Fachbereich Mathematik 
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Dr. Matthias Beckmann

Foto Department of Mathematics
Center for Optimization and Approximation
Bundesstraße 55 (Geomatikum)
20146 Hamburg

Room T07
Tel.: 040 42838-6240
Fax: 040 42838-5117
E-Mail: matthias.beckmann (at) uni-hamburg.de

From October 2014 to September 2021 I was a research assistant in Prof. Dr. Armin Iske's working group at the Center for Optimization and Approximation.
During Summer Semester 2021 (01.04.2021 - 30.09.2021) I was interim professor at the Center for Industrial Mathematics at University of Bremen.

Personal homepage: mbeckmann.de


Research interests

  • Approximation theory
  • Inverse problems (esp. computerized tomography)
  • Signal processing and image analyse


Dissertation

Matthias Beckmann (2018)
Error Estimates and Convergence Rates for Filtered Back Projection Reconstructions.
University of Hamburg, 2018.


Preprints

Matthias Beckmann, Ayush Bhandari and Felix Krahmer (2021)
The Modulo Radon Transform: Theory, Algorithms and Applications.
arXiv: 2105.04194.


Publications

Peer-reviewed journal articles

Matthias Beckmann, Peter Maass and Judith Nickel (2021)
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 (2020)
Saturation Rates of Filtered Back Projection Approximations.
Calcolo 57(1), 2020, 12.
DOI: 10.1007/s10092-020-00360-y.

Matthias Beckmann and Armin Iske (2019)
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

Matthias Beckmann, Felix Krahmer and Ayush Bhandari (2020)
HDR Tomography via Modulo Tomography.
IEEE International Conference on Image Processing (ICIP), 2020, 3025-3029.
DOI: 10.1109/ICIP40778.2020.9190878.

Ayush Bhandari, Matthias Beckmann and Felix Krahmer (2020)
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 (2019)
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 (2017)
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 (2015)
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

Matthias Beckmann and Armin Iske (2016)
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

Matthias Beckmann and Armin Iske (2017)
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 (2016)
Analysis of the Inherent Reconstruction Error in Filtered Back Projection.
Hamburger Beiträge zur Angewandten Mathematik (HBAM) 2016-01, 2016.


Conferences, Workshops and Scientific Talks

Joint Annual Meeting of DMV and ÖMG (DMV2021)
September 27 - Oktober 01, 2021, Passau, Germany.
Talk: Error Analysis for Filtered Back Projection Reconstructions.
Invited by Prof. Dr. Armin Iske & Prof. Dr. Dirk Praetorius

13th International Conference on Sampling Theory and Applications (SampTA2019)
July 08 - 12, 2019, University of Bordeaux, Bordeaux, France.
Talk: Convergence Rates for Hölder-Windows in Filtered Back Projection.

16th International Conference on Approximation Theory (AT2019)
May 19 - 22, 2019, Vanderbilt University, Nashville, TN, USA.
Talk: Approximation of Bivariate Functions by Filtered Back Projection.

Mecklenburg Workshop "Approximation Methods and Fast Algorithms" (MW2018)
September 10 - 14, 2018, University of Lübeck, Hasenwinkel, Germany.
Talk: Saturation Rates for Filtered Back Projection.

SIAM Conference on Imaging Science (IS2018)
June 05 - 08, 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)
March 26 - 29, 2018, Technical University of Hamburg, Plön, Germany.
Talk: Saturation Rates for Filtered Back Projection Reconstructions.

89. Annual Meeting of GAMM (GAMM2018)
March 19 - 23, 2018, Munich, Germany.
Talk: Saturation Rates for Filtered Back Projection Reconstructions.

GAMM-MSIP Workshop on Mathematical Signal Processing and Data Analysis (GAMM-MSIP2017)
September 18 - 20, 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)
July 03 - 07, 2017, Tallinn University, Tallinn, Estonia.
Talk: Sobolev Error Estimates for Filtered Back Projection Reconstructions.

Oberseminar: Mathematics of Data Analysis (TUM2017)
May 18, 2017, Technical University of Munich, Munich, Germany.
Talk: Sobolev Error Estimates for Filtered Back Projection Reconstructions.
Invited by Dr. Frank Filbir & Prof. Dr. Felix Krahmer

88. Annual Meeting of GAMM (GAMM2017)
March 06 - 10, 2017, Weimar, Germany.
Talk: Error Analysis for Filtered Back Projection Reconstructions in Fractional Sobolev Spaces.

IM-Workshop on Signals, Images, and Approximation (IM2017)
February 27 - March 03, 2017, Bernried, Germany.
Talk: Error Analysis for Filtered Back Projection Reconstructions in Fractional Sobolev Spaces.

27. Rhein-Ruhr-Workshop on Applied Analysis (RRW2017)
January 27 - 28, 2017, Bestwig, Germany.
Poster: Analysis of the Inherent Reconstruction Error in Filtered Back Projection.

International Workshop on Mathematical Imaging and Emerging Modalities (MIEM2016)
June 27 - 30, 2016, University of Osnabrück, Osnabrück, Germany.
Talk: Analysis of the Inherent Reconstrution Error in Filtered Back Projection.

SIAM Conference on Imaging Science (IS2016)
May 23 - 26, 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)
March 21 - 24, 2016, University of Hamburg, Plön, Germany.
Talk: On the Error Behaviour of the Filtered Back Projection.

Joint Annual Meeting of DMV and GAMM (DMV2016)
March 07 - 11, 2016, Braunschweig, Germany.
Talk: On the Error Behaviour of the Filtered Back Projection.

IM-Workshop on Signals, Images, and Approximation (IM2016)
February 29 - March 04, 2016, Bernried, Germany.
Talk: Error Estimates and Convergence Rates for Filtered Back Projection.

26. Rhein-Ruhr-Workshop on Applied Analysis (RRW2016)
January 29 - 30, 2016, Bestwig, Germany.
Talk: Fehlerabschätzungen und Konvergenzraten für die gefilterte Rückwärtsprojektion.

ICERM Workshop "Computational and Analytical Aspects of Image Reconstruction" (CAAIR2015)
July 13 - 17, 2015, Brown University, Providence, RI, USA.
Poster: Error Estimates for Filtered Back Projection.

11th International Conference on Sampling Theory and Applications (SampTA2015)
May 25 - 29, 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)
March 09 - 13, 2015, Christian-Albrechts University of Kiel, Plön, Germany.
Talk: L² - Error Estimates for Filtered Back Projection.

25. Rhein-Ruhr-Workshop on Applied Analysis (RRW2015)
January 30 - 31, 2015, Bestwig, Germany.
Talk: Fehlerabschätzungen für die gefilterte Rückwärtsprojektion.


Teaching

SoSe 2021: Mathematical Foundations of Machine Learning (Uni Bremen)

SoSe 2021: Mathematics 2b for Production Engineers (Uni Bremen)

WiSe 2020/2021: Computer Tomography

WiSe 2020/2021: Approximation

SoSe 2020: Project: Machine Learning

SoSe 2020: Exercise classes in Complex Functions (TUHH)

WiSe 2019/2020: Computer Tomography (Lecture und Exercise class)

SoSe 2019: Exercise classes in Functional Analysis

SoSe 2019: Exercise classes in Complex Functions (TUHH)

WiSe 2018/2019: (Pro)Seminar on Approximation (with Prof. Dr. Armin Iske)

WiSe 2018/2019: Exercise classes in Differential Equations I (TUHH)

WiSe 2018/2019: Exercise classes in Analysis III (TUHH)

SoSe 2018: Exercise classes in Analysis II (TUHH)

WiSe 2017/2018: Exercise class in Approximation

WiSe 2017/2018: Exercise classes in Analysis I (TUHH)

SoSe 2017: Exercise classes in Complex Functions (TUHH)

WiSe 2016/2017: Exercise class in Approximation

WiSe 2016/2017: Exercise classes in Analysis I (TUHH)

SoSe 2016: Exercise classes in Complex Functions (TUHH)

WiSe 2015/2016: Exercise class in Approximation

WiSe 2015/2016: Exercise classes in Differential Equations I (TUHH)

SoSe 2015: Exercise classes in Analysis II (TUHH)

WiSe 2014/2015: Exercise class in Approximation


 
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