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Institute for Applied and Numerical Mathematics

Research Group 3: Scientific Computing

Prof. Dr. Andreas Rieder

Prof. Dr. Andreas Rieder

Publications

Prof. Dr. Andreas Rieder

$Office hour for students$ By appointment only until further notice.
$Building$ Kollegiengebäude Mathematik (20.30)
$Room$ 3.040
$Tel.$ +49 721 608 42678
$Fax$ +49 721 608 43197
andreas.rieder(at)kit.edu

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:

An all-at-once solver for visco-acoustic full waveform inversion in the time-domain, CRC1173 Preprint 2025.
On the mathematical foundation of full waveform inversion in viscoelastic vertically transverse isotropic media, Inverse Problems 41 (2025) 055009. Open Access.
A microlocal and visual comparison of 2D Kirchhoff migration formulas in seismic imaging, Inverse Problems 40 (2024) 115001. Open Access.
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
Inexact Newton regularizations with uniformly convex stability terms: a unified convergence analysis, CRC1173 Preprint 2023.
Approximate inversion of a class of generalized Radon transforms, SIAM J. Imaging Sci. 16(2), 842-866, 2023.
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 $L^{\infty}$ , Numer. Math. 154, 209–247 (2023). Open Access.

Some conferences, workshops, and summer schools that I have been or will be involved in somehow:

Current List of Courses

Semester	Titel	Typ
Sommersemester 2025	AG Inverse Probleme	Seminar (S)
Wintersemester 24/25	Inverse Probleme	Vorlesung (V)
	Übungen zu 0105100 (Inverse Probleme)	Übung (Ü)
	Proseminar (Unrestringierte Optimierung)	Proseminar (PS)
	AG Inverse Probleme	Seminar (S)
Sommersemester 2024	Optimierungstheorie	Vorlesung (V)
	Übungen zu 0155400 (Optimierungstheorie)	Übung (Ü)
	Mathematische Methoden der Bildgebung	Vorlesung (V)
	Übungen zu 0102900 (mathematische Methoden der Bildgebung)	Übung (Ü)
	AG Inverse Probleme	Seminar (S)
Wintersemester 23/24	Finite Elemente Methoden	Vorlesung (V)
	Übungen zu 0110300 (Finite Elemente Methoden)	Übung (Ü)
	Numerische Optimierungsmethoden	Vorlesung (V)
	Übungen zu 0124000 (numerische Optimierungsmethoden)	Übung (Ü)
	AG Inverse Probleme	Seminar (S)
Wintersemester 25/26	Mathematische Methoden der Bildgebung	Vorlesung (V)
	Übungen zu 0102900 (mathematische Methoden der Bildgebung)	Übung (Ü)
	Wavelets	Vorlesung (V)
	Übungen zu 0166200 (Wavelets)	Übung (Ü)
	AG Inverse Probleme	Oberseminar (OS)
Sommersemester 2026	Compressive Sensing	Vorlesung (V)
	Übungen zu 0154000 (Compressive Sensing)	Übung (Ü)
	Mathematische Methoden der Signal- und Bildverarbeitung	Vorlesung (V)
	Übungen zu Mathematische Methoden der Signal- und Bildverarbeitung (0178300)	Übung (Ü)
	AG Inverse Probleme	Seminar (S)

Semester	Titel	Typ
Winter Semester 2024/25	Unrestringierte nichtlineare Optimierung	Proseminar
Summer Semester 2022		Seminar
Summer Semester 2020	Mathematische Methoden der Bildgebung	Lecture
	Mathematik II für Wirtschaftsinformatik	Lecture
Winter Semester 2019/20	Mathematik 1 für die Fachrichtung Wirtschaftsinformatik	Lecture
	Methods of Optimization	Seminar
Winter Semester 2018/19	Finite Elemente Methoden	Lecture
	Nichtlineare inverse Probleme in Banachräumen	Lecture
Summer Semester 2018	Einführung in das Wissenschaftliche Rechnen	Lecture
	Summer School "Full Waveform Inversion: Mathematics and Geophysics"	Lecture
Winter Semester 2017/18	Inverse Probleme	Lecture
	Numerische Methoden für Differentialgleichungen	Lecture
Summer Semester 2017	Mathematical methods of imaging	Lecture
	Numerische Mathematik 2	Lecture
	Unrestringierte nichtlineare Optimierung	Proseminar
Winter Semester 2016/17	Numerische Mathematik 1	Lecture
	Numerische Optimierungsmethoden	Lecture
Winter Semester 2015/16	Advanced Inverse Problems: Nonlinearity and Banach Spaces	Lecture
		Lecture
Summer Semester 2015	Compressive Sensing	Lecture
	Optimierungstheorie	Lecture
		Seminar
Winter Semester 2014/15	Inverse Probleme	Lecture
	Unrestringierte nichtlineare Optimierung	Proseminar
Summer Semester 2014	Compressive Sensing	Lecture
	Optimierungstheorie	Lecture
Winter Semester 2013/14	Wavelets	Lecture
	Unrestringierte nichtlineare Optimierung	Proseminar
Summer Semester 2013	Mathematik II für Informationswirtschaft	Lecture
	Seminar (Inverse Probleme)	Seminar
Winter Semester 2012/13	Inverse Probleme	Lecture
	Mathematik I für die Fachrichtung Informationswirtschaft	Lecture
Summer Semester 2012	Optimierungstheorie	Lecture
	Numerische Mathematik für die Fachrichtungen Informatik und Ingenieurwesen	Lecture
Summer Semester 2011	Numerische Mathematik 2	Lecture
Winter Semester 2010/11	Numerische Mathematik 1	Lecture
Summer Semester 2010	Mathematik II für Informationswirtschaft	Lecture
Winter Semester 2009/10	Mathematik I für die Fachrichtung Informationswirtschaft	Lecture
Summer Semester 2009	Mathematische Methoden in der Medizintechnik	Lecture
	Wavelets with Applications in Scientific Computing	Seminar

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