Books

• A Taste of Inverse Problems. Basic Theory and Examples.
  SIAM, Philadelphia, 2017.
  ISBN 978 1 611974 93 5.
• Grundlagen der Numerischen Mathematik und des Wissenschaftlichen Rechnens
  Teubner Verlag, Wiesbaden, 2. Auflage, 2006,
  ISBN: 3 8351 0090 9.
• (with H.W. Engl and A. Neubauer)
  Regularization of Inverse Problems
  Kluwer Academic Publishers, Dordrecht, 1996,
  ISBN 0 7923 4157 4.
• Conjugate Gradient Type Methods for Ill-Posed Problems
  Pitman Research Notes in Mathematics,
  Longman House, Harlow, Essex, 1995,
  ISBN 0 582 27370 6.

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Selected Publications

• Lipschitz stability of a nonlinear inverse conductivity problem with two Cauchy data pairs, submitted.
• On the shape derivative of polygonal inclusions in the conductivity problem, submitted.
• Stochastic modeling of stationary scalar Gaussian processes in continuous time from autocorrelation data, submitted.
  Code and data for this paper are available here.
• (with M.P. Bernhardt and N.F.A. van der Vegt) Stability, speed, and constraints for structural coarse-graining in VOTCA, J. Chem. Theor. Comput. (2023)
• (with F. Frommer) A variational framework for the inverse Henderson problem of statistical mechanics. Lett. Math. Phys. 112, Article number: 71 (2022).
• Mathematical analysis of some iterative methods for the reconstruction of memory kernels. ETNA 54, 483-498 (2021).
• (with N. Bockius, J. Shea, G. Jung, and F. Schmid) Model reduction techniques for the computation of extended Markov parameterizations for generalized Langevin equations. J. Phys.: Condens. Matter 33, 214003 (2021).
• (with M.P. Bernhardt and N.F.A. van der Vegt)  Iterative integral equation methods for structural coarse-graining. J. Chem. Phys. 154, 0184118 (2021). (pdf)
• (with G.S. Reuber, L. Holbach, A.A. Popov, and B.J.P. Kaus) Inferring rheology and geometry of subsurface structures by adjoint-based inversion of principal stress directions. Geophys. J. Int. 223 (2020), 851–861. (pdf)
• (with N. Porz) Unique solvability of a system of ordinary differential equations modeling a warm cloud parcel. SIAM J. Appl. Math. 80 (2020), 706–724. (pdf)
• (with F. Delbary and D. Ivanizki) A generalized Newton iteration for computing the solution of the inverse Henderson problem. Inverse Probl. Sci. Eng. 28 (2020), 1166-1190. (pdf)
  
• (with F. Frommer and S. Jansen) A note on the uniqueness result for the inverse Henderson problem. J. Math. Phys. 60, 093303 (2019). (pdf)
• (with N. Porz, M. Baumgartner, and P. Spichtinger)  A model for warm clouds with implicit droplet activation, avoiding saturation adjustment. Math. Clim. Weather Forecast. 4 (2018), 50-78.
• (with G. Jung and F. Schmid) Generalized Langevin dynamics: construction and numerical integration of non-Markovian particle-based models. Soft matter 14 (2018), 9368-9382. (pdf)
• Well-posedness of the Iterative Boltzmann Inversion. J. Stat. Phys. 170 (2018), 536-553. (pdf)
• Fréchet differentiability of molecular distribution functions II. The Ursell function. Lett. Math. Phys. 108 (2018), 307-329. (pdf)
  
• Fréchet differentiability of molecular distribution functions I. L^\infty analysis. Lett. Math. Phys. 108 (2018), 285-306. (pdf)
• A note on the MUSIC algorithm for impedance tomography, Inverse Problems 33 (2017), 025001. (pdf)
• (with D. Rosenberger and N.F.A. van der Vegt) Comparison of iterative inverse coarse-graining methods. Eur. Phys. J. Special Topics 225 (2016), 1323-1345. (pdf)
• (with R. Griesmaier) Polarization tensors of planar domains as functions of the admittivity contrast. Appl. Anal. 96 (2016), 970-987. (pdf)
• (with R. Griesmaier) Multifrequency impedance imaging with multiple signal classification.
  SIAM J. Imaging Sci. 8 (2015), 939-967. (pdf)
• A note on the nonlinear Landweber iteration.
  Numer. Funct. Anal. Optim. 35 (2014), 1500-1510. (pdf)
• (with R. Griesmaier and J. Sylvester) Far field splitting for the Helmholtz equation.
  SIAM J. Numer. Anal. 52 (2014), 343-362.
• (with R. Griesmaier and T. Raasch) Inverse source problems for the Helmholtz equation and the windowed Fourier transform II.
  SIAM J. Sci. Comput. 35 (2013), A2188-A2206.
• (with M. Donatelli) Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring.
  Inverse Problems 29 (2013) 095008. (pdf)
• (with R. Griesmaier and T. Raasch) Inverse source problems for the Helmholtz equation and the windowed Fourier transform.
  SIAM J. Sci. Comput. 34 (2012), A1544-A1562. (pdf)
• One shot inverse scattering via rational approximation.
  SIAM J. Imaging Sci. 5 (2012), 465-482. (pdf)
• (with L. Warth) Electrostatic backscattering by insulating obstacles.
   J. Comp. Appl. Math. 236 (2012), 2158-2166. (pdf)
• Locating several small inclusions in impedance tomography from backscatter data.
  SIAM J. Numer. Anal. 49 (2011), 1991-2016. (pdf)
• (with B. von Harrach and N. Hyvönen) Justification of point electrode models in electrical impedance tomography.
  Math. Models Methods Appl. Sci. 21 (2011), 1395-1413. (pdf)
  
• (with N. Hyvönen and S. Reusswig) Erratum: An Inverse Backscatter Problem for Electric Impedance Tomography.
  SIAM J. Math. Anal. 43 (2011), 1495-1497. (pdf)
• (with L. Harhanen, N. Hyvönen, E. Schweickert) Convex source support in three dimensions.
  BIT 52 (2012), 45-63. (pdf)
• (with W. Rundell) On rational approximation methods for inverse source problems.
  Inverse Probl. Imaging 5 (2011), 185-202. (pdf)
• (with A. Kirsch) Sampling Methods, in Handbook of Mathematical Methods in Imaging, O. Scherzer, ed., Springer, New York, 2011, S. 501-550.
• (with N. Hyvönen and S. Reusswig) Convex backscattering support in electric impedance tomography.
  Numer. Math. 117 (2011), 373-396.
  
• The regularizing Levenberg-Marquardt scheme is of optimal order.
  J. Integral Equations Appl. 22 (2010), 259-283.
• (with H. Egger, C. Schneider, J. Schöberl,  S. Zaglmayr) Adjoint based sampling methods for electromagnetic scattering.
  Inverse Problems 26 (2010) 074006. (pdf)
• (with M. Donatelli) On the condition number of the antireflective transform.
  Linear Algebra Appl. 432 (2010), 1772-1784. (pdf)
  
• (with N. Hyvönen and S. Reusswig) An inverse backscatter problem for electric impedance tomography.
  SIAM J. Math. Anal. 41 (2009), 1948-1966. (pdf)
  Erratum (appeared in Vol. 43 (2011), 1495-1497). (pdf)
• (with R. Griesmaier) An asymptotic factorization method for inverse electromagnetic scattering in layered media II: A numerical study.
  In: "Imaging Microstructures: Mathematical and Computational Challenges", H. Ammari and H. Kang (Eds.),
  Contemporary Mathematics, Vol. 494, AMS, Providence, 2009
• (with R. Griesmaier) MUSIC-characterization of small scatterers for normal measurement data.
  Inverse Problems 25 (2009) 075012. (pdf)
• (with N. Hyvönen and S. Reusswig) Convex source support and its application to electric impedance tomography.
  SIAM J. Imaging Sci. 1 (2008), 364-378. (pdf)
• Why linear sampling really seems to work.
  Inverse Probl. Imaging 2 (2008), 373-395. (pdf)
• (with N. Hyvönen, M. Lehn and S. Reusswig) Source supports in electrostatics.
  BIT 48 (2008), 245-264. (pdf)
• Mathematik contra Landminen.
  Forschungsmagazin der Johannes Gutenberg-Universität Mainz, 24 (2008), 15-17 (in German).
• On real-time algorithms for the location search of discontinuous conductivities with one measurement.
  Inverse Problems 24 (2008) 045005.
• (with M. Christiansen) Deblurring methods using antireflective boundary conditions.
  SIAM J. Sci. Comput. 30 (2008), 855-872.
  
• (with B. Schappel) The factorization method for electrical impedance tomography in the half space.
  SIAM J. Appl. Math. 68 (2008), 907-924.
  
• (with B. Gebauer and C. Schneider) Sampling methods for low-frequency electromagnetic imaging.
  Inverse Problems 24 (2008) 015007.
• (with M. Azzouz, C. Oesterlein and K. Schilcher) The factorization method for electrical impedance tomography data from a new planar device
  International J. Biomedical Imaging 2007 (2007), Article ID 83016, 7 pages, doi:10.1155/2007/83016.
• (with H. Ammari and R. Griesmaier) Identification of small inhomogeneities: Asymptotic factorization
  Math. Comp. 76 (2007), 1425-1448. (pdf)
• (with B. Gebauer, A. Kirsch, W. Muniz, and C. Schneider) A sampling method for detecting buried objects using electromagnetic scattering
  Inverse Problems 21 (2005), 2035-2050.
• (with E. Rösler) Computation of local volatilities from regularized Dupire equations
  Int. J. Theor. Appl. Finance 8 (2005), 207-221. (pdf)
• (with M. Brühl) Recent progress in electrical impedance tomography
  Inverse Problems 19 (2003), S65-S90. (pdf)
• A note on Tikhonov regularization of large linear problems
  BIT 43 (2003), 449-451. (pdf)
• (with M. Brühl and M. S. Vogelius) A direct impedance tomography algorithm for locating small inhomogeneities,
  Numer. Math. 93 (2003), 635-654.
• On Lanczos based methods for the regularization of discrete ill-posed problems,
  BIT 41 (2001), 1008-1018. (pdf)
• (with O. Scherzer) Inverse problems light: Numerical differentiation,
  Amer. Math. Monthly 108 (2001), 512-521. (pdf)
• (with M. Brühl and M. Pidcock) Crack detection using electrostatic measurements,
  M2AN Math. Model. Numer. Anal. 35 (2001), 595-605. (pdf)
• Iterative regularization techniques in image restoration,
  in Surveys on Solution Methods for Inverse Problems, D. Colton et al, eds., pp. 35-52, Springer-Verlag, Wien, 2000.
• (with H. Frankenberger) Kernel polynomials for the solution of indefinite and ill-posed problems,
  Numerical Algorithms 25 (2000), 197-212. (pdf)
• (with M. Brühl) Kann Mathematik der elektrischen Impedanztomographie zum Durchbruch verhelfen?
  Forschungsmagazin der Johannes Gutenberg-Universität Mainz, 16 (2000), 32-40 (in German).
• (with M. Brühl) Numerical implementation of two noniterative methods for locating inclusions by impedance tomography
  Inverse Problems 16 (2000), 1029-1042. (pdf)
• (with C.W. Groetsch) Nonstationary iterated Tikhonov regularization,
  J. Optim. Th. Appl. 98 (1998), 37-53. (pdf)
• A regularizing Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems,
  Inverse Problems 13 (1997), 79-95.
• Limitations of the L-curve method in ill-posed problems,
  BIT 36 (1996), 287-301.
• (with J.G. Nagy) Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques,
  Inverse Problems 12 (1996), 157-173.
• The minimal error conjugate gradient method is a regularization method,
  Proc. Amer. Math. Soc. 123 (1995), 3487-3497.
• (with A. Neubauer and O. Scherzer) A convergence analysis of the Landweber iteration for nonlinear ill-posed problems,
  Numer. Math. 72 (1995), 21-37.
• (with H.W. Engl) An optimal stopping rule for the \nu-method for solving ill-posed problems, using Christoffel functions,
  J. Approx. Th. 79 (1994), 89-108.
• (with I. Gohberg and I. Koltracht) Fast preconditioned conjugate gradient algorithms for Wiener-Hopf integral equations,
  SIAM J. Numer. Anal. 31 (1994), 429-443.
• (with P.C. Hansen) Regularization methods for large-scale problems,
  Surveys Math. Indust. 3 (1993), 253-315.
• Accelerated Landweber iterations for the solution of ill-posed equations,
  Numer. Math. 60 (1991), 341-373.