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 4509
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, Magnetic Resonance Imaging (MRI)
  • transparent boundary condition, resonances
    • spectrally convergent methods, in particular Hardy space infinite elements
    • numerical computation of resonances
    • Helmholtz, Maxwell, and elasticity equations
    • back-propagating modes


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, Jakob-Grimm Schule, Rotenburg/Fulda, Germany
    1988-1989    exchange student at Liberty High School in Renton, WA, USA
  • professional experience
    since 2009    full (W3) professor at Georg-August Universität Göttingen
    2007--2009    associate (W2) professor at Georg-August Univerität Göttingen
    1996--1998   research assistent at Institute of Industrial Mathematics, Johannes-Kepler University Linz, Austria
    2000--2002    posdoc at Zuse Institute Berlin with Peter Deuflhard
    2002--2007    junior professor at Institute of Numerical and Applied Mathematics, Georg-August Universität Göttingen
    1998--2000    research assistent at CRC F013 Numerical and Symbolic Scientific Computing, Linz, Austria
  • other activities and honors

    • 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



Publications

google scholar profile



    Refereed journal papers


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


    • 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   
    • Tan, Zhengguo, Hohage, Thorsten, Kalentev, Oleksandr , Wang, Xiaoqing, Voit, Dirk, Merboldt, Klaus-Dietmar, Frahm, Jens. 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   
    • 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. to appear.
      download   
    • 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   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   
    • J Jackiewicz, A C Birch, L Gizon, S Hanasoge, T Hohage, J B Ruffio, M 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   
    • F. Werner, T. 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   
    • H. Harbrecht, T. 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   
    • F. Bauer, T. Hohage, A. 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   
    • T. Hohage, M. 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   
    • T. Hohage, K. Giewekemeyer, T. 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      
    • M. Uecker, T. Hohage, K. T. Block, J. 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.
      doi:10.1016/j.cam.2007.04.046      
    • T. Hohage, M.-L. Rapun, F.-J. Sayas. 2007. Detecting corrosion using thermal measurements. Inverse Problems 23(1): 53-72.
      doi:10.1088/0266-5611/23/1/003   download   
    • S. Langer, T. 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   
    • S. Hein, T. Hohage, W. Koch, J. Schöberl. 2007. Acoustic resonances in a high-lift configuration. J. Fluid Mech. 582: 179-202.
      doi:10.1017/S0022112007005770   download   
    • N. Bissantz, T. Hohage, A. Munk, F. 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   
    • H. Harbrecht, T. 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   
    • T. 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   download   
    • T. Hohage, F.-J. 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   
    • T. Arens, T. Hohage. 2005. On radiation conditions for rough surface scattering problems. IMA J. Appl. Math. 70(6): 839-847.
      doi:10.1093/imamat/hxh065      
    • 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   
    • F. Bauer, T. 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   
    • S. Hein, T. Hohage, W. Koch. 2004. On resonances in open systems. J. Fluid Mech. 506: 255-284.
      doi:10.1017/S0022112004008584      
    • N. Bissantz, T. Hohage, A. 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      
    • T. Hohage, F. Schmidt, L. 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   
    • T. Hohage, F. Schmidt, L. 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.
      download   
    • 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.
      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.
      download   
    • 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.
      download   



    Theses


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



    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. 33-45.download
    • 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.download



    Submitted papers





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