Contact
Pfaffenwaldring 57
70569 Stuttgart
Deutschland
Room: 8.164
Office Hours
on appointment
Subject
Dynamic inverse problems
Inverse problems arise whenever a searched-for quantity cannot be directly observed but has to be extracted indirectly from measured data. Classic examples constitute imaging modalities such as computerized tomography which provide information about the interior of a patient or an object in a non-invasive way.
The classic regularisation theory is based on the assumption that the searched-for quantity is stationary during the acquisition. However, in many applications from medicine to non-destructive testing, this assumption is not satisfied. Therefore, we work on the development and (numerical) analysis of time-dependent regularization methods which incorporate the dynamics of the object.
Imaging and tomography
Developing new methods in imaging and new fields of applications necessitates novel approaches in mathematical modelling, data processing and image reconstruction. A special focus of our group lies in this respect on computerized tomography and magnetic resonance imaging.
Data analysis and image processing
In order to extract features and properties of the studied medium, the reconstruction results are typically subject to further processing steps. Since an ever-increasing amount of data arises in modern applications, special algorithms are required to extract the desired infomation in an efficient and stable way.
2024
- M. Nitzsche and B. N. Hahn, Dynamic image reconstruction in MPI with RESESOP-Kaczmarz. 2024.
- M. S. Feinler and B. N. Hahn, GAN-based iterative motion estimation in HASTE MRI. 2024.
- M. S. Feinler and B. N. Hahn, Learned RESESOP for solving inverse problems with inexact forward operator. 2024.
2023
- B. N. Hahn, G. Rigaud, and R. Schmähl, A class of regularizations based on nonlinear isotropic diffusion for inverse problems, IMA Journal of Numerical Analysis, Feb. 2023.
- B. N. Hahn, E. T. Quinto, and G. Rigaud, Foreword to special issue of Inverse Problems on modern challenges in imaging, Inverse Problems, vol. 39, no. 3, p. 030401, Feb. 2023.
- B. Hahn and B. Wirth, Convex reconstruction of moving particles with inexact motion model, PAMM, vol. 23, no. 2, Sep. 2023.
- M. S. Feinler and B. N. Hahn, Retrospective Motion Correction in Gradient Echo MRI by Explicit Motion Estimation Using Deep CNNs. 2023.
- S. R. Arridge, M. Burger, B. Hahn, and E. T. Quinto, Tomographic Inverse Problems: Mathematical Challenges and Novel Applications, Oberwolfach Reports, vol. 20, no. 2, pp. 1105–1194, Dec. 2023.
2022
- M. Nitzsche, H. Albers, T. Kluth, and B. Hahn, Compensating model imperfections during image reconstruction via Resesop, International Journal on Magnetic Particle Imaging, p. Vol 8 No 1 Suppl 1 (2022), 2022.
- B. N. Hahn, M.-L. K. Garrido, C. Klingenberg, and S. Warnecke, Using the Navier-Cauchy equation for motion estimation in dynamic imaging, Inverse Problems and Imaging, vol. 16, no. 5, p. 1179, 2022.
2021
- B. N. Hahn, M. L. Kienle-Garrido, and E. T. Quinto, Microlocal properties of dynamic Fourier integral operators, 2021.
- B. N. Hahn, Motion compensation strategies in tomography, 2021.
2020
- G. Rigaud and B. N. Hahn, Reconstruction algorithm for 3D Compton scattering imaging with incomplete data, Inverse Problems in Science and Engineering, vol. 29, no. 7, pp. 967--989, 2020.
- A. P. Polyakova, I. E. Svetov, and B. N. Hahn, The Singular Value Decomposition of the Operators of the Dynamic Ray Transforms Acting on 2D Vector Fields, in Numerical Computations: Theory and Algorithms, Cham, 2020, pp. 446--453.
- B. N. Hahn, M. L. Kienle-Garrido, C. Klingenberg, and S. Warnecke, Using the Navier-Cauchy equation for motion estimation in dynamic imaging. 2020.
- S. E. Blanke, B. N. Hahn, and A. Wald, Inverse problems with inexact forward operator: iterative regularization and application in dynamic imaging, Inverse Problems, vol. 36, no. 12, p. 124001, 2020.
2019
- Mathematisches Forschungsinstitut Oberwolfach, Tomographic Inverse Problems: Theory and Applications, Workshop Reports, 2019.
- T. Kluth, B. N. Hahn, and C. Brandt, Spatio-temporal concentration reconstruction using motion priors in magnetic particle imaging, in Proc. Int. Workshop Magnetic Particle Imaging, 2019.
- B. N. Hahn and M.-L. Kienle Garrido, An efficient reconstruction approach for a class of dynamic imaging operators, Inverse Problems, vol. 35, no. 9, p. 094005, 2019.
2018
- T. Schuster, B. Hahn, and M. Burger, Dynamic inverse problems: modelling—regularization—numerics, Inverse Problems, vol. 34, no. 4, p. 040301, Mar. 2018.
- G. Rigaud and B. N. Hahn, 3D Compton scattering imaging and contour reconstruction for a class of Radon transforms, Inverse Problems, vol. 34, no. 7, p. 075004, 2018.
2017
- B. N. Hahn, Motion Estimation and Compensation Strategies in Dynamic Computerized Tomography, Sensing and Imaging, vol. 18, no. 10, pp. 1–20, 2017.
- B. N. Hahn, A motion artefact study and locally deforming objects in computerized tomography, Inverse Problems, vol. 33, no. 11, p. 114001, 2017.
2016
- B. N. Hahn and E. T. Quinto, Detectable singularities from dynamic Radon data, SIAM J. Imaging Sciences, vol. 9, no. 3, pp. 1195–1225, 2016.
- B. N. Hahn, Null space and resolution in dynamic computerized tomography, Inverse Problems, vol. 32, no. 2, p. 025006, 2016.
2015
- B. N. Hahn, Dynamic linear inverse problems with moderate movements of the object: Ill-posedness and regularization, Inverse Problems & Imaging, vol. 9, no. 2, pp. 395–413, 2015.
- D. Gerth, B. N. Hahn, and R. Ramlau, The method of the approximate inverse for atmospheric tomography, Inverse Problems, vol. 31, no. 6, p. 065002, 2015.
2014
- B. N. Hahn, Reconstruction of dynamic objects with affine deformations in computerized tomography, Journal of Inverse and Ill-posed Problems, vol. 22, no. 3, pp. 323–339, 2014.
- B. N. Hahn, Efficient algorithms for linear dynamic inverse problems with known motion, Inverse Problems, vol. 30, no. 3, p. 035008, 2014.
2013
- B. N. Hahn, A. K. Louis, M. Maisl, and C. Schorr, Combined reconstruction and edge detection in dimensioning, Meas. Sci. Technol, vol. 24, no. 12, p. 125601, 2013.
2012
- B. N. Hahn and A. K. Louis, Reconstruction in the three-dimensional parallel scanning geometry with application in synchrotronbased x-ray tomography, Inverse Problems, vol. 28, no. 4, p. 045013, 2012.
- B. N. Hahn, Reconstruction of dynamic objects in computerized tomography, Oberwolfach Reports, vol. 9, pp. 3069-3071B, 2012.
Current semester
Current courses can be found on the Teaching Page or directly in Campus.
Previous semesters
Summer term 2024:
- research semester
Winter term 2023/24:
- Höhere Mathematik 3 für el, kyb, mecha, phys
Summer term 2023:
- Master seminar: Dynamic inverse problems
- Fortgeschrittene Analysis für SimTech 2
Winter term 2022/23:
- Mathematical image processing
Summer term 2022:
- Introduction to Inverse Problems
Winter term 2021/22:
- Introduction to Optimization
Summer term 2021:
- Mathematical Image Processing
- Seminar zu Optimierung und inversen Problemen
Winter term 2020/21:
- Introduction to Optimization
- Seminar: Medizinische Bildgebung
Summer term 2020:
- Regularization of Inverse problems
theorie and application - Seminar: Sparsity und Compressed Sensing
since 04 / 2020 |
Professor at University of Stuttgart |
10 / 2018 | Positive Evaluation of the Junior Professorship |
04 / 2016 - 03 / 2020 | Junior Professor at University of Würzburg |
01 / 2015 - 03 / 2016 | Research and teaching assistant at the Institute of Applied Mathematics, Saarland University |
09 / 2014 - 12 / 2014 | Visiting Scholar and Lecturer at Tufts University, Medford, MA, USA |
01 / 2011 - 08 / 2014 | Research and teaching assistant at the Institute of Applied Mathematics, Saarland University |
09 / 2009 - 12 / 2010 | Graduate assistant within the DFG project "Combining Image Reconstruction and Image Evaluation", Saarland University |
04 / 2008 - 10 / 2009 | Student assistant at the Department of Mathematics, Saarland University |
Member of the Editorial Board
- Inverse Problems
- Sensing and Imaging
Organisation
- 05/2024: Workshop Inverse Problems - theories, methods and implementations as part of the Sino-German Mobility programme (CDZ), Stuttgart
- 04/2023: Oberwolfach Workshop Tomographic Inverse Problems: Mathematical Challenges and Novel Applications, with Prof. Arridge, Prof. Burger and Prof. Quinto
- 03/2022: Minisymposium Time-dependent parameter identification in imaging, at the "SIAM Conference on Imaging Science 2022", with PD. Dr. Kluth and Prof. Wald
- 07/2020: Minisymposium Time-dependent inverse problems in imaging at the "SIAM Conference on Imaging Science, virtual series", with Dr. Kluth and Dr. Wald
- 10/2019: Member of the Scientific Programme Committee for "Machine Learning in Medical Image Reconstruction Workshop“ at MICCAI 2019, Shenzhen
- 09/2019: Member of the Scientific Committee for the "Chemnitz Symposium on Inverse Problems", Frankfurt
- 08/2019: Conference Modern Challenges in Imaging - In the Footsteps of Allan Cormack, Tufts University, US, with Prof. Quinto, Prof. Gonzalez, Prof. Kilmer, Prof. Miller and Dr. Rigaud
- 01/2019: Oberwolfach Workshop Tomographic inverse problems: Theory and applications, with Prof. Burger and Prof. Quinto
- 06/2018: Minisymposium Limited data problems in imaging at the "SIAM Conference on Imaging Science", Bologna, Italien, with Prof. Frikel and Dr. Rigaud
- 06/2017: Member of the Programme Committee for the "International Conference on Sensing and Imaging“, Chengdu, China
- 03/2017: Minisymposium Radon-type transforms: Basis for emerging imaging im Rahmen der Konferenz "100 years of the Radon transform“, Linz, mit Dr. Rigaud
- 07/2016: Member of the Technical Committee for the "International Conference on Sensing and Imaging“, Taiyuan, China
- 05/2016: Minisymposium Tomographic Inverse Problems and Applications at the Conference "Inverse Problems: Modeling and Simulation“, Fethiye, Turkey with Prof. Quinto, Tufts University
- 08/2014: Minisymposium Tomography at the Conference "Inverse Problems - from Theory to Application“, Bristol, UK with Prof. Jiang, Peking University
- Lecture award of the student council mathematics in the category Bachelor additional modules for lecture "Optimization" (winter term 2021)
- Lecture award of the student council mathematics for digital teaching (summer term 2020)
- EAIP Young Scientist Award for distinguished contributions to inverse problems (2018)
- Highlights of IOP Inverse Problems (2012, 2014, 2015, 2016, 2017)