Prof. Dr. Andreas Rieder
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Until further notice only on appointment.
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Kollegiengebäude Mathematik (20.30)
3.040
+49 721 608 42678
+49 721 608 43197
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andreas.rieder(at)kit.edu
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Karlsruher Institut für Technologie (KIT)
Institut für Angewandte und Numerische Mathematik
Arbeitsgruppe 3: Wissenschaftliches Rechnen
Kaiserstr. 89-93
D-76133 Karlsruhe
My research interests cover the design, analysis, and implementation of numerical schemes for solving inverse and illposed problems in general and for imaging in particular. Related questions of signal and image processing appeal to me as well. I am board member of CRC 1173 wave phenomena - analysis and numerics and in charge of projects C1 as well as C2, both of which consider seismic imaging. Further, I am member of the advisory panel of the scientific journal Inverse Problems.
In project C2 we have developed the sofware PyFWI to interactively simulate seismic inversion.
Here you will find a list of my publications. For a list of selected talks see the bottom of this page.
Recent preprints and publications:
- On the mathematical foundation of full waveform inversion in viscoelastic vertically transverse isotropic media, Preprint CRC 1173, 2024
- A microlocal and visual comparison of 2D Kirchhoff migration formulas in seismic imaging, Inverse Problems 40 (2024) 115001. Open Access.
- Inexact Newton regularizations with uniformly convex stability terms: a unified convergence analysis, CRC1173 Preprint 2023.
- 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
- Approximate inversion of a class of generalized Radon transforms, SIAM J. Imaging Sci. 16(2), 842-866, 2023.
- Multiparameter 2D viscoelastic full-waveform inversion of Rayleigh waves: a field experiment at Krauthausen test site, Geophys. J. Int. (2023) 234, 297–312
- Seismic imaging with generalized Radon transforms: stability of the Bolker condition, Pure Appl. Math. Q. 19(4), 1985-2036 (2023).
- On the iterative regularization of non-linear ill-posed problems in
, Numer. Math. 154, 209–247 (2023). Open Access.
- Tangential cone condition and Lipschitz stability for the full waveform forward operator in the acoustic regime, Inverse Problems 37 (2021) 085011. Open Access.
Some conferences, workshops, and summer schools that I have been or will be involved in somehow:
- Oberwolfach Workshop -- Tomographic Inverse Problems: Mathematical Challenges and Novel Applications, Oberwolfach, May 2023
- Rich and Nonlinear Tomography, Isaac Newton Institute, Cambridge, 2023
- Conference on Mathematics of Wave Phenomena, Karlsruhe, February 2022
- Oberwolfach Seminar: Wave Phenomena: Analysis and Numerics, Oberwolfach, November 2019
- Modern Challenges in Imaging in the Footsteps of Allan Cormack, Boston, August 2019
Research Interests
- Inverse and ill posed problems
- Wavelet methods in signal and image processing
- Numerical solution of partial differential equations
Publications
Here you will find a list of my publications.
Selected Talks
- Approximate inverse for the common offset acquisition geometry in 2D seismic imaging, 100 Years of the Radon Transform, Linz, March 2017, Folien
- An abstract framework for inverse wave problems with applications, Inverse Problems: Modeling and Simulation, May 2016, Folien
- Model-aware Newton-type regularization in electrical impedance tomography, Applied Inverse Problems, Helsinki, May 2015, slides
- Semi-discrete equations in Banach spaces: the approximate inverse approach, Applied Inverse Problems, Helsinki, May 2015, slides
- Resolution-controlled conductivity discretization in electrical impedance tomography, Mathematics and Algorithms in Tomography, Oberwolfach, August 2014, slides
- Seismic tomograpy is locally ill-posed, Inverse Problems: Modeling and Simulation, May 2014, slides
- Local SONAR inversion, Mathematics and Algorithms in Tomography, Oberwolfach, April 2010, slides (the animations will only work if viewed using Acrobat reader 6.5 or higher on Windows or MacOS)
- A new view on phantom views, Applied Inverse Problems, Vienna, July 2009, slides
- Towards a general convergence theory of inexact Newton regularizations, Applied Inverse Problems, Vienna, July 2009, slides
- Tangential cone condition and other open problems in electrical impedance tomography, Workshop on Hybrid Imaging, University Center Innsbruck in Obergurgl, January 2008, slides
- Newton-CG for nonlinear inverse problems, Symposium on Inverse Problems, Chemnitz, September 2006, slides
- Optimality of the fully discrete filtered backprojection algorithm in 2D, Conference Mathematical methods in tomography, Oberwolfach, August 2006, slides
- Runge-Kutta integrators yield optimal regularization schemes, Joint Mathematics Meeting of the AMS and MAA, Atlanta, GA, Januar 2005, slides