Research interests

Discrete Inverse Problems, Discrete Optimization, Data Science, Tomography, Discrete Mathematics, Computational Complexity, Mathematical Imaging, The Prouhet-Tarry-Escott Problem

Publications in refereed journals and books

(Click here for Google Scholar citations and here for ResearchGate citations.)

  • A. Alpers, M. Fiedler, P. Gritzmann, F. Klemm: "Turning grain maps into diagrams," SIAM Journal on Imaging Sciences, (accepted for publication), Sept., 2022 (download publication [arXiv]).

  • A. Alpers, P. Gritzmann: "On the Reconstruction of Static and Dynamic Discrete Structures," Book chapter in: R. Ramlau and O. Scherzer (Eds.), The Radon Transform: The First 100 Years and Beyond, pp. 297–342, De Gruyter, 2019 (download publication [arXiv], link to book).

  • A. Alpers, P. Gritzmann: "On Double-Resolution Imaging and Discrete Tomography," SIAM Journal on Discrete Mathematics, 32 (2), pp. 1369–1399, 2018 (download publication [arXiv], link to journal).

  • A. Alpers, P. Gritzmann: "Dynamic Discrete Tomography," Inverse Problems, 34 (3), 034003 (26pp), 2018 (download publication [arXiv], link to journal).

  • A. Alpers, P. Gritzmann: "Reconstructing Binary Matrices Under Window Constraints from Their Row and Column Sums," Fundamenta Informaticae, 155 (4), pp. 321–340, 2017 (download publication [arXiv], link to journal).

  • A. Alpers, A. Brieden, P. Gritzmann, A. Lyckegaard, H.F. Poulsen: "Generalized Balanced Power Diagrams for 3D Representations of Polycrystals," Philosophical Magazine, 95 (9), pp. 1016–1028, 2015 (download publication [arXiv], link to journal).

  • J. Zhu, J. Gao, A. Ehn, M. Aldén, Z. Li, D. Moseev, Y. Kusano, M. Salewski, A. Alpers, P. Gritzmann, M. Schwenk: "Measurements of 3D Slip Velocities and Plasma Column Lengths of a Gliding Arc Discharge," Applied Physics Letters, 106 (4), 044101 (4pp), 2015 (download publication [PDF], link to journal).

  • A. Alpers, D.G. Larman: "The Smallest Sets of Points not Determined by Their X-rays," Bulletin of the London Mathematical Society, 47 (1), pp. 171–176, 2015 (download publication [arXiv], link to journal).

  • A. Alpers, P. Gritzmann, D. Moseev, M. Salewski: "3D Particle Tracking Velocimetry using Dynamic Discrete Tomography," Computer Physics Communications, 187 (1), pp. 130–136, 2015 (download publication [arXiv], link to journal).

  • A. Alpers, R.J. Gardner, S. König, R.S. Pennington, C.B. Boothroyd, L. Houben, R.E. Dunin-Borkowski, K.J. Batenburg: "Geometric Reconstruction Methods for Electron Tomography," Ultramicroscopy, 128 (C), pp. 42–54, 2013 (download publication [arXiv], link to journal).

  • A. Alpers, G.T. Herman, H.F. Poulsen, S. Schmidt: "Phase Retrieval for Superposed Signals from Multiple Binary Objects," Journal of the Optical Society of America A, 27 (9), pp. 1927–1937, 2010 (download publication [PDF], link to journal).

  • A. Alpers, L.E. Trotter: "Teaching Computational Discrete Optimization at the Undergraduate Level," INFORMS Transactions on Education, 9 (2), pp. 63–69, 2009 (download publication [PDF], link to journal).

  • A.K. Kulshreshth, A. Alpers, G.T. Herman, E. Knudsen, L. Rodek, H.F. Poulsen: "A Greedy Method for Reconstructing Polycrystals from Three-Dimensional X-ray Diffraction Data," Inverse Problems and Imaging, 3 (1), pp. 69–85, 2009 (download publication [PDF], link to journal).

  • A. Alpers, L. Rodek, H.F. Poulsen, E. Knudsen, G.T. Herman: "Discrete Tomography for Generating Grain Maps of Polycrystals," Book chapter in: G.T. Herman and A. Kuba (Eds.), Advances in Discrete Tomography and Its Applications, pp. 271–301, Birkhäuser, 2007 (request a copy, link to book).

  • A. Alpers, S. Brunetti: "Stability Results for the Reconstruction of Binary Pictures from Two Projections," Image and Vision Computing, 25 (10), pp. 1599–1608, 2007 (download publication [PDF], link to journal).

  • A. Alpers, R. Tijdeman: "The Two-Dimensional Prouhet-Tarry-Escott Problem," Journal of Number Theory, 123 (2), pp. 403–412, 2007 (download publication [PDF], link to journal).

  • A. Alpers, P. Gritzmann: "On Stability, Error Correction, and Noise Compensation in Discrete Tomography," SIAM Journal on Discrete Mathematics, 20 (1), pp. 227–239, 2006 (download publication [PDF], link to journal).

  • A. Alpers, H.F. Poulsen, E. Knudsen, G.T. Herman: "A Discrete Tomography Algorithm for Improving the Quality of 3DXRD Grain Maps," Journal of Applied Crystallography, 39 (4), pp. 582–588, 2006 (download publication [PDF], link to journal).

  • A. Alpers: "Digital Topology: Regular Sets and Root Images of the Cross-Median Filter," Journal of Mathematical Imaging and Vision, 17 (1), pp. 7–14, 2002 (download publication [PDF], link to journal).

  • A. Alpers, P. Gritzmann, L. Thorens: "Stability and Instability in Discrete Tomography," Lecture Notes in Computer Science 2243; Digital and Image Geometry (Advanced Lectures), G. Bertrand, A. Imiya, R. Klette (Eds.), pp. 175–186, Springer, 2001 (download publication [PDF], link to journal).

    • Monographs

  • A. Alpers: "On the Tomography of Discrete Structures: Mathematics, Complexity, Algorithms, and its Applications in Materials Science and Plasma Physics," Habilitation thesis, 2018 (download [PDF], link to repository).

  • A. Alpers: "Instability and Stability in Discrete Tomography," Dissertation, Technische Universität München, 2003, Shaker Verlag, ISBN 3-8322-2355-X (request a copy, link to publication).

    • Publications in refereed conference proceedings

  • R.S. Pennington, S. König, A. Alpers, C.B. Boothroyd, R.E. Dunin-Borkowski: "Reconstruction of an InAs Nanowire using Geometric and Algebraic Tomography," Journal of Physics: Conference Series, 326, pp. 012045-1–4, 2011 (download publication [PDF], link to journal).

  • A. Lyckegaard, A. Alpers, W. Ludwig, R.W. Fonda, L. Margulies, A. Götz, H.O. Sørensen, S.R. Deyk, H.F. Poulsen, E.M. Lauridsen: "3D Grain Reconstruction from Boxscan Data," Proceedings of the 31st Risø International Symposium on Materials Science: Challenges in materials science and possibilities in 3D and 4D characterization techniques, pp. 329–336, 2010 (download publication [PDF], link to conference website).

  • A. Alpers, S. Brunetti: "On the Stability of Reconstructing Lattice Sets from X-rays Along Two Directions," Lecture Notes in Computer Science 3429; Digital Geometry for Computer Imagery,  E. Andres, G. Damiand, P. Lienhardt (Eds.), pp. 92–103, Springer, 2005 (download publication [PDF], link to journal).

  • A. Alpers, E. Knudsen, H.F. Poulsen, G.T. Herman: "Resolving Ambiguities in Reconstructed Grain Maps using Discrete Tomography," Electronic Notes in Discrete Mathematics, 20 (1), pp. 419–437, 2005 (download publication [PDF], link to journal).

    • Other publications (submitted preprints, technical reports, selected posters, artworks)

  • A. Alpers, M. Fiedler, P. Gritzmann, F. Klemm: "Dynamic grain models via fast heuristics for diagram representations," submitted, April, 2022 (download publication [arXiv]).

  • A. Alpers, P. Gritzmann, S. Fraß (support): "November Image," German Research Foundation (DFG) Calendar, 2014 (download calendar [PDF], link to website), (mathematical artwork).

  • M. Beleggia, A. Alpers, T. Kasama, H.F. Poulsen, C. Frandsen, M. Varón Izquierdo, V. Puntes, R.E. Dunin-Borkowski: "Quantitative Magnetization States of Collodial Systems via Simplified-LLG and Model-based Fitting of Phase Images," 2nd International Symposium on Advanced Microscopy and Theoretical Calculations (AMTC2), Nagoya, Japan, 24-26 June 2010 (download poster [PDF]), (poster).

  • H.F. Poulsen, S. Schmidt, J. Wright, H.O. Sørensen, J. Oddershede, A. Alpers: "3DXRD and TotalCryst Geometry," SourceForge, 2009  (download publication [PDF], link to FABLE website), (technical report).

  • A. Alpers: "A Short Introduction to Tomographic Grain Map Reconstruction," Pure Mathematics and Applications. PU.M.A., 20 (1-2), pp. 157–163, 2009  (download publication [PDF], link to journal), (extended abstract).

    • Principal investigator

  • DFG Research Grant (jointly with P. Gritzmann): Geometric Reconstruction in Refraction- and Diffraction-based Tomography, 2011-2013.