Univ.-Prof. Dr. Dr. h. c. mult. A. K. Louis
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Tel. [49] (0)681/302-3018
Room 4.10 (Building E1 1)
Research Interests
- Inverse Problems
- Medical Imaging, Nondestructive Testing
- Parameter Estimation
- Wavelets
- Industrial Mathematics
Short Vita
1949 | born |
1972 | Saarbrücken: Diploma in Mathematics |
1976 | Mainz: Doctorate |
1982 | Münster: Habilitation for Mathematics |
1983-1986 | Kaiserslautern: Associate Professor |
1986-1990 | Berlin: Full Professor Technical University |
since 1990 | Saarbrücken: Full Professor |
Visiting Positions
1980/81 | University of New York, Buffalo |
August/September 1982 | University of Pennsylvania, Philadelphia |
March 2000 | Université de Montpellier |
October 2011 |
Sobolev Institute of Russian Academy of Science, Novosibirsk |
Others
- 1997: Call to LMU München as Full Professor for Applied Mathematics
- 2000: Call to Louisiana State University, Baton Rouge, LA, U.S.A. as Full Professor
- 1997/99: Vice-president of Saarland University
- 1992-1998: Member of the Board of GAMM
- 1999-2018: Member of the Scientific Board of Zuse Institute Berlin (ZIB) and from 1999-2013 its speaker
- 2007-2016: Member of the Scientific Board of Radon Institute Linz, 2014-2016 Chair of the SAB
- since 2013: Member of the International Advisory Board of the Institute of Advanced Studies of the University Cergy-Pontoise
- since 1997: Owner of ISCA Prof. Louis
Honors
- 2005: Chevalier de l'Ordre des Palmes Académiques
- 2012: Honorary Doctorate Universität Bremen
- 2013: Honorary Doctorate Novosibirsk State University
- 2019: Russian Academy of Science's Sobolev Institute of Mathematics 2019 Gold Medal for distinguished impact in mathematics as lifetime achievement
Membership in Editorial Boards
- Inverse Problems, Editor-in-Chief, 2010-2014
- Documenta Mathematica, geschäftsführender Herausgeber 1996-2012
- SIAM J Imaging Sciences, 2008-2017
- International Journal of Biomedical Imaging, 2006-2020
- Journal of Inverse and Ill-Posed Problems, since 2014
- Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, since 2014
- 1993-1997: Inverse Problems
- 1993-1998: IEEE Transaction Medical Imaging
- 1995-1997: Computing
- 1991-2004: Surveys on Mathematics for Industry
Projects:
- DFG-Project: Combining of Image Reconstruction and Image Analysis
- DFG-Project: Stereology for Fibrous Random Media via Numerical Inversion of Spherical Radon Transforms
- Chinese-German Project granted by Sino-German Center for Research Promotin, Beijing
Recent Publications
Alfred K. Louis
List of Publications
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Rundungsfehler beim expliziten Differenzenverfahren zur Integration der Wellengleichung. ZAMM 54, T228-T229, 1974
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Fehlerabschätzungen für das Galerkin - Verfahren bei quasilinearen elliptischen Differentialgleichungen. ZAMM 57, T290-T291, 1977
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Quasioptimalität der Finite -Elemente - Methode bei nichtlinearen elliptischen Differentialgleichungen. ZAMM 59, 455-460, 1979
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Konvergenzbeschleunigung für Finite - Elemente - Lösungen der Poisson-Gleichung. ZAMM 59, T66-T67, 1979
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Acceleration of Convergence for Finite Element Solutions of the Poisson Equation. Numer. Math.
33, 43-53, 1979
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Numerische Rekonstruktion von Bildern bei unvollständigen Daten. ZAMM 60, T301-T303, 1980
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Picture Reconstruction from Projections in Restricted Range.Math. Meth. Appl. Sci. 2, 209-220, 1980
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Ghosts in Tomography - The Null Space of the Radon Transform.Math. Meth. Appl. Sci. 3, 1-10, 1981
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Approximation of the Radon Transform from Samples in Limited Range. In : Herman, G.T.; Natterer, F. (eds.): Mathematical Aspects of Computerized Tomography. Springer LNMI 8, 127-139, 1981
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Orthogonal Function Series Expansions and the Null Space of the Radon Transform. SIAM J. Math. Anal 15, 621-633, 1984
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Nonuniquenes Problems in Computerized Tomography. ZAMM 62, T290-T292, 1982
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Optimal Sampling in Nuclear Magnetic Resonance ( NMR ) Tomography. J. Comput. Assist. Tomogr. 6, 334-340, 1982
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Approximate Inversion of the 3D Radon Transform. Math. Meth. Appl. Sci. 5 176-185, 1983
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(with F. Natterer) Mathematical Problems in Computerized Tomography. ProceedingsIEEE 71, 379-389, 1983 reprinted in : Lee, H.; Wade, G. (eds.): Imaging Technology. IEEE press, 179 -189, 1986
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Optimal Sampling of Directions in NMR Imaging. J. Magnetic Resonance in Medicine, 1, 1982
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Nonuniqueness in Inverse Radon Problems: The Frequency Distribution of the Ghosts. Math. Z. 185, 429-440, 1984
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The Limited Angle Problem in Computerized Tomography.In: Neunzert, H. (ed.): Mathematics in Industry, Teubner, 194-208, 1984
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Incomplete Data Problems in X-Ray Computerized Tomography. I: Singular Value Decomposition of the Limited Angle Transform. Numer. Math. 48, 251-262, 1986
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Fast Scanning Geometries in X-Ray Computerized Tomography. In: Boffi, V.; Neunzert, H. (eds.): Mathematics in Technology. Teubner, 324-329, 1984
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Tikhonov-Phillips Regularization of the Radon Transform.In: Hämmerlin, G.; Hoffman, K.-H. (eds.): Constructive Methods for the Practical Treatment of Integral Equations. Birkhäuser, 211-223, 1985
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Laguerre and Computerized Tomography : Consistency Conditions and Stability of the Radon Transform. In : Proc. of the Symposium on Orthogonal Polynomials and their Applications for the 150th Anniversary of E.N. Laguerre, Springer LNM 1171, 524-531, 1985
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Computerized Tomography : Physical Background and Mathematical Modelling. Physicalia Magazine 7, 71-91, 1985
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(with R.M. Lewitt) Numerical Backprojection in the 3D Radon Transform. In : Deuflhard, P.; Engquist, B.(eds): Large Scale Scientific Computing. Birkhäuser, 235-244, 1987
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An Identification Problem for Linear Dynamical Systems. In: Neunzert, H.(ed.): The Road-Vehicle System and Related Mathematics. Teubner, 152-154, 1985
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Convergence of the Conjugate Gradient Method for Compact Operators. In: Engl, H.W., Groetsch, C.W. (eds.): Inverse and Ill-Posed Problems. Academic Press, 177-184, 1987
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(with A. Rieder) Incomplete Data Problems in X-Ray Computerized Tomography. II: Truncated Projections and Region-of-Interest Tomography. Numer. Math. 56, 371-383, 1989
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(with P. Wust, J. Nadobny, R. Felix, P. Deuflhard, W.) Numerical Approaches to Treatment Planning in Deep RF -Hyperthermia. Strahlenther. Onkol. 165, 751-757, 1989
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Inverse Problems in Medicine. In : V. Boffi, H. Neunzert (eds.) : Applications of Mathematics in Industry and Technology, Teubner, 277-287, 1989
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Eikonal Approximation in Ultrasound Computerized Tomography.In : Grünbaum, F.A., Helton, J.W., Khargonekar, P. (eds.) :Signal Processing II : Control and Applications, Springer, New York, 285-291, 1990
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Two - Dimensional Inverse Scattering Methods in Ultrasound Computer -- Tomography. IFAC Symposium Control of Distributed Systems, M. Amouroux and A. El Jai(eds), Perpignan, 1989, Pergamon Press, 165-168, 1989
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(with G. Schwierz) Rekonstruktionsverfahren in der medizinischen Bildgebung. ZAMM 70, T533- T539, 1990
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(with B. Eicke, R. Plato) The instability of some gradient methods for ill - posed problems. Numer. Math. 58, 129-134, 1990
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(with P. Wust, J. Nadobny, R. Felix, P. Deuflhard, F. John ) Strategies for optimized application of annular - phased array systems in clinical hyperthermia. Int. J. Hyperthermia, 7, 157-173,1990
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(with P. Maaß) A mollifier method for linear operator equations of the first kind. Inverse Problems
6, 427-440, 1990
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(with J. Kremer) On the mathematical foundation of hyperthermia therapy. Math. Meth. Appl. Sci.,
13, 467-479, 1990
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(with P. Maaß) Smoothed projection methods for the moment problem. Numer. Math. 59, 277-294, 1991
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Medical imaging : State - of - the art and future development. In : P.C. Sabatier (ed.): Inverse problems in action, Proceedings of the multicentennial meeting, Montpellier,Springer, 22-28, 1990
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Numerik Inverser Probleme. GAMM - Mitteilungen, Heft 1, 5-27, 1990
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Mathematical questions of a biomagnetic imaging problem. In : G.T. Herman, A.K. Louis, F. Natterer (Eds.) : Mathematical methods in tomography, Springer LNM 1497, 126-132, 1991
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Parametric reconstruction in biomagmetic imaging. In: Bertero, M., Pike, E.R. (eds.): Inverse Problems in Scattering and Imaging, Adam Hilger, 156-163, 1992
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Medical Imaging : State of the Art and Future Development, Inverse Problems 8, 709-738, 1992
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(with P. Maaß) Contour Reconstruction in 3D X- Ray CT, IEEE Transactions on Medical Imaging
12, 764-769, 1993
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(with M. Böhm, J. Kremer) Efficient Algorithm for Computing Optimal Control of Antennas in Hyperthermia, Surveys on Mathematics for Industry 3, 233-251, 1993
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A wavelet approach to identification problems, Proceedings of the international workshop on inverse problems, CRI K-1/93, Hannover, 67 -75, 1993
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Approximate Inverse for Linear and Some Nonlinear Problems, Inverse Problems 12, 175-190, 1996
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(with T. Schuster) A novel filter design technique in 2D X-ray CT, Inverse Problems 12, 685-696, 1996
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(with C. Wolters, A. Rienäcker, R. Beckmann, H. Jarausch, H. Buchner, R. Grebe) Stable inverse current reconstruction in real anatomy using combinatorial optimization techniques combined with regularization methods, Proceedings of the Third International Hans Berger Congress 'Quantitative and Topological EEG and MEG analysis, 1996
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(with R. Dietz) Algorithmen für die 3D-Computer-Tomographie bei zerstörungsfreien Prüfverfahren, in Mathematik - Schlüsseltechnologie für die Zukunft, Springer-Verlag Heidelberg/ Berlin, Herausgeber: K.H. Hoffmann, W. Jäger, T. Lohmann, H Schunck, S. 397-407, 1996
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Application of the Approximate Inverse to Inverse Scattering, in Conference on inverse problems of wave propagation and diffraction, Springer-Verlag Heidelberg, Editors: G. Chavent, P. Sabatier, 125-129, 1997
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(with M. Ende, P. Maaß, G. Mayer-Kress) EEG signal analysis by continuous wavelet transform techniques, in Nonlinear Techniques in Physiological Time Series Analysis, Springer, Editors: H. Kuntz, J. Kurths, G. Mayer-Kress, 1996
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Application of the Approximate Inverse to 3D X-Ray CT and Ultrasound Tomography,in Inverse Problems in Medical Imaging and Nondestructive Testing, Springer-Verlag Wien, New York, Editors: H.W. Engl, A.K. Louis, W. Rundell, S.120-133, 1997
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(with C. Wolters, A. Rienäcker, R. Beckmann, H. Jarausch, H. Buchner, R. Grebe) Stable inverse current reconstruction in real anatomy using combinatorial optimization techniques combined with regularization methods. In Quantitative and topological EEG and MEG analysis, Universitätsverlag Meyer, Jena, Editors: Wittie, H., Zwiener, U., Schack, B., Doering, A., S. 487 - 490, 1997
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Constructing an approximate inverse for linear and some nonlinear problems in engineering, in Inverse Problems in Engineering - Theory and Practice, The American Society of Mechanical Engeneers, New York, Editors: D. Delaunay, Y. Jarug, K.A. Woodbury, S. 367-374, 1998
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(with B. Dahlmanns, H. Buchner, M. Fuchs, G. Knoll) Neuronal source reconstruction using the finite element model, Electroenceph clin Neurophysiol 107, 45 P., 1998
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A Unified Approach to Regularization Methods for Linear Ill-Posed ProblemsInverse Problems,
15, pp. 489-498, 1999
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(with P. Lobel, C. Pichot, L.Blanc-Ferraud, M. Barlaud) Image reconstruction from the 1997 Ipswich data using a conjugate gradient algorithm, IEEE Antennas and Propagation, 41, 48-51, 1999
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(with P. Jonas) A Sobolev Space Analysis of Linear Regularization Methods for Ill-Posed Problems, Journal of Inverse and Ill-Posed Problems, J. Inverse and Ill-Posed Problems, 9, 59-74, 2001
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(with H. Abdullah) The Approximate Inverse for Solving an Inverse Scattering Problem for Acoustic Waves in an Inhomgeneous Medium, Inverse Problems, 15, 1213 - 1230, 1999
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(with E.T. Quinto) Local Tomographic Methods in SONAR, in Surveys on Solution Methods for Inverse Problems, Springer-Verlag Wien/New 147-155, Editors: D. Colton, H.W. Engl, A.K. Louis,
J. McLaughlin, W. Rundell, 2000
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(with P. Jonas) Approximate Inverse for a One-Dimensional Inverse Heat Conduction Problem, Inverse Problems 16, 175 - 185, 2000
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(with E. Yu. Derevtsov, R. Dietz, T. Schuster) Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem, J. Inverse and Ill-Posed Problems, 8, 161-191, 2000
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(with P. Dörr, C. Gruss, H. Petry) Measurement of Paint Layer Thickness with Photothermal Infrared Radiometry, in: Mathematics – Key Technology for the Future, Springer, Berlin, 460-471, 2003, Editors : W. Jäger, H-J Krebs
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(with F. Darvas, M. Fuchs, G. Knoll, H. Buchner, U. Schmitt) Spatio-temporal current density reconstruction (stCDR) from EEG-/MEG-data, in : Mathematics – Key Technology for the Future, Springer, Berlin, 472-482, 2003, Editors : W. Jäger, H-J Krebs
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(with U. Schmitt, F. Darvas, H. Buchner, M. Fuchs) Numerical Aspects of Spatio-Temporal Current Density Reconstruction from EEG-/ MEG Data , IEEE Trans. Med. Imaging, Vol. 20, Nr. 4, pp. 314-324, 2001
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(with F. Darvas, U. Schmitt, M. Fuchs, G. Knoll, H. Buchner) Spatio-Temporal Current Density Reconstruction (stCDR) from EEG/MEG-Data , Brain Topography, 13, pp. 195-207, 2001
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(with U. Schmitt) Efficient Algorithms for the Regularization of dynamic inverse Problems - Part I : Theory , Inverse Problems, 18, 645-658, 2002
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(with U. Schmitt, A. K. Louis, C. Wolters, M. Vaukhonen) Efficient Algorithms for the Regularization of dynamic inverse Problems - Part II :Applications, Inverse Problems, 18, 659-676, 2002
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(with T. Schuster, J. Plöger) Depth Resolved Residual Stress Evaluation from X-ray Diffraction Measurement Data using the Approximate Inverse Method, Zeitschrift für Metallkunde, 94,
934-937, 2003
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(with G.H. Klein, K.U. Modrich) Use of metal detectors for electromagnetic induction local 3D imaging, Conference Proceedings Eudem2 - SCOT2003
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(with T. Schuster, E.Yu. Derevtsov) Two Approaches to the problem of defect correction in vector field tomography solving boundary value problems, Journal of Inverse and Ill-Posed Problems, 12, 597-626, 2004
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Filter design in three-dimensional cone beam tomography: circular scanning geometry, Inverse Problems, 19, S31-S40, 2003
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(with P. Jonas) Phase Contrast Tomography using Holographic Measurements, Inverse Problems 20, 75-102, 2004
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(with F. Schöpfer, T. Schuster) Nonlinear iterative methods for linear ill-posed problems in Banach spaces, Inverse Problems 22, 311-330, 2006
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Development of algorithms in computerized tomography, in G Ólafsson, ET Quinto(eds): The Radon transform, inverse problems, and tomography, American Mathematical Society, PSAM 63, 25-42, 2006
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(with E. Wallacher) Complete sets of radiating parts of a source and their fields with applications in inverse scattering limited angle problems, Int. J. Biomedical Imaging 2006, Article ID 93074, 13 pages, 2006
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(with S. Oeckl, T. Schön, A. Knauf) Multiresolution 3D-computerized tomography and its application to NDT, Proceedings, 9th European Conference on Non-Destructive Testing (ECNDT), Sept. 25 – 29, 2006, Berlin
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Image Analysis in Tomography. In: Yair Censor, Ming Jiang, Alfred K. Louis (eds.) Mathematical methods in biomedical imaging and intensity-modulated radiation therapy (IMRT), CRM Series, Pisa, 2008,
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(with M. Bock, R. Müller, C. Oehler) Computer supported calculation and evaluation of the correct composition of BOF converter, Slag, Iron&Steel review, 283-287, 2007
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Optimal reconstruction kernels in medical imaging, In: Optimization in Medicine, Editors: C.J.S. Alves, P.M. Pardalos, L.N. Vicente, Springer, 2008, p. 153-168
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Combining Image Reconstruction and Image Analysis with an Application to 2D - Tomography, SIAM J. Imaging Sciences, 1, 188-208, 2008
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(with T. Weber und D. Theis) Computing reconstruction kernels for circular 3D cone beam tomography, IEEE Trans. Medical Imaging, 27, 880-886, 2008
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(with T. Schuster und D. Theis) A reconstruction approach for imaging in 3D cone beam vector field tomography, Int. J. Biomedical Imaging, Article ID 174283, 17 pages,
2009. DOI:10.1155/2008/174283
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(with F. Schöpfer, T. Schuster) An iterative regularization method for the solution of the split feasibility problem in Banach spaces, Inverse Problems 24 ( 2008) 055008 (20pp)
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(with A.Lakhal) Locating radiating sources for Maxwell's equations, Inverse Problems 24 (2008) 045020 (18pp)
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(with F. Schöpfer und T. Schuster) Metric and Bregman projections onto affine subspaces and their computation via sequential subspace optimisation methods, Journal of Inverse and Ill- Posed Problems, 16, 479-506, 2008
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(with T. Weber) Image reconstruction and image analysis in tomography: fan beam and 3D cone beam, In: Yair Censor, Ming Jiang, Alfred K. Louis (eds.) Mathematical methods in biomedical imaging and intensity-modulated radiation therapy (IMRT), CRM Series, Pisa, 2008, pp 211- 229
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(with J. Krebs, H. Wendland) Sobolev error estimates and a priori parameter selection for semi- discrete Tikhonov regularization, J Inverse and Ill-Posed Problems 17, 845-869, 2009
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(with P. Deuflhard, O. Dössel, S. Zachow) Mehr Mathematik wagen in der Medizin, In: Grötschel, M., Lucas, K., Mehrmann, V. (eds.) Produktionsfaktor Mathematik, Springer, Berlin, Heidelberg. 435-459, https://doi.org/10.1007/978-3-540-89435-3_19
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(with A. Groh, F. Weichert, T. Richards, M. Wagner) Mathematische Modellierung in der Systembiologie, Der Pathologe, 2, 135-140, 2008
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(with A. Groh) Stochastic modelling of biased cell migration and collagen matrix modification, J. Math. Biol. 61, 617-647, 2010
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(with A.Lakhal, M. Lakhal) Calibrating local volatility in inverse option pricing using the Levenberg-Marquardt method, Journal on Inverse and Ill-Posed Problems, 18 (2010)
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Diffusion reconstruction from very noisy tomographic data, Inverse Problems and Imaging, 4, 675-683, 2010
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(with C. Fehringer, C. Massing, T. Heider, G. Hohenberg, Y. Johann, U. Dillmann) Gait analysis in healthy subjects and parkinsonian patients: analysis of side asymmetries, Movement Disorders 24, S334-S334, 2009
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(with C. Massing, C. Fehringer, Y. Johann, S. Bechtel, K. Fassbender, U. Dillmann, G. Hohenberg) Discrete wavelet transformation in gait analysis: comparison of methods in healthy subjects and parkinsonian patients, Movement Disorders 24, S333-S333. 2009
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(with C. Fehringer, C. Massing, T. Heider, G. Hohenberg, Y. Johann, U. Dillmann) Gait analysis in healthy subjects and parkinsonian patients: analysis of side asymmetries, Movement Disorders 24, S.334, 2009
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(with P. Deuflhard, O. Dössel, S. Zachow) More Mathematics into Medicine!. In: Grötschel, M., Lucas, K., Mehrmann, V. (eds) Production Factor Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11248-5_19
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(with M. Riplinger, M. Spiess und E. Spodarev) Inversion algorithms for the spherical Radon and cosine transform, Inverse Problems 27, 03015, 2011, doi: 10.1088/0266-5611/27/3/035015
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(with H. Kohr) Fast and high-quality reconstruction in electron tomography based on an enhanced linear forward model, Inverse Problems, 27 045008 doi:
10.1088/0266-5611/27/4/045008, 2011
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Feature reconstruction in inverse problems, Inverse Problems, 27 065010 doi: 10.1088/0266-5611/27/6/065010, 2011
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(with G. Rigaud, M.K. Nguyen) Circular harmonic decomposition approach for numerical inversion of circular Radon transforms, 1st International ICST workshop on New Com- putational Methods for Inverse Problems (NCMIP), May 2011, Cachan, France. pp.1. hal-00665828
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(with G. Rigaud, M.K. Nguyen) Numerical Inversions of two Circular Radon Transforms in Compton Scattering Tomography, Inverse Problems in Science & Engineering, 2012, DOI: 10.1080/17415977.2011.653008
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(with Y. Zhou, T. Zhou, M. Jiang) Partial Coherence Theory for X-ray Phase Contrast Imaging Technique With Gratings, Optics Communications, Vol. 285, 4763-4774, 2012
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(with E.Y. Derevtsov, A.V. Efimov, T. Schuster) Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography, Journal of Inverse and Ill- Posed Problems, 19, 689–715, 2011
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(with B. Hahn) Reconstruction in three-dimensional parallel scanning geometry applied to synchrotron-based x-ray tomography, Inverse Problems 28 (2012) 045013 (18pp)
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(with G. Rigaud, M.K. Nguyen) Novel numerical inversion of two circular-arcRadon transforms in Compton scattering tomography, Inverse Problems in Science and Engineering, 20(6), 809-839, 2012
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(with G. Rigaud, M. K. Nguyen) Modelling and Simulation Results on a new Compton Scattering Tomography Modality, Simulation Modelling Practice and Theory (SIMPAT), 33, 28-44, 2013
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(with B. Hahn, M. Maisl, C. Schorr) Combined reconstruction and edge detection in dimensioning, Meas. Sci. Technol. 24, 125601(10pp) 2013
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(with P. Jonas) Cone beam reconstruction for small objects in phase contrast tomography, Inverse Problems, 29 095013s, 2013
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(with S.W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C.W. Ahn) Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory. Journal of Korean Physical Society 63, 2093-2097, 2013
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(with M.A.Abazid, A. Lakhal) Non-destructive testing of anti-reflection coatings for solar cells, Proc. European Workshop on renewable enery systems (EWRES)
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(with U. Dillmann, C. Holzhoffer, Y. Johann, S. Bechtel, S. Gräber, C. Massing, J. Spiegel, S. Behnke, J. Bürmann) Principal Component Analysis of gait in Parkinson´s disease: significance of gait velocity, Gait&Posture, Vol. 39 2014, Pages 882-887
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(with G. Rigaud, A. Lakhal) Series expansions of the reconstruction kernel of the Radon transform over a Cormack-type families of curves with applications in tomography, SIAM J Imaging Sciences 7, 924-943, 2014
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(with M. Riplinger, M. Krause, C. Xu) A new dimming algorithm based on the simplex method.
Comput. Optim. Appl. 64,243, 2016
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(with M. A. Abazid, A. Lakhal) A stable numerical algorithm for the design of anti-reflection coatings for solar cells) Int. J. Renewable Energy Technology, 7, 97-111, 2016
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(with M. A. Abazid, A. Lakhal) Inverse Design of anti-reflection coatings using the nonlinear approximate inverse, Inverse Problems in Science and Engineering 24, 917-935, 2016
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Exact cone beam reconstruction formulae for functions and their gradients for spherical and flat detectors, Inverse Problems 32, 115005, 2016
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(with A. Groh, H. Kohr) Numerical rate function determination in partial differential equations modelling cell population dynamics, J. Math. Biol. 74, 533-565, 2017
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(with P. Trampert, J. Vogelgesang, C. Schorr, M. Maisl, S. Bogachev, N. Marniok, T. Dahmen, P. Slusallek) Spherically symmetric volume elements as basis for image reconstructions in computed laminography, J.X-Ray Science and Technology, 25, 533-546, 2017
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(with E.Yu. Derevtsov, S.V. Maltseva, A.P. Polyakova, I.E. Svetov) Numerical solvers based on the method of approximate inverse for 2D vector and 2-tensor tomography problems, Inverse Problems 33(12), 124001, 2017
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Numerical aspects of cone beam reconstruction, Sens. Imag. 18, 15,2017
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(with T. Schön, K. Dietmayer) New n-dimensional reconstruction formula for flat detector tomography, Proc. Fully 3D Conference, 2017
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(with M. Krause, M. Riplinger, C. Xu) A new class of very efficient algorithms for local dimming, Optim Eng, 19, 1, 2018
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(with M. Quellmalz, R. Hielscher) The cone-beam transform and spherical convolution operators, Inverse Problems 34, 105006, 2018
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Uncertainty, ghosts, and resolution in Radon problems. In: R. Ramlau, O. Scherzer (eds). The Radon Transform: The First 100 Years and Beyond De Gruyter | 2019, https://doi.org/ 10.1515/9783110560855-008
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(with I.E. Svetov, S.V. Maltseva) The Method of Approximate Inverse in Slice-by-Slice Vector Tomography Problems, NUMTA 2, 487-494, 2019
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(with D. He, M. Jiang, P. Maass, T. Page) Joint Bi-Modal Image Reconstruction Of Dot And XCT With An Extended Mumford-Shah Functional. ISBI 2019: 1463-1466
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(with S. V. Maltseva, A. P. Polyakova, T. Schuster, I. E. Svetov) On solving the slice-by-slice three-dimensional 2-tensor tomography problems using the approximate inverse method, J. Phys.: Conf. Ser. 1715 012036, 2021
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(with S V Maltseva, I E Svetov ) An iterative algorithm for reconstructing a 2D vector field by its limited-angle ray transform, J. Phys.: Conf. Ser. 1715 012037, 2021
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Inversion Formulae for Ray Transforms in Vector and Tensor Tomography, Inverse Problems 38 065008, 2022
Books
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Inverse und schlecht gestellte Probleme, Teubner, Stuttgart, 1989
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(with G.T. Herman, F. Natterer) Mathemtical Methods in Tomography, Springer Berlin Heidelberg, ISBN: 978-3-540-54970-3, 1990
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(with P. Maaß, A. Rieder) Wavelets, Teubner, 2nd edition 1998
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(with P. Maaß, A. Rieder) Wavelets – Theory and Applications, Wiley, 1998
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(with H.W. Engl, W. Rundell: Inverse Problems in Medical Imaging and nondestructive testing, Springer, Wien, 1996
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(with H.W. Engl, W. Rundell) Inverse Problems in Geophysical Applications, SIAM, 1997
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(with D. Colton, H.W. Engl, J. McLaughlin, W. Rundell) Surveys on Solution Methods for Inverse Problems, Springer, Wien, 2000
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(with Y. Censor, M. Jiang) Mathematical Methods in Biomedical Imaging and Intensity- Moduled Radiation Therapy (IMRT), Birkhauser Verlag AG, ISBN: 978-88-7642-314-7, 2008
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(with M. Jiang, E.T. Quinto, N. Ida) The Proceedings of the International Conference on Sensing and Imaging, Springer, Lecture Notes in Electrical Engineering 506, ISBN: 3319916580, 2018
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(with E.T. Quinto, N. Ida, M. Jiang) The Proceedings of the International Conference on Sensing and Imaging, 2018, Springer, Lecture Notes in Electrical Engineering 606, ISBN 978-3-030-30827-8, 2019
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Co-Inventor in Patents:
- P. Maass, A. K. Louis.
Verfahren und Vorrichtung zur dreidimensionalen Computertomographie.
Deutsches Patentamt DE19623271A1,
Anmeldenummer: 19623271.6, Anmeldedatum: 31.05.1996 Veröffentlicht im Patentblatt Nr. 1997/49 am 04.12.1997.
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Deutsches Patent Nr. 199 07 804 : Single Sample Calibaration Erfinder : Dörr, P., Gruss, C., Louis, A.K., Petry, H., 2000
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Method and evaluation device for evaluating projection data of an object being examined Erfinder: S Oeckl, AK Louis, T. Schön
US patent 10,134,156
Inverse Problems 38 065008, 2022
2021
S V Maltseva, I E Svetov and A K Louis
An iterative algorithm for reconstructing a 2D vector field by its limited-angle ray transform
J. Phys.: Conf. Ser. 1715 012037
A K Louis, S V Maltseva, A P Polyakova, T Schuster and I E Svetov
On solving the slice-by-slice three-dimensional 2-tensor tomography problems using the approximate inverse method
J. Phys.: Conf. Ser. 1715 012036
2020
Svetov I.E., Maltseva S.V., Louis A.K.
The method of approximate inverse in slice-by-slice vector tomography problems.
Lecture Notes in Computer Science. 2020. Vol 11974. P. 487–494.
2019
D. He, M. Jiang, A. K. Louis, P. Maass, T. Page:
Joint Bi-Modal Image Reconstruction Of Dot And XCT With An Extended Mumford-Shah Functional. ISBI 2019: 1463-1466
E. Svetov, S. V. Maltseva, A. K. Louis:
The Method of Approximate Inverse in Slice-by-Slice Vector Tomography Problems, NUMTA (2) 2019: 487-494
Louis, A.K.:
Uncertainty, ghosts, and resolution in Radon problems.
In: R. Ramlau, O. Scherzer (eds). The Radon Transform: The First 100 Years and Beyond
De Gruyter | 2019, https://doi.org/10.1515/9783110560855-008
Publications
- Uncertainty, Ghosts and Resolution in Radon Problems To appear in Ramlau, R., Scherzer, O. (eds): The first 100 years of the Radon Transform.
- The cone-beam transform and spherical convolution operators Inverse Problems, 34, 105006
- A new class of very efficient algorithms for local dimming Optim Eng (2018) 19: 1
- Numerical solvers based on the method of approximate inverse for 2D vector and 2-tensor tomography problems Inverse Problems 33 (2017) 124001.
- New n-dimensional reconstruction formula for flat detector geometry Preprint Fully 3D Conference 2017
- Numerical Aspects of Cone Beam Contour Reconstruction Sens Imaging (2017) 18:15.
- Spherically symmetric volume elements as basis functions for image reconstructions in computed laminography Journal of X-Ray Science and Technology 25 (2017) 533–546
- Numerical rate function determination in partial differential equations modeling cell population dynamics J. Math. Biol. (2017), 74(3), 533-565.
- Exact cone beam reconstruction formulae for functions and their gradients for spherical and flat detectors Inverse Problems 32 (2016) 115005
- Inverse Design of Anti-Reflection Coatings using the Nonlinear Approximate Inverse Inverse Problems in Science and Engineering, 24(6), 917-935.
- A Stable Numerical Algorithm for the Design of Anti-Reflection Coatings for Solar Cells Int. J. Renewable Energy Technology, 7, 97-111, 2016
- A new local dimming algorithm based on the simplex method Comput Optim Appl (2016) 64: 243
- Series Expansions of the Reconstruction Kernel of the Radon Transform over a Cormack-Type Family of Curves with Applications in Tomography SIAM Journal on Imaging Sciences, 7(2), 924–943.
- Principal Component Analysis of gait in Parkinson ́s disease: relevance of gait velocity Gait & Posture 39 (2014) 882-887
- Non-Destructive Testing of Anti-Reflection Coatings for Solar Cells Proceedings of the European Workshop on Renewable Energy Systems (EWRES), 2013
- Visibility Studies of Grating-based Neutron Phase Contrast and Dark-field Imaging by Using Partial Coherence Theory Journal of Korean Physical Society, Vol. 63, No. 11, pp. 2093 - 2097, 2013
- Cone Beam Geometry for Small Objects in Phase Contrast Tomography Inverse Problems 29 (2013) 095013s
- Combined Reconstruction and Edge Detection in Dimensioning Meas. Sci. Technol. 24 (2013) 125601 (10pp)
- Modeling and Simulation Results on a new Compton Scattering Tomography Modality Simulation Modeling Practice and Theory (SIMPAT), 33(2013), 28-44
- Partial Coherence Theory for X-ray Phase Contrast Imaging Technique With Gratings Optics Communications, 285, 4736-4774, 2012
- Reconstruction in the three-dimensional parallel scanning geometry with application in synchrotron-based x-ray tomography
Inverse Problems 28 (2012) 045013 (19pp)
Paper Selected in "2012 Highlights for Inverse Problems" - Novel Numerical Inversions of two Circular-Arc Radon Transforms in Compton scattering tomography Inverse Problems in Science and Engineering, 20, 809-839, 2012
- Singular Value Decomposition and its Application to Numerical Inversion for Ray Transforms in 2D Vector Tomography Journal of Inverse and Ill-Posed Problems 19, 689–715, 2011
- Feature Reconstruction in Inverse Problems
Inverse Problems 27 (2011) 065010 (21pp)
Paper Selected in "2011 Highlights for Inverse Problems" - Circular Harmonic Decomposition Approach for Numerical Inversion of Circular Radon Transforms Proceedings of the workshop New Computational Methods for Inverse Problems, Cachan, France, 2011
- Fast and high-quality reconstruction in electron tomography based on an enhanced linear forward model Inverse Problems 27 (2011) 045008 (20pp)
- Inversion algorithms for the spherical Radon and cosine transform Inverse Problems 27 (2011) 035015 (25pp)
- Calibrating local volatility in inverse option pricing using the Levenberg-Marquardt method Journal of Inverse and Ill-Posed Problems 18, 2010
- Diffusion Reconstruction From Very Noisy Tomographic Data Inverse Problems and Imaging 4, 675-683, 2010
- More Mathematics into Medicine! In: M. Grötschel, K. Lucas, V. Mehrmann (eds.), Productions Factor Mathematics. acatech – German Academy of Science and Engineering, Springer-Verlag Berlin Heidelberg, pp. 357-378 (2010)
- Discrete wavelet transformation in gait analysis: comparison of methods in healthy subjects and parkinsonian patients Movement Disorders 24, S.333
- Gait analysis in healthy subjects and parkinsonian patients: analysis of side asymmetries Movement Disorders 24, S.334
- Stochastic modelling of biased cell migration and collagen matrix modification Journal of Mathematical Biology 61, 617-647, 2010
- Sobolev error estimates and a priori parameter selection for semi-discrete Tikhonov regularization J. Inv. Ill-Posed Problems 17 (2009), 845-869
- Mehr Mathematik wagen in der Medizin In: M. Grötschel, K. Lucas, V. Mehrmann (eds.), Produktionsfaktor Mathematik. Wie Mathematik Technik und Wirtschaft bewegt. acatech - Deutsche Akademie der Technikwissenschaften, Springer-Verlag Berlin Heidelberg, pp. 435-459 (2009)
- An iterative regularization method for the solution of the split feasibility problem in Banach spaces. (English summary) Inverse Problems, 24 (2008), no. 5, 055008, 20 pp.
- Computer supported calculation and evaluation of BOF slag composition Millennium Steel MS08, S. 55-59, 2008
- Mathematische Modellierung in der Systembiologie Der Pathologe, 29 (2008), 135-140.
- Image reconstruction and image analysis in tomography: fan beam and 3D cone beam in: Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT), 2008, 211-229, ISBN: 978-88-7642-314-7
- A Reconstruction Approach for Imaging in 3D Cone Beam Vector Field Tomography International Journal of Biomedical Imaging, 2008, Article ID 174283, 17 pages.
- Locating radiating sources for Maxwell's equations using the approximate inverse
Inverse Problems, 24 (2008/04)
Paper Selected in "2008 Highlights for Inverse Problems" - Metric and Bregman Projections onto Affine Subspaces and their Computation via Sequential Subspace Optimization Methods Journal of Inverse and Ill-Posed Problems, 16 (2008/05), 479–506
- Computing Reconstruction Kernels for circular 3D Cone Beam Tomography IEEE Transactions on Medical Imaging, Special Issue on Fully 3D Image Reconstruction, 27 (2008/07), 880-886
- Combining Image Reconstruction and Image Analysis with an Application to 2D - Tomography SIAM J. Imaging Sciences, 01 (2008/02), 188-208
- Computing Reconstruction Kernels for circular 3D Cone Beam Tomography Conference Proceedings - Fully 3D 2007 9th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine July 9 - 13, 2007, Lindau, Germany
- Optimal reconstruction kernels in medical imaging
in: Optimization in Medicine
Herausgeber: C.J.S. Alves, P.M. Paradalos, L.N. Vicente
Springer 2007 - Multiresolution 3D-Computerized Tomography and its Application to NDT 9th European Conference on Non-Destructive Testing (ECNDT), Berlin 2006
- Complete sets of radiating parts of a source and their fields with applications in inverse scattering limited angle problem International Journal of Biomedical Imaging 2006 (2006), Artikel ID 93074, 13 Seiten
- Development of Algorithms in Computerized Tomography Proceedings of Symposia in Applied Mathematics (63), American Mathematical Society, Herausgeber: Gestur Olafsson und Eric Todd Quinto, ISBN: 0-8218-3930-6, 25-42, 2006
- Nonlinear iterative methods for linear ill-posed problems in Banach spaces Inverse Problems, 22 (2006/01), 311-329
- Two Approaches to the problem of defect correction in vector field tomography solving boundary value problems Journal of Inverse and Ill-Posed Problems, 12 (2004/05), 557-669
- Phase Contrast Tomography using Holographic Measurements Inverse Problems, 20 (2004), 75-102
- Spatio-Temporal Current Density Reconstruction from EEG-/MEG-Data Mathematics - Key Technology for the Future / Ed.: Jäger, W., Krebs, H.-J.. - Berlin : Springer. 2003, 472-482
- Einfluß der Landnutzung auf Hochwasserentstehung Preprint
- Depth Resolved Residual Stress Evaluation from X-ray Diffraction Measure-ment Data using the Approximate Inverse Method Zeitschrift für METALLKUNDE, 94 (2003/08), 934-937
- Use of metal detectors for electromagnetic induction local 3D imaging Conference Proceedings Eudem2 - SCOT2003
- Filter design in three-dimensional cone beam tomography: circular scanning geometry Inverse Problems, 19 (2003), S31-S40
- Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem Journal of Inverse and Ill-Posed Problems, 8 (2002/2), 161-191
- Efficient Algorithms for the Regularization of dynamic inverse Problems - Part II : Applications Inverse Problems, 18 (2002), 659-676
- Efficient Algorithms for the Regularization of dynamic inverse Problems - Part I : Theory Inverse Problems, 18 (2002), 645-658
- Modelling and Simualtion in Preventive Flood Control Measures by Means of Types of Land Use Preprint
- Using rotational Invariances of Operators for the Implementation of Discrete Algorithms Preprint
- A Sobolev Space Analysis of Linear Regularization Methods for Ill-Posed Problems Journal of Inverse and Ill-Posed Problems, 9 (2001/1), 59-74
- Numerical Aspects of Spatio-Temporal Current Density Reconstruktion from EEG-/ MEG Data IEEE Transactions on Medical Imaging, 20 (2001/4), 314-324
- Spatio-Temporal Current Density Reconstruction (stCDR) from EEG/MEG-Data Brain Topography, 13 (2001), 195-207
- Local Tomographic Methods in SONAR Surveys on Solution Methods for Inverse Problems Springer-Verlag Wien/New York Herausgeber: D. Colton, H.W. Engl, A.K. Louis, J. McLaughlin, W. Rundell, 2000
- Measurement of Paint Layer Thickness with Photothermal Radiometry Mathematics - Key Technology for the Future
- Approximate Inverse for a one dimensional Inverse Heat Conduction Problem Inverse Problems, 16 (2000), 175-185
- A Unified Approach to Regularization Methods for Linear Ill-Posed Problems Inverse Problems, 15 (1999), 489-498
- The Approximate Inverse for Solving an Inverse Scattering Problem for Acoustic Waves in an Inhomogeneous Medium Inverse Problems, 15 (1999), 1213-1230
- Neuronal source reconstruction using the finite element model Electroenceph clin Neurophysiol 107:45P, 1998
- Constructing an approximate inverse for linear and some nonlinear problems in engineering Inverse Problems in Engineering - Theory and Practice The American Society of Mechanical Engeneers, New York Herausgeber: D. Delaunay, Y. Jarug, K.A. Woodbury S. 367-374, 1998
- Application of the Approximate Inverse to 3D X-Ray CT and Ultrasound Tomography Inverse Problems in Medical Imaging and Nondestructive Testing Springer-Verlag Wien, New York Herausgeber: H.W.Engl, A.K.Louis, W.Rundell S. 120-133, 1997
- Approximate inverse for linear and some nonlinear problems Inverse Problems, 12 (1996), 175-190
- A novel filter design technique in 2D computerized tomography Inverse Problems, 12 (1996), 685-696
- Algorithmen für die 3D-Computer-Tomographie bei zerstörungsfreien Prüfverfahren Mathematik-Schlüsseltechnologie für die Zukunft, Springer-Verlag Heidelberg/Berlin, Herausgeber: K.H. Hoffmann, W. Jäger, T. Lohmann, H. Schunck, S. 397-407, 1996
- EEG signal analysis by continuous wavelet transform techniques Nonlinear Techniques in Physiological Time Series Analysis Springer, Herausgeber: H. Kuntz, J. Kurths, G. Mayer-Kress, 1996
- Contour reconstruction in 3-D X-Ray CT IEEE Transactions on Medical Imaging, 12 (1993/4), 764-769
- Parametric reconstruction of a biomagnetic imaging Inverse Problems in Scattering and Imaging, pp. 156-163, 1992 Herausgeber: M. Bertero, E.R. Pike, Adam Hilger
- Medical Imaging: State of the art and future development Inverse Problems, 8 (1992), 709-738
- Smoothed projection methods for the moment problem Numerische Mathematik, 59 (1991), 277-294
- Eikonal Approximation in Ultrasound Computerized Tomography Signal Processing II: Control and Applications, Springer, New York pp. 285-291, 1990, Herausgeber: F.A. Grünbaum, J.W. Helton, P. Khargonekar
- The instability of some gradient methods for ill - posed problems Numerische Mathematik, 58 (1990), 129-134
- Strategies for optimized application of annular - phased array systems in clinical hyperthermia International Journal of Hyperthermia, 1990, 157-173
- A mollifier method for linear operator equations of the first kind Inverse Problems, 6 (1990), 427-440
- On the mathematical foundation of hyperthermia treatment Math. Meth. Appl. Sci., 13, pp. 467-479, 1990
- Incomplete Data Problems in X-Ray Computerized Tomography Numerische Mathematik, 56 (1989), 371-383
- Numerical Approaches to Treatment Planning in Deep RF- Hyperthemia Strahlentherapie und Onkologie, 165 (1989), 751-757