Profile of Thorsten Hohage



Thorsten Hohage
Institut für Numerische und Angewandte Mathematik
Lotzestraße 16-18
D-37083 Göttingen, Germany


room 115
phone +49 551 39 24509
hohage@math.uni-goettingen.de



research interests

• inverse problems
• inverse problems in partial differential equations, in particular inverse scattering problems
• regularization theory for statistical inverse problems
• variational regularization
• efficient algorithms
• application areas: helioseismology, phase retrieval problems in optics, energy conversion, Magnetic Resonance Imaging (MRI)
• transparent boundary condition, resonances
• spectrally convergent methods, in particular learned infinite elements and Hardy space infinite elements
• numerical computation of resonances

short CV

• personal data
• born Sept. 28, 1971
• married to Susanne Petri
• two sons: Anton (born 2010) and Jakob (born 2011)
• education
  

  1999		degree Dr.~techn. PhD advisor: Heinz Engl. Title: Iterative Methods in Inverse Obstacle Scattering: Regularization. Theory of Linear and Nonlinear Exponentially Ill-Posed Problems
  1996-1999		PhD studies, Johannes-Kepler University Linz, Austria
  1996		diploma in mathematics, advisor: Rainer Kreß
  1993-1996		studies of mathematics and physics at Georg-August University Göttingen, Germany
  1993		pre-diploma in mathematics and physics
  1991-1993		studies of physics and mathematics at Philipps University Marburg, Germany
  1991		Abitur

• professional experience
  

  since 2009		full (W3) professor at Georg-August Universität Göttingen
  2007--2009		associate (W2) professor at Georg-August Univerität Göttingen
  2002--2007		junior professor at Institute of Numerical and Applied Mathematics, Georg-August Universität Göttingen
  1998--2000		research assistant at CRC F013 Numerical and Symbolic Scientific Computing, Linz, Austria
  2000--2002		posdoc at Zuse Institute Berlin with Peter Deuflhard
  1996--1998		research assistent at Institute of Industrial Mathematics, Johannes-Kepler University Linz, Austria

• other activities and honors
  
  
  • Spokesperson of the Collaborative Research Center (CRC) 1456 Mathematics of Experiment: The challenge of indirect measurements in the natural sciences (since 2021)
  • First Chairman of Gesellschaft für Inverse Problems e.V. (Society of Inverse Problems in German Speaking Countries) (since 2019)
  • Founding president of Inverse Problems International Association (IPIA) (05/2022 - 01/2023)
  • Max Planck fellow at MPI for Solar Systems Research (since 2017)
  • Member of the editorial boards of Inverse Problems , Journal of Inverse and Ill-Posed Problems , and International Journal on Geomathematics
  • Spokesperson of the Research Training Group (RTG) 1023 Identification in mathematical Models: Synergy of stochastic and numerical methods" (2009-2014)

Publications

google scholar profile
Orcid ID: 0000-0002-5408-2780

Refereed journal papers


The linked pdf-files do not necessarily coincide with the article's published version!



• John H. Gaida, Hugo Lourenco-Martins, Sergey V. Yalunin, Armin Feist, Murat Sivis, Thorsten Hohage, F. Javier Garcia de Abajo, Claus Ropers. 2023. Lorentz microscopy of optical fields. Nature Comm. 14: 5863.
  doi:10.1038/s41467-023-42054-3      
• Björn Müller, Thorsten Hohage, Damien Fournier, Laurent Gizon. 2023. Quantitative passive imaging by iterative holography: The example of helioseismic holography.
     
• Thorsten Hohage, Pierre Maréchal, Léopold Simar, Anne Vanhems. 2022. A mollifier approach to the deconvolution of probability densities. Econometric Theory. 40pp.
  doi:10.1017/S0266466622000457      
• Thorsten Hohage, Frank Werner. 2022. Error estimates for variational regularization of inverse problems with general noise models for data and operator. ETNA 57: 127-152.
  doi:10.1553/etna_vol57s127      
• Philip Miller, Thorsten Hohage. 2022. Convergence rates for oversmoothing Banach space regularization. ETNA 57: 101 - 126.
  doi:10.1553/etna_vol57s101      
• Thorsten Hohage, Christoph Lehrenfeld, Janosch Preuß. 2021. Learned Infinite Elements. SIAM J. Scientific Computing 43(5): A3552-A3579.
  doi:https://doi.org/10.1137/20M1381757      
• Philip Miller, Thorsten Hohage. 2021. Maximal Spaces for Approximation Rates in \ell^1-regularization. Numerische Mathematik 149(2): 341-374.
  doi:10.1007/s00211-021-01225-4      
• Martin Halla, Thorsten Hohage. 2021. On the well-posedness of the damped time-harmonic Galbrun equation and the equations of stellar oscillations. SIAM J. Math. Anal. 53(4): 4068-4095.
  doi:10.1137/20M1348558      
• Thorsten Hohage, Hans-Georg Raumer, Carsten Spehr. 2020. Uniqueness of an inverse source problem in experimental aeroacoustics. Inverse Problems 36: 075012 (18pp).
  doi:10.1088/1361-6420/ab8484      
• Thorsten Hohage, Benjamin Sprung, Frederic Weidling. 2020. Inverse Problems. In Nanoscale Photonic Imaging. 134: Springer. 145-164.
  doi:https://doi.org/10.1007/978-3-030-34413-9_5      
• Simon Maretzke, Thorsten Hohage. 2020. Constrained Reconstructions in X-ray Phase Contrast Imaging: Uniqueness, Stability and Algorithms. In Nanoscale Photonic Imaging. 134: Springer. 377-403.
  doi:https://doi.org/10.1007/978-3-030-34413-9_14      
• Janosch Preuß, Thorsten Hohage, Christoph Lehrenfeld. 2020. Sweeping preconditioners for stratified media in the presence of reflections. Springer Nature Partial Differential Equations and Applications 1: 17.
  doi:10.1007/s42985-020-00019-x      
• Hans-Georg Raumer, Carsten Spehr, Thorsten Hohage, Daniel Ernst. 2020. Weighted Data Spaces for Correlation Based Array Imaging in Experimental Aeroacoustics. Journal of Sound and Vibration.
  doi:10.1016/j.jsv.2020.115878      
• Frederic Weidling, Benjamin Sprung, Thorsten Hohage. 2020. Optimal convergence rates for Tikhonov regularization in Besov spaces. SIAM J. Numer. Anal. 58: 21-47.
  doi:10.1137/18M1178098      
• Cong Shi, Claus Ropers, Thorsten Hohage. 2020. Density Matrix Reconstructions in Ultrafast Transmission Electron Microscopy: Uniqueness, Stability, and Convergence Rates. Inverse Problems 36: 025005.
  doi:10.1088/1361-6420/ab539a      
• Alexey Agaltsov, Thorsten Hohage, Roman Novikov. 2020. Global uniqueness in a passive inverse problem of helioseismology. Inverse Problems 36: 055004 (21pp).
  doi:10.1088/1361-6420/ab77d9      
• Thorsten Hohage, Roman G Novikov. 2019. Inverse wave propagation problems without phase information. Inverse Problems 35(7): 070301.
  doi:10.1088/1361-6420/ab1aaf      
• Thorsten Hohage, Philip Miller. 2019. Optimal convergence rates for sparsity promoting wavelet-regularization in Besov spaces. Inverse Problems 35: 65005 (27pp).
  doi:10.1088/1361-6420/ab0b15      
• Julian Eckhardt, Ralf Hiptmair, Thorsten Hohage, Henrik Schumacher, Max Wardetzky. 2019. Elastic energy regularization for inverse obstacle scattering problems. Inverse Problems 35: 104009 (20pp).
  doi:10.1088/1361-6420/ab3034      
• Helen Schomburg, Thorsten Hohage. 2019. Formulation and Efficient Computation of l1- and Smoothness Penalized Estimates for Microstructure-Informed Tractography. IEEE Trans. Med. Imag. 38: 1899-1909.
  doi:10.1109/TMI.2019.2902787      
• Benjamin Sprung, Thorsten Hohage. 2019. Higher order convergence rates for Bregman iterated variational regularization of inverse problems. Numer. Math. 141: 215-252.
  doi:10.1007/s00211-018-0987-x      
• Alexey Agaltsov, Thorsten Hohage, Roman Novikov. 2018. Monochromatic identities for the Green function and uniqueness results for passive imaging. SIAM J. Appl. Math. 78(5): 2865-2890.
  doi:10.1137/18M1182218      
• Alexey Agaltsov, Thorsten Hohage, Roman Novikov. 2018. An iterative approach to monochromatic phaseless inverse scattering. Inverse Problems 35(2): 024001.
  doi:10.1088/1361-6420/aaf097      
• Zhengguo Tan, Thorsten Hohage, Oleksandr Kalentev , Xiaoqing Wang, Dirk Voit, Klaus-Dietmar Merboldt, Jens Frahm. 2017. An eigenvalue approach for the automatic scaling of unknowns in model-based reconstructions: application to real-time phase-contrast flow MRI. NMR in Biomedicine. e3835-n/a.
  doi:10.1002/nbm.3835      
• Thorsten Hohage, Frederic Weidling. 2017. Characterizations of variational source conditions, converse results, and maxisets of spectral regularization methods. SIAM J. Numer. Anal. 55(2): 598-620.
  doi:10.3934/ipi.2017010      
• Simon Maretzke, Thorsten Hohage. 2017. Stability estimates for linearized near-field phase retrieval in X-ray phase contrast imaging. SIAM J. Appl. Math. 77(2): 384-408.
  doi:10.1137/16M1086170      
• Laurent Gizon, Hélène Barucq, Marc Duruflé, Chris Hanson, Michael Leguèbe, Aaron Birch, Juliette Chabassier, Damien Fournier, Thorsten Hohage, Emanuele Papini. 2017. Computational helioseismology in the frequency domain: acoustic waves in axisymmetric solar models with flows. Astronomy & Astrophysics 600: A35.
  doi:10.1051/0004-6361/201629470      
• Katharina E. Priebe, Christopher Rathje, Sergey V. Yalunin, Thorsten Hohage, Armin Feist, Sascha Schäfer, Claus Ropers. 2017. Attosecond Electron Pulse Trains and Quantum State Reconstruction in Ultrafast Transmission Electron Microscopy. Nature Photonics 11: 793-797.
  doi:10.1038/s41566-017-0045-8      
• Helen Schomburg, Thorsten Hohage. 2017. Semi-Local Tractography Strategies Using Neighborhood Information. Medical Image Analysis 38: 165-183.
  doi:10.1016/j.media.2017.03.003      
• Frederic Weidling, Thorsten Hohage. 2017. Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems. Inverse Problems and Imaging 11(1): 203-220.
  doi:10.3934/ipi.2017010      
• Thorsten Hohage, Frank Werner. 2016. Inverse Problems with Poisson Data: statistical regularization theory, applications and algorithms. Inverse Problems 32: 093001:56pp.
  doi:10.1088/0266-5611/32/9/093001      
• Simon Maretzke, Matthias Bartels, Martin Krenkel, Tim Salditt, Thorsten Hohage. 2016. Regularized Newton methods for X-ray phase contrast and general imaging problems. Optics Express 24(6): 6490-6506.
  doi:10.1364/OE.24.006490      
• Martin Halla, Thorsten Hohage, Lothar Nannen, Joachim Schöberl. 2016. Hardy space infinite elements for time harmonic wave equations with phase and group velocities of different signs. Numer. Math. 133: Springer Berlin Heidelberg. 103-139.
  doi:10.1007/s00211-015-0739-0      
• Damien Fournier, Laurent Gizon, Martin Holzke, Thorsten Hohage. 2016. Pinsker estimators for local helioseismology: inversion of travel times for mass-conserving flows. Inverse Problems 32(10): 105002:27pp.
  doi:10.1088/0266-5611/32/10/105002      
• Claudia König, Frank Werner, Thorsten Hohage. 2016. Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise. SIAM J. Numer. Anal. 54(1): 341-360.
  doi:10.1137/15M1022252      
• Thorsten Hohage, Lothar Nannen. 2015. Convergence of infinite element methods for scalar waveguide problems. BIT Numer. Math. 55(1): 215-254.
  doi:0.1007/s10543-014-0525-x      
• Thorsten Hohage, Frederic Weidling. 2015. Verification of a variational source condition for acoustic inverse medium scattering problems. Inverse Problems 31(7): 075006:14pp.
  doi:10.1088/0266-5611/31/7/075006      
• Thorsten Hohage, Christoph Rügge. 2015. A coherence enhancing penalty for diffusion MRI: Regularizing property and discrete approximation. SIAM J. Imaging Sci. 8(3): 1874-1893.
  doi:10.1137/140998767      
• Carolin Homann, Thorsten Hohage, Johannes Hagemann, Anna-Lena Robisch, Tim Salditt. 2015. Validity of the empty-beam correction in near-field imaging. Physical Review A 91: 013821.
  doi:10.1103/PhysRevA.91.013821      
• Thorsten Hohage, Frank Werner. 2014. Convergence Rates for Inverse Problems with Impulsive Noise. SIAM J. Numer. Anal. 52(3): 1203-1221.
  doi:10.1137/130932661      
• Sophie Frick, Thorsten Hohage, Axel Munk. 2014. Asymptotic laws for change point estimation in inverse regression. Statistica Sinica 24(2): 555-575.
  doi:10.5705/ss.2012.007      
• J. Hagemann, A. L. Robisch, D. R. Luke, C. Homann, T. Hohage, P. Cloetens, H. Suhonen, T. Salditt. 2014. Wave Front Reconstruction for Extended hard X-ray Beams from a set of Detection Planes. Optics Express 22: 11552-11569.
  doi:10.1364/OE.22.011552      
• Fabian Dunker, Thorsten Hohage. 2014. On parameter identification in stochastic differential equations by penalized maximum likelihood. Inverse Problems 30: 095001:20pp.
  doi:10.1088/0266-5611/30/9/095001      
• Fabian Dunker, Jean-Pierre Florens, Thorsten Hohage, Jan Johannes, Enno Mammen. 2014. Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression. Journal of Econometrics 178: 444-455.
  doi:10.1016/j.jeconom.2013.06.001      
• Damien Fournier, Laurent Gizon, Thorsten Hohage, Aaron Birch. 2014. Generalization of the noise model for time-distance helioseismology. Astronomy & Astrophysics 567: A317:20pp.
  doi:10.1051/0004-6361/201423580      
• Thorsten Hohage, Sofiane Soussi. 2013. Riesz bases and Jordan form of the translation operator in semi-infinite periodic waveguides. J. Math. Pures Appl. (9) 100(1): 113-135.
  doi:10.1016/j.matpur.2012.10.013      
• Thorsten Hohage, Frank Werner. 2013. Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data. Numer. Math. 123: 745-779.
  doi:10.1007/s00211-012-0499-z      
• Lothar Nannen, Thorsten Hohage, Achim Schädle, Joachim Schöberl. 2013. Exact sequences of high order Hardy space inifinite elements for exterior Maxwell problems. SIAM J. Sci. Comput. 35(2): A1024-A1048.
  doi:10.1137/110860148      
• Robert Stück, Martin Burger, Thorsten Hohage. 2012. The iteratively regularized Gauß-Newton method with convex constraints and applications in 4Pi microscopy. Inverse Problems 28: 015012:16pp.
  doi:10.1088/0266-5611/28/1/015012      
• Jason Jackiewicz, Aaron C Birch, Laurent Gizon, Shravan Hanasoge, Thorsten Hohage, Jean-B. Ruffio, Michal Svanda. 2012. Multichannel Three-dimensional OLA Inversion for Local Helioseismology Solar Physics. Solar Phys 276: 19-33.
  doi:10.1007/s11207-011-9873-8      
• Frank Werner, Thorsten Hohage. 2012. Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data. Inverse Problems 28(10): 104004:15pp.
  doi:10.1088/0266-5611/28/10/104004      
• A. Paarmann, M. Gulde, M. Müller, S. Schäfer, S. Schweda, M. Maiti, C. Xu, T. Hohage, F. Schenk, C. Ropers, R. Ernstorfer. 2012. Coherent femtosecond low-energy single-electron pulses for time-resolved diffraction and imaging: A numerical study. Journal of Applied Physics 112: 113109.
  doi:10.1063/1.4768204      
• Thorsten Hohage, Stefan Langer. 2010. Acceleration techniques for regularized Newton methods applied to electromagnetic inverse medium scattering problems. Inverse Problems 26: 074011:15pp.
  doi:10.1088/0266-5611/26/7/074011      
• Thorsten Hohage, Lothar Nannen. 2009. Hardy space infinite elements for scattering and resonance problems. SIAM J. Numer. Anal. 47: 972-996.
  doi:10.1137/070708044      
• Helmut Harbrecht, Thorsten Hohage. 2009. A Newton method for reconstructing non star-shaped domains in electrical impedance tomography. Inverse Probl. Imaging 3(2): 353-371.
  doi:10.3934/ipi.2009.3.353      
• Frank Bauer, Thorsten Hohage, Axel Munk. 2009. Iteratively regularized Gauss-Newton method for nonlinear inverse problems with random noise. SIAM J. Numer. Anal. 47(3): 1827-1846.
  doi:10.1137/080721789      
• Thorsten Hohage, Mihaela Pricop. 2008. Nonlinear Tikhonov regularization in Hilbert scales for inverse boundary value problems with random noise. Inverse Probl. Imaging 2(2): 271-290.
  doi:10.3934/ipi.2008.2.271      
• Thorsten Hohage, Klaus Giewekemeyer, Tim Salditt. 2008. Iterative reconstruction of a refractive index from x-ray or neutron reflectivity measurements. Physical Review E. 77: 051604.
  doi:10.1103/PhysRevE.77.051604      
• Martin Uecker, Thorsten Hohage, Kai T. Block, Jens Frahm. 2008. Image Reconstruction by Regularized Nonlinear Inversion - Joint Estimation of Coil Sensitivities and Image Content. Magnetic Resonance in Medicine 60: 674-682.
  doi:10.1002/mrm.21691      
• Frank Schmidt, Thorsten Hohage, Roland Klose, Achim Schädle, Lin Zschiedrich. 2008. Pole condition: A numerical method for Helmholtz-type scattering problems with inhomogeneous exterior domain. J. Comput. Appl. Math. 218(1): 61-69.
  doi:10.1016/j.cam.2007.04.046      
• Thorsten Hohage, Marie-Luisa Rapun, Francisco-Javier Sayas. 2007. Detecting corrosion using thermal measurements. Inverse Problems 23(1): 53-72.
  doi:10.1088/0266-5611/23/1/003      
• Stefan Langer, Thorsten Hohage. 2007. Convergence analysis of an inexact iteratively regularized Gauss-Newton method under general source conditions. J. Inverse Ill-Posed Probl. 15(3): 311-327.
  doi:10.1515/jiip.2007.017      
• Stefan Hein, Thorsten Hohage, Werner Koch, Joachim Schöberl. 2007. Acoustic resonances in a high-lift configuration. J. Fluid Mech. 582: 179-202.
  doi:10.1017/S0022112007005770      
• Nicolai Bissantz, Thorsten Hohage, Axel Munk, Fritz Ruymgaart. 2007. Convergence rates of general regularization methods for statistical inverse problems and applications. SIAM J. Numer. Anal. 45(6): 2610-2636.
  doi:10.1137/060651884      
• Helmut Harbrecht, Thorsten Hohage. 2007. Fast methods for three-dimensional inverse obstacle scattering problems. J. Integral Equations Appl. 19(3): 237-260.
  doi:10.1216/jiea/1190905486      
• Thorsten Hohage. 2006. Fast numerical solution of the electromagnetic medium scattering problem and applications to the inverse problem. J. Comput. Phys. 214(1): 224-238.
  doi:10.1016/j.jcp.2005.09.025      
• Tilo Arens, Thorsten Hohage. 2005. On radiation conditions for rough surface scattering problems. IMA J. Appl. Math. 70(6): 839-847.
  doi:10.1093/imamat/hxh065      
• Thorsten Hohage, Francisco-Javier Sayas. 2005. Numerical solution of a heat diffusion problem by boundary element methods using the Laplace transform. Numerische Mathematik 102(1): 67-92.
  doi:10.1007/s00211-005-0645-y      
• Frank Bauer, Thorsten Hohage. 2005. A Lepskij`s stopping rule for Newton-type methods with random noise. PAMM 5: 15-18.
  doi:10.1002/pamm.200510005      
• Frank Bauer, Thorsten Hohage. 2005. A Lepskij-type stopping rule for regularized Newton methods. Inverse Problems 21(6): 1975-1991.
  doi:10.1088/0266-5611/21/6/011      
• Stefan Hein, Thorsten Hohage, Werner Koch. 2004. On resonances in open systems. J. Fluid Mech. 506: 255-284.
  doi:10.1017/S0022112004008584      
• Nicolai Bissantz, Thorsten Hohage, Axel Munk. 2004. Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise. Inverse Problems 20(6): 1773-1789.
  doi:10.1088/0266-5611/20/6/005      
• Thorsten Hohage, Frank Schmidt, Lin Zschiedrich. 2003. Solving time-harmonic scattering problems based on the pole condition. II. Convergence of the PML method. SIAM J. Math. Anal. 35(3): 547-560.
  doi:10.1137/S0036141002406485      
• Thorsten Hohage, Frank Schmidt, Lin Zschiedrich. 2003. Solving time-harmonic scattering problems based on the pole condition. I. Theory. SIAM J. Math. Anal. 35(1): 183-210.
  doi:10.1137/S0036141002406473      
• Thorsten Hohage. 2001. On the numerical solution of a three-dimensional inverse medium scattering problem. Inverse Problems 17: 1743-1763.
     
• Peter Hähner, Thorsten Hohage. 2001. New Stability estimates for the inverse acoustic inhomogeneous medium problem and applications. SIAM J. Math. Anal. 62: 670-685.
  doi:10.1137/S0036141001383564      
• Thorsten Hohage. 2000. Regularization of Exponentially ill-posed Problems. Numer. Funct. Anal. Optim. 21: 439-464.
  doi:10.1080/01630560008816965      
• Thorsten Hohage. 1998. Convergence Rates of a Regularized Newton Method in Sound-Hard Inverse Scattering. SIAM J. Numer. Anal. 36: 125-142.
  doi:10.1137/S0036142997327750      
• Thorsten Hohage, Christoph Schormann. 1998. A Newton-type method for a transmission problem in inverse scattering. Inverse Problems 14: 1207-1227.
     
• Thorsten Hohage. 1997. Logarithmic Convergence Rates of the iteratively regularized Gauss-Newton method for an inverse potential and an inverse scattering problem. Inverse Problems 13: 1279-1299.
     



Theses



• Thorsten Hohage. 1999. Iterative Methods in Inverse Obstacle Scattering: Regularization Theory of Linear and Nonlinear Exponentially ill-posed Problems. University of Linz.
• Thorsten Hohage. 1996. Newton-Verfahren beim inversen Neumann-Problem zur Helmholtz-Gleichung. University of Göttingen. Diplomarbeit.



Selected conference proceedings papers



• Thorsten Hohage. 2005. An iterative method for inverse medium scattering problems based on factorization of the far field operator. In The 2nd International Converence on Inverse Problems: Recent Theoretical Development and Numerical Approaches. Fudan University, Shanghai. 12: IOP. 33-45.
• Thorsten Hohage, Frank Schmidt, Lin Zschiedrich. 2002. A new method for the solution of scattering problems. In Proceedings of the European Symposium on Numerical Methods in Electromagnetics: JEE 02. 251-256. ONERA, Toulouse.



Submitted papers






BibTeX-file of publications by T. Hohage
Link to all publications of the Research Group Inverse Problems