Research Interests

Andreas Alpers

Personal Details

University Post: Senior Lecturer
Room 404, Mathematical Sciences Building (number 206 on the campus map, 4th floor)

Research Interests

Discrete Inverse Problems
Geometric Clustering
Discrete & Geometric Tomography
Mathematical Problems of Imaging & Materials Science

Research Profile Links

Research Grants

Principal Investigator, £234,024, "Optimal Grain Diagrams: Mathematical Analysis and Algorithms", EP/X035883/1, EPSRC New Investigator Award, 10/2023–09/2025. (Webpage)
Principal Investigator, €123,500, "Geometric Reconstruction in Refraction- and Diffraction-based Tomography", AL 1431/1-1, DFG Research Grant "Eigene Stelle", 05/2011–04/2013.

Research Group

Aigerim Saken (Postdoc)
Georgia Lupton (PhD student)
Jisui Huang (PhD student)

Publications in Refereed Journals and Books

A. Alpers, M. Fiedler, P. Gritzmann, F. Klemm: "Dynamic Grain Models via Fast Heuristics for Diagram Representations," Philosophical Magazine 103 (10), pp. 948–968, 2023 (download publication [arXiv], link to journal, open access).

A. Alpers, M. Fiedler, P. Gritzmann, F. Klemm: "Turning Grain Maps Into Diagrams," SIAM Journal on Imaging Sciences, 16 (1), pp. 223–249, 2023 (download publication [arXiv], link to journal).

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 (download publication, 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, Technische Universität München, 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 (link to journal, open access).

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).

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 (link to journal, open access).

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 (link to journal, open access).

Other Publications (Preprints, Technical Reports, Selected Posters, Artworks)

A. Alpers, Y. Zhai: "Christmas Power Diagram," Hurwitz Jahrbrief (Cover Image), 2021 (download publication [PDF]) (mathematical artwork).

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

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]), (extended abstract).