riemannian calculus on shell space. In Andrea Bonito and Ricardo Nochetto, editors, Geometric partial differential equations, volume 21 of Handbook of Numerical Analysis, pages 621–679. January 2020. doi:10.1016/bs.hna.2019.06.005.

$\bullet $ Andrea Marchese and Benedikt Wirth. Approximation of rectifiable 1-currents and weak-∗ relaxation of the $h$-mass. J. Math. Anal. Appl., 479(2):2268–2283, November 2019. doi:10.1016/j.jmaa.2019.07.059.

$\bullet $ Muna Taha, Mohammed Aldirawi, Sigrid März, Jochen Seebach, Maria Odenthal-Schnittler, Olga Bondareva, Vesna Bojovic, Thomas Schmandra, Benedikt Wirth, Magdalena Mietkowska, Klemens Rottner, and Hans Schnittler. EPLIN-α and -β isoforms modulate endothelial cell dynamics through a spatiotemporally differentiated interaction with actin. Cell Rep., 29(4):1010–1026.e6, October 2019. doi:10.1016/j.celrep.2019.09.043.

$\bullet $ Benedikt Wirth. Phase field models for two-dimensional branched transportation problems. Calc. Var. Partial Dif., 58(5):164, September 2019. doi:10.1007/s00526-019-1615-z.

$\bullet $ Bernhard Schmitzer and Benedikt Wirth. Dynamic models of Wasserstein-1-type unbalanced transport. ESAIM Control Optim. Calc. Var., 25(23):54, July 2019. doi:10.1051/cocv/2018017.

$\bullet $ Patrick W. Dondl, Matteo Novaga, Benedikt Wirth, and Stephan Wojtowytsch. A phase-field approximation of the perimeter under a connectedness constraint. SIAM J. Math. Anal., 51(5):3902–3920, January 2019. doi:10.1137/18M1225197.

$\bullet $ Bernhard Schmitzer and Benedikt Wirth. A framework for Wasserstein-1-type metrics. J. Convex Anal., 26(2):353–396, January 2019.

$\bullet $ Behrend Heeren, Martin Rumpf, and Benedikt Wirth. Variational time discretization of Riemannian splines. IMA J. Numer. Anal., 39(1):61–104, January 2019. doi:10.1093/imanum/drx077.