Department of Mathematics
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Department of Mathematics
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Institutes
Institute for Applied and Numerical Mathematics
Research Group 3: Scientific Computing
Prof. Dr. Andreas Rieder
Publications

Publications by Andreas Rieder

Preprints and Work in Progress

Papers (refereed)

  1. A microlocal and visual comparison of 2D Kirchhoff migration formulas in seismic imaging, Inverse Problems 40 (2024) 115001. Open Access, with K. Ganster and E. T. Quinto.
  2. Tangential cone condition for the full waveform forward operator in the viscoelastic regime: the non-local case, SIAM J. Appl. Math. 84(2), 412 - 432, 2024, with M. Eller and R. Griesmaier
  3. Seismic imaging with generalized Radon transforms: Stability of the Bolker condition, Pure Appl. Math. Q. 19(4), 1985-2036 (2023), with P. Kunstmann and E. T. Quinto.
  4. On the iterative regularization of non-linear ill-posed problems in L^{\infty}, Numer. Math. 154, 209–247 (2023), Open Access, with L. Pieronek
  5. Approximate inversion of a class of generalized Radon transforms, SIAM J. Imaging Sci. 16(2), 842-866, 2023, with K. Ganster.
  6. Multiparameter 2D viscoelastic full-waveform inversion of Rayleigh waves: a field experiment at Krauthausen test site, Geophys. J. Int. (2023) 234, 297–312 , with L. Gao, Y. Pan, T. Bohlen, and W. Mao
  7. Visco-acoustic full waveform inversion: from a DG forward solver to a Newton-CG inverse solver, Comput. Math. Appl. 100 (2021), 126-140, with T. Bohlen, M. Fernandez, J. Ernesti, C. Rheinbay, and C. Wieners. Open Access until November 5, 2021.
  8. Multiparameter viscoelastic full waveform inversion of shallow seismic surface waves with a preconditioned truncated-Newton method, Geophys. J. Int. 227 (2021), 2044-2057, with Th. Bohlen, L. Gao, and Y. Pan.
  9. Tangential cone condition and Lipschitz stability for the full waveform forward operator in the acoustic regime, Inverse Problems 37 (2021) 085011, Open Access, with M. Eller.
  10. An all-at-once approach to full waveform seismic inversion in the viscoelastic regime, Math. Meth. Appl. Sci. 44(8), 6376-6388, 2021 Open Access.
  11. Imaging with the elliptic Radon transform in 3D from an analytical and numerical perspective, SIAM J. Imaging Sci. 13(4), 2250-2280, 2020, with C. Grathwohl, P. Kunstmann, and E. T. Quinto.
  12. Inverse problems for abstract evolution equations II: higher order differentiability for viscoelasticity, SIAM J. Appl. Math. 79(6), 2639–2662, 2019, with A. Kirsch. See Corrigendum.
  13. Microlocal analysis of imaging operators for effective common offset seismic reconstruction, Inverse Problems 34 (2018) 114001, with C. Grathwohl, P. Kunstmann, and E. T. Quinto.
  14. Approximate inverse for the common offset acquisition geometry in 2D seismic imaging, Inverse Problems 34 (2018) 014002, with C. Grathwohl, P. Kunstmann, and E. T. Quinto.
  15. Adaptive wavelet collocation method for simulation of a 2D micro-ring resonator, Optik 131, 655-670, 2017, with H. Li, K. Hiremath, and W. Freude.
  16. Inverse problems for abstract evolution equations with applications in electrodynamics and elasticity, Inverse Problems 32 (2016) 085001 with A. Kirsch.
  17. Model-aware Newton-type inversion scheme for electrical impedance tomography, Inverse Problems 31 (2015) 045009, with R. Winkler.
  18. An inexact Newton regularization in Banach spaces based on the nonstationary iterated Tikhonov method, J. Inverse Ill-Posed Prob. 23(4), 2015, with F. Margotti
  19. On the linearization of operators related to the full waveform inversion in seismology, Math. Meth. Appl. Sci. 37(18), 2995–3007, 2014, with A. Kirsch
  20. Resolution-controlled conductivity discretization in electrical impedance tomography, SIAM J. Imaging Sci. 7(4), 2048–2077, 2014, with R. Winkler
  21. Seismic tomography is locally ill-posed, Inverse Problems 30 (2014) 125001, with A. Kirsch. There is a corrigendum for this article Inverse Problems 31 (2015) 119501.
  22. A Kaczmarz version of the REGINN-Landweber iteration for ill-posed problems in Banach spaces, SIAM J. Numer. Anal. 52(3), 1439-1465, 2014, with F. Margotti and A. Leitão
  23. Geometric reconstruction in bioluminescene tomography, Inverse Problems and Imaging 8(1), 173-197, 2014, with T. Kreutzmann
  24. The approximate inverse in action IV: semi-discrete equations in a Banach space setting, Inverse Problems 28 (2012) 104001, with T. Schuster and F. Schöpfer
  25. Local inversion of the Sonar transform regularized by the approximate inverse, Inverse Problems 27 (2011) 035006, with Todd Quinto and Thomas Schuster. Inverse Problems 2011 Highlight.
  26. Towards a general convergence theory for inexact Newton regularizations, Numer. Math. 114(3), 521-548, 2010, with A. Lechleiter.
  27. Newton regularization for impedance tomography: convergence by local injectivity, Inverse Problems 24 (2008) 065009, with A. Lechleiter.
  28. Shape from specular reflections and optical flow, Int. J. Comput. Vis. 80(2), 226-241, 2008, with J. Lellman, J. Balzer and J. Beyerer.
  29. Optimality of the fully discrete filtered backprojection algorithm for tomographic inversion, Numer. Math. 108(1), 151-175, 2007, with A. Schneck.
  30. Newton regularizations for impedance tomography: a numerical study, Inverse Problems 22(6), 1967-1987, 2006, with A. Lechleiter.
    Chosen by IOPSelect.
  31. Inexact Newton regularization using conjugate gradients as inner iteration, SIAM J. Numer. Anal. 43, 604-622, 2005.
  32. Runge-Kutta integrators yield optimal regularization schemes, Inverse Problems, 21(2), 453-471, 2005.
  33. Approximate inverse in action III: Doppler tomography, Numer. Math. 97, 353-378, 2004 , with Th. Schuster.
  34. The semi-discrete filtered backprojection algorithm is optimal for tomographic inversion, SIAM J. Numer. Anal. 41, 869-892, 2003, with A. Faridani.
  35. Approximate inverse in action II: convergence and stability, Math. Comput. 72, 1399-1415, 2003, with Th. Schuster.
  36. Split-step wavelet collocation method for nonlinear optical pulse propagation, IEICE Trans. on Electronics, special issue on "Signals, Systems, and Electronics Technology", E85-C(3), 534-543, 2002, with T. Kremp, A. Killi, and W. Freude.
  37. On filter design principles in 2D computerized tomography, in "Radon Transforms and Tomography", E. T. Quinto et al. (eds.), Contemporary Mathematics 278, AMS Publications, 207-226, 2001.
  38. Classification of endocardial electrograms using adapted wavelet packets and neural networks, Annals of Biomedical Engineering, 2001, with D. Strauß, Y. Manoli, and J. Jung.
  39. On convergence rates of inexact Newton regularizations, Numer. Math. 88(2), 347-365, 2001.
  40. A promising approach to signal dicrimination in electrocardiology: adapted multiresolution signal decompositions, Applied Signal Process. 6(4), 182-193, 1999 (appeared March 2001), with D. Strauß, Th. Sinnwell, Y. Manoli, and J. Jung.
  41. Embedding and a-priori wavelet adaptivity for Dirichlet problems, M^2AN, 34(6), 1189-1202, 2000.
  42. Approximate inverse in action with an application to 2D-computerized tomography, SIAM J. Numer. Anal., 37(6), 1909-1929, 2000, with Th. Schuster.
  43. Approximate inverse meets local tomography, Math. Meth. Appl. Sci., 23, 1373-1387, 2000, with R. Dietz and Th. Schuster.
  44. On the regularization of nonlinear ill-posed problems via inexact Newton iterations, Inverse Problems 15(1), 309-327, 1999.
  45. A painless and direct way from integral to discrete fast wavelet transforms, ZAMM, 8(11), 781-785, 1998.
  46. A domain embedding method for Dirichlet problems in arbitrary space dimension, M^2AN, 32(4), 405-431, 1998.
  47. Wavelet multilevel solvers for linear ill-posed problems stabilized by Tikhonov regularization, in "Multiscale Wavelet Methods for Partial Differential Equations", W. Dahmen, A. Kurdila, and P. Oswald (eds.), Academic Press, San Diego, 1997, 347-380.
  48. On embedding techniques for 2nd-order elliptic problems, in "Computational Science for the 21st Century", M.-O. Bristeau et al. (eds.), Wiley, Chichester, 1997, 179-188.
  49. Wavelet-accelerated Tikhonov-Phillips regularization with applications, in "Inverse Problems in Medical Imaging and Nondestructive Testing", H. W. Engl, A. K. Louis, and W. Rundell (eds.),Springer-Verlag, Wien 1997, 134-159, with P. Maaß.
  50. A wavelet multilevel method for ill-posed problems stabilized by Tikhonov regularization, Numer. Math. 75(4), 501-522, 1997.
  51. A wavelet multigrid preconditioner for Dirichlet boundary-value problems in general domains, M^2AN, 30(6), 711-729, 1996, with R. Glowinski, R. O. Wells Jr. and X. Zhou.
  52. On the robustness of the damped V-cycle of the wavelet frequency decomposition multigrid method, Computing 53(2), 155-171, 1994, with X. Zhou.
  53. A wavelet approach to robust multilevel solvers for anisotropic elliptic problems, Applied and Computational Harmonic Analysis, 1(4), 355-367, 1994, with R. O. Wells Jr. and X. Zhou.
  54. Multilevel methods based on wavelet decompositions, East-West J. Numer. Math., 2(4), 313-330, 1999.
  55. The high frequency behaviour of continuous wavelet transforms, Applicable Analysis, 52, 125-141, 1994.
  56. The wavelet transform on Sobolev spaces and its approximation properties, Numer. Math. 58, 875-894, 1991.
  57. Incomplete data problems in X-ray computerized tomography, Numer. Math. 56, 371-383, 1989, with A. K. Louis.

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Proceedings

  1. On the approximate inversion of generalized Radon transforms emerging in seismic imaging, Oberwolfach Reports 20(2), 1113-1116, 2023, with K. Ganster.
  2. Beyond Kirchhoff migration in 2D seismic imaging, Oberwolfach Reports 14(2), 1526-1528, 2017, with C. Grathwohl, P. Kunstmann and E. T. Quinto.
  3. Resolution-controlled conductivity discretization in electrical impedance tomography, Oberwolfach Reports 11(3), 2096-2097, 2014, with Robert Winkler.
  4. Fine-tuning of the complete electrode model, Proc. 15th Inter. Conf. on Biomedical Applications of Electrical Impedance Tomography, A. Adler, B. Grychtol (Eds.), page 28, 2014, with R. Winkler, S. Staboulis and N. Hyvönen
  5. Defect Classification on Specular Surfaces Using Wavelets, A. Kuijper et al. (Eds.): SSVM 2013, LNCS 7893, pp. 501–512, 2013, with Andreas Hahn, Mathias Ziebarth and Michael Heizmann.
  6. Geometric Reconstruction in Bioluminescence Imaging, Oberwolfach Reports 9(4), 3078-3080, 2012, with Tim Kreutzmann.
  7. K-REGINN: An inexact Newton regularization of Kaczmarz type, Oberwolfach Reports 8(1), 234-237, 2011, with Antonio Leitao.
  8. Local SONAR inversion, Oberwolfach Reports 7(2), 1058-1060, 2010, with Todd Quinto and Thomas Schuster.
  9. Tangential cone condition for electrical impedance tomography, Oberwolfach Reports 4(1), 719-721, 2007, with Armin Lechleiter.
  10. Optimality of the fully discrete filtered backprojection algorithm in 2D, Oberwolfach Reports 3(3), 2101-2104, 2006, with Arne Schneck.
  11. Optimal coating of laser mirrors for the generation of ultrashort laser pulses, PAMM Proc. Appl. Math. Mech. 5, 643-644, 2005, with J. Brunk and U. Morgner.
  12. Adaptive multiresolution split-step wavelet collocation method for nonlinear optical pulse propagation, "Proceedings Lasers and Electro-Optics" (CLEO 2002), Long Beach (CA), Session CThO, with T. Kremp, A. Killi, and W. Freude.
  13. Evaluating the reconstruction limits and the effect of modeling errors in noninvasive cardiac source imaging, Biomedizinische Technik, 46(2), 88-90, 2001, with O. Skipa, N. Holtrop, C. D. Werner, F. B. Sachse, O. Dössel.
  14. Das inverse Problem der Elektrokardiographie: Rekonstruktion realistischer Quellverteilungen, Biomedizinischen Technik, 46(1), 508-509, 2001, with N. Holtrop, O. Skipa, C. D. Werner, F. B. Sachse, O. Dössel.
  15. How to scale reconstruction filters in 2D-computerized tomography, ZAMM 81(Supplement 3), S621-S622, 2001.
  16. The recognition of antegrade and retrograde atrial activation patterns using hybrid wavelet-neural network schemes, Proceedings "Computers in Cardiology 2000" Boston, IEEE, with D. Strauß and J. Jung.
  17. A unified convergence theory for the iterative regularization of nonlinear ill-posed problems, ZAMM 80(Supplement 1), S245-S248, 2000.
  18. Additive and multiplicative Schwarz algorithms for linear ill-posed problems, ZAMM 76(Supplement 1), 187-190, 1996.
  19. A preconditioned CG-method for wavelet-Galerkin discretizations of elliptic problems, ZAMM 75, S683 - S684, 1995, with R. Glowinski, R. O. Wells Jr., and X. Zhou.
  20. On the wavelet frequency decomposition method in "Wavelet Applications", Harold H. Szu (ed.), Proc. SPIE 2242, 14-18, 1994,with R. O. Wells Jr. and X. Zhou.
  21. Wavelet analysis of auscultory blood pressure signals, Abstracts of the second European Conference on Engineering and Medicine 1993, Elsevier, 1993, 322-323, with H. Hammer, P. Maaß and J.-U. Meyer.
  22. Approximationseigenschaften der Wavelet-Transformation, ZAMM 70(6), T577-T578, 1989.

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Books and Monographs

As author

  1. Wave Phenomena: Mathematical Analysis and Numerical Approximation, Birkhäuser Cham, 2023, with W. Dörfler, M. Hochbruck, J. Köhler, R. Schnaubelt, and C. Wieners.
  2. Keine Probleme mit Inversen Problemen, Vieweg, 2003.
  3. Wavelets - Theorie und Anwendungen, Teubner, Stuttgart, 2. Auflage, 1998, with A. K. Louis and P. Maaß.
  4. Wavelet-Methoden für schlecht-gestellte und elliptische Probleme, Annales Universitatis Saraviensis, Series Mathematicae 7(4), 75-194, 1997.
  5. Wavelets - Theory and Applications, Wiley, 1997, with A. K. Louis and P. Maaß.

As editor

  1. Mathematics of Wave Phenomena, Birkhäuser, 2020, with W. Dörfler, M. Hochbruck, D. Hundertmark, W. Reichel, R. Schnaubelt, and B. Schörkhuber.

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