Institute for Numerical and Applied Mathematics - Research Group Inverse Problems
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

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


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!

    • Björn Müller, Thorsten Hohage, Damien Fournier, Laurent Gizon. 2024. Quantitative passive imaging by iterative holography: The example of helioseismic holography. Inverse Problems 40(4): 045016 (32pp).
      doi:10.1088/1361-6420/ad2b9a   download   
    • 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   download   
    • Thorsten Hohage, Pierre Maréchal, Léopold Simar, Anne Vanhems. 2022. A mollifier approach to the deconvolution of probability densities. Econometric Theory. 40pp.
    • 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.
    • Philip Miller, Thorsten Hohage. 2022. Convergence rates for oversmoothing Banach space regularization. ETNA 57: 101 - 126.
      doi:10.1553/etna_vol57s101   download   
    • Thorsten Hohage, Christoph Lehrenfeld, Janosch Preuß. 2021. Learned Infinite Elements. SIAM J. Scientific Computing 43(5): A3552-A3579.
      doi:   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • Thorsten Hohage, Benjamin Sprung, Frederic Weidling. 2020. Inverse Problems. In Nanoscale Photonic Imaging134: Springer. 145-164.
    • Simon Maretzke, Thorsten Hohage. 2020. Constrained Reconstructions in X-ray Phase Contrast Imaging: Uniqueness, Stability and Algorithms. In Nanoscale Photonic Imaging134: Springer. 377-403.
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • Thorsten Hohage, Roman G Novikov. 2019. Inverse wave propagation problems without phase information. Inverse Problems 35(7): 070301.
      doi:10.1088/1361-6420/ab1aaf   download   
    • 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   download   
    • 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   download   
    • 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.
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • Helen Schomburg, Thorsten Hohage. 2017. Semi-Local Tractography Strategies Using Neighborhood Information. Medical Image Analysis 38: 165-183.
      doi:10.1016/   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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.
    • 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   download   
    • 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.
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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   download   
    • 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/   download   
    • Tilo Arens, Thorsten Hohage. 2005. On radiation conditions for rough surface scattering problems. IMA J. Appl. Math. 70(6): 839-847.
    • 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   download   
    • 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   download   
    • 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   download   
    • Stefan Hein, Thorsten Hohage, Werner Koch. 2004. On resonances in open systems. J. Fluid Mech. 506: 255-284.
    • 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.
    • 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   download   
    • 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   download   
    • 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   download   
    • Thorsten Hohage. 2000. Regularization of Exponentially ill-posed Problems. Numer. Funct. Anal. Optim. 21: 439-464.
      doi:10.1080/01630560008816965   download   
    • Thorsten Hohage. 1998. Convergence Rates of a Regularized Newton Method in Sound-Hard Inverse Scattering. SIAM J. Numer. Anal. 36: 125-142.
    • 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.


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

    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, Shanghai12: IOP.
    • 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,

    Submitted papers

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