
Dr. Matthias Beckmann
Applied Mathematician
Center for Industrial Mathematics
University of Bremen
Bibliothekstr. 5
28359 Bremen
E-Mail: info (at) mbeckmann.de
Overview
CV
- From June 2022 on I am Visiting Researcher at the Department of Electrical and Electronic Engineering at Imperial College London.
- Since September 2021 I am a research associate in Prof. Dr. Dr. h.c. Peter Maaß's working group at University of Bremen.
- During Summer Semester 2021 (01.04.2021 - 30.09.2021) I was interim professor at the Center for Industrial Mathematics at University of Bremen.
- From March 2020 to December 2020 I was Visiting Researcher in Dr. Ayush Bhandari's working group at Imperial College London.
- From October 2014 to September 2021 I was a research assistant/associate in Prof. Dr. Armin Iske's working group at University of Hamburg.
Research Interests
- Approximation theory
- Inverse problems (esp. computerized tomography)
- Machine learning (esp. for inverse problems)
- Signal processing and image analyse
Publications
Dissertation
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Matthias Beckmann
Error Estimates and Convergence Rates for Filtered Back Projection Reconstructions.
Universität Hamburg, 2018.
Preprints
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Matthias Beckmann, Ayush Bhandari and Meira Iske
Fourier-Domain Inversion for the Modulo Radon Transform.
arXiv: 2307.13114.
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Matthias Beckmann and Nick Heilenkötter
Equivariant Neural Networks for Indirect Measurements.
arXiv: 2306.16506.
Peer-reviewed Journal Articles
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Matthias Beckmann, Ayush Bhandari and Felix Krahmer
The Modulo Radon Transform: Theory, Algorithms and Applications.
SIAM Journal on Imaging Sciences 15(2), 2022, 455-490.
DOI: 10.1137/21M1424615. -
Matthias Beckmann, Peter Maass and Judith Nickel
Error Analysis for Filtered Back Projection Reconstructions in Besov Spaces.
Inverse Problems 37(1), 2021, 014002.
DOI: 10.1088/1361-6420/aba5ee. -
Matthias Beckmann and Armin Iske
Saturation Rates of Filtered Back Projection Approximations.
Calcolo 57(1), 2020, 12.
DOI: 10.1007/s10092-020-00360-y. -
Matthias Beckmann and Armin Iske
Error Estimates and Convergence Rates for Filtered Back Projection.
Mathematics of Computation 88(316), 2019, 801-835.
DOI: 10.1090/mcom/3343.
Peer-reviewed Proceedings
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Matthias Beckmann and Ayush Bhandari
MR. TOMP: Inversion of the Modulo Radon Transform (MRT) via Orthogonal Matching Pursuit (OMP).
IEEE International Conference on Image Processing (ICIP), 2022, 3748-3752.
DOI: 10.1109/ICIP46576.2022.9897428. -
Matthias Beckmann, Felix Krahmer and Ayush Bhandari
HDR Tomography via Modulo Radon Transform.
IEEE International Conference on Image Processing (ICIP), 2020, 3025-3029.
DOI: 10.1109/ICIP40778.2020.9190878. -
Ayush Bhandari, Matthias Beckmann and Felix Krahmer
The Modulo Radon Transform and its Inversion.
European Signal Processing Conference (EUSIPCO), 2020, 770-774.
DOI: 10.23919/Eusipco47968.2020.9287586. -
Matthias Beckmann and Armin Iske
Convergence Rates for Hölder-Windows in Filtered Back Projection.
IEEE International Conference on Sampling Theory and Applications (SampTA), 2019.
DOI: 10.1109/SampTA45681.2019.9030855. -
Matthias Beckmann and Armin Iske
Sobolev Error Estimates for Filtered Back Projection Reconstructions.
IEEE International Conference on Sampling Theory and Applications (SampTA), 2017, 251-255.
DOI: 10.1109/SAMPTA.2017.8024439. -
Matthias Beckmann and Armin Iske
Error Estimates for Filtered Back Projection.
IEEE International Conference on Sampling Theory and Applications (SampTA), 2015, 553-557.
DOI: 10.1109/SAMPTA.2015.7148952.
Other Proceedings
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Matthias Beckmann and Armin Iske
On the Error Behaviour of the Filtered Back Projection.
Proc. Appl. Math. Mech. (PAMM) 16(1), 2016, 833-834.
DOI: 10.1002/pamm.201610405.
Technical Reports
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Matthias Beckmann and Armin Iske
Approximation of Bivariate Functions from Fractional Sobolev Spaces by Filtered Back Projection.
Hamburger Beiträge zur Angewandten Mathematik (HBAM) 2017-05, 2017. -
Matthias Beckmann and Armin Iske
Analysis of the Inherent Reconstruction Error in Filtered Back Projection.
Hamburger Beiträge zur Angewandten Mathematik (HBAM) 2016-01, 2016.
Lecture Notes
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Matthias Beckmann
Lecture Notes on Computerized Tomography.
arXiv: 2312.02393.
Scientific Talks
Invited Talks
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11th Applied Inverse Problems Conference (AIP2023)
04. - 08. September 2023, Göttingen, Germany.
Talk: Inversion of the Modulo Radon Transform via Orthogonal Matching Pursuit.
Invited to Minisymposium MS22: Imaging with Non-Linear Measurements: Tomography and Reconstruction from Phaseless or Folded Data. -
10th International Congress on Industrial and Applied Mathematics (ICIAM2023)
21. - 25. August 2023, Tokyo, Japan.
Talk: High Dynamic Range Tomography via Modulo Radon Transform.
Invited to Minisymposium MS622: Inverse Problems and Imaging. -
SIAM Conference on Computational Sciences and Engineering (CSE2023)
26. February - 3. March 2023, Amsterdam, Netherlands.
Talk: High Dynamic Range Tomography via Modulo Radon Transform.
Invited to Minisymposium MS61: Problems and Solutions in 3-D Reconstruction. -
Inverse Problems: Modelling and Simulation (IPMS2022)
22. May - 28. May 2022, Mellieha, Malta.
Talk: The Modulo Radon Transform and Its Inversion.
Invited to Minisymposium M6: Generalized Radon Transforms and Applications. -
SIAM Conference on Imaging Science (IS2022)
21. March - 25. March 2022, Berlin, Germany.
Talk: The Modulo Radon Transform and Its Inversion.
Invited to Minisymposium MS8: Tomographic Image Reconstruction with Radon-Type Transforms. -
Oberseminar: Mathematics of Data Analysis (TUM2017)
18. May 2017, Technische Universität München, München, Germany.
Talk: Sobolev Error Estimates for Filtered Back Projection Reconstructions.
Invited by Dr. Frank Filbir & Prof. Dr. Felix Krahmer.
Contributed Talks
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93. Annual Meeting of GAMM (GAMM2023)
30. May - 02. June 2023, Dresden, Germany.
Talk: Inversion of the Modulo Radon Transform via Orthogonal Matching Pursuit.
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92. Annual Meeting of GAMM (GAMM2022)
15. - 19. August 2022, Aachen, Germany.
Talk: High Dynamic Range Tomography via Modulo Radon Transform.
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Joint Annual Meeting of DMV and ÖMG (DMV2021)
27. September - 01. October 2021, Passau, Germany.
Talk: Error Analysis for Filtered Back Projection Reconstructions.
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SIAM Conference on Imaging Science (IS2020)
06. - 17. July 2020, Toronto, Canada.
Talk: High Dynamic Range Tomography via Modulo Radon Transform. -
13th International Conference on Sampling Theory and Applications (SampTA2019)
08. - 12. July 2019, Université de Bordeaux, Bordeaux, France.
Talk: Convergence Rates for Hölder-Windows in Filtered Back Projection. -
16th International Conference on Approximation Theory (AT2019)
19. - 22. May 2019, Vanderbilt University, Nashville, TN, USA.
Talk: Approximation of Bivariate Functions by Filtered Back Projection. -
Mecklenburg Workshop "Approximation Methods and Fast Algorithms" (MW2018)
10. - 14. September 2018, University of Lübeck, Hasenwinkel, Germany.
Talk: Saturation Rates for Filtered Back Projection. -
SIAM Conference on Imaging Science (IS2018)
05. - 08. June 2018, Bologna, Italy.
Talk: Error Analysis for Filtered Back Projection Reconstructions in Fractional Sobolev Spaces. -
YR Meeting & CSE Workshop "Recent Trends and Future Developments in Computational Science & Engineering" (CSE2018)
26. - 29. March 2018, Technical University Hamburg, Plön, Germany.
Talk: Saturation Rates for Filtered Back Projection Reconstructions. -
89. Annual Meeting of GAMM (GAMM2018)
19. - 23. March 2018, München, Germany.
Talk: Saturation Rates for Filtered Back Projection Reconstructions. -
GAMM-MSIP Workshop on Mathematical Signal Processing and Data Analysis (GAMM-MSIP2017)
18. - 20. September 2017, University of Bremen, Bremen, Germany.
Talk: Error Analysis for Filtered Back Projection Reconstructions in Fractional Sobolev Spaces. -
12th International Conference on Sampling Theory and Applications (SampTA2017)
03. - 07. July 2017, Tallinn University, Tallinn, Estland.
Talk: Sobolev Error Estimates for Filtered Back Projection Reconstructions. -
88. Annual Meeting of GAMM (GAMM2017)
06. - 10. March 2017, Weimar, Germany.
Talk: Error Analysis for Filtered Back Projection Reconstructions in Fractional Sobolev Spaces. -
IM-Workshop on Signals, Images, and Approximation (IM2017)
27. February - 03. March 2017, Bernried, Germany.
Talk: Error Analysis for Filtered Back Projection Reconstructions in Fractional Sobolev Spaces. -
27. Rhein-Ruhr-Workshop on Applied Analysis (RRW2017)
27. - 28. January 2017, Bestwig, Germany.
Poster: Analysis of the Inherent Reconstruction Error in Filtered Back Projection. -
International Workshop on Mathematical Imaging and Emerging Modalities (MIEM2016)
27. - 30. June 2016, University of Osnabrück, Osnabrück, Germany.
Talk: Analysis of the Inherent Reconstrution Error in Filtered Back Projection. -
SIAM Conference on Imaging Science (IS2016)
23. - 26. May 2016, Albuquerque, NM, USA.
Talk: Error Estimates and Convergence Rates for Filtered Back Projection. -
YR Meeting & CSE Workshop "Recent Trends and Future Developments in Computational Science & Engineering" (CSE2016)
21. - 24. March 2016, University of Hamburg, Plön, Germany.
Talk: On the Error Behaviour of the Filtered Back Projection. -
Annual Meeting of DMV and GAMM (GAMM2016)
07. - 11. March 2016, Braunschweig, Germany.
Talk: On the Error Behaviour of the Filtered Back Projection. -
IM-Workshop on Signals, Images, and Approximation (IM2016)
29. February - 04. March 2016, Bernried, Germany.
Talk: Error Estimates and Convergence Rates for Filtered Back Projection. -
26. Rhein-Ruhr-Workshop on Applied Analysis (RRW2016)
29. - 30. January 2016, Bestwig, Germany.
Talk: Fehlerabschätzungen und Konvergenzraten für die gefilterte Rückwärtsprojektion. -
ICERM Workshop "Computational and Analytical Aspects of Image Reconstruction" (CAAIR2015)
13. - 17. July 2015, Brown University, Providence, RI, USA.
Poster: Error Estimates for Filtered Back Projection. -
11th International Conference on Sampling Theory and Applications (SampTA2015)
25. - 29. May 2015, American University, Washington, DC, USA.
Talk: Error Estimates for Filtered Back Projection. -
YR Meeting & CSE Workshop "Recent Trends and Future Developments in Computational Science & Engineering" (CSE2015)
09. - 13. March 2015, Christian-Albrechts-Universität zu Kiel, Plön, Germany.
Talk: L² - Error Estimates for Filtered Back Projection. -
25. Rhein-Ruhr-Workshop on Applied Analysis (RRW2015)
30. - 31. January 2015, Bestwig, Germany.
Talk: Fehlerabschätzungen für die gefilterte Rückwärtsprojektion.
Teaching
Supervision of Student Theses
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Current: Carla Dittert, M.Sc. Mathematics, University of Bremen
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Current: Jürgen Jeschke, M.Sc. Mathematics, University of Bremen
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09/2023: Lia Pribnow, M.Sc. Industrial Mathematics, University of Bremen
The Radon Cumulative Distribution Transform in Image Classification -
12/2022: Meira Iske, M.Sc. Mathematics, University of Bremen
Inversion of the Modulo Radon Transform via Direct Fourier Reconstruction -
11/2022: Nick Heilenkötter, M.Sc. Industrial Mathematics, University of Bremen
Equivariant Neural Networks for Indirect Measurements -
03/2021: Max Lewerenz, B.Sc. Mathematics, University of Hamburg
Support vector machines from statistical learning theoretic point of view (in German) -
06/2020: Tigran Andrikyan, B.Sc. Mathematics, University of Hamburg
The short time Fourier transform and Gabor frames in time-frequency analysis (in German)
Courses at University of Bremen
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WiSe 2023/2024: Inverse Problems in Imaging
Lecture (with Prof. Dr. Dr. h.c. Peter Maaß) -
SoSe 2023: Mathematical Foundations of Machine Learning
Lecture -
WiSe 2022/2023: Inverse Problems
Lecture -
SoSe 2022: Mathematical Foundations of Machine Learning
Lecture -
WiSe 2021/2022: Mathematical Methods for Signal and Image Processing
Lecture -
SoSe 2021: Mathematical Foundations of Machine Learning
Lecture and Exercise Class -
SoSe 2021: Mathematics 2b for Production Engineers
Lecture
Courses at University of Hamburg
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WiSe 2020/2021: Computer Tomography
Lecture -
WiSe 2020/2021: Approximation
Lecture -
SoSe 2020: Project: Machine Learning
Project -
WiSe 2019/2020: Computer Tomography
Lecture and Exercise Class -
SoSe 2019: Functional Analysis
Exercise Class -
WiSe 2018/2019: (Pro)Seminar über Approximation
Seminar (with Prof. Dr. Armin Iske) -
WiSe 2017/2018: Approximation
Exercise Class -
WiSe 2016/2017: Approximation
Exercise Class -
WiSe 2015/2016: Approximation
Exercise Class -
WiSe 2014/2015: Approximation
Exercise Class
Courses at Technical University Hamburg
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SoSe 2020: Complex Functions
Exercise Classes -
SoSe 2019: Complex Functions
Exercise Classes -
WiSe 2018/2019: Differential Equations I
Exercise Classes -
WiSe 2018/2019: Analysis III
Exercise Classes -
SoSe 2018: Analysis II
Exercise Classes -
WiSe 2017/2018: Analysis I
Exercise Classes -
SoSe 2017: Complex Functions
Exercise Classes -
WiSe 2016/2017: Analysis I
Exercise Classes -
SoSe 2016: Complex Functions
Exercise Classes -
WiSe 2015/2016: Differential Equations I
Exercise Classes -
SoSe 2015: Analysis II
Exercise Classes
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Photo: Matthias Beckmann