Tervetuloa, Welcome, Willkommen!
About me
I am an applied mathematician and assistant professor for computational and mathematical methods for imaging at the University of Hamburg. Therefore, I am member of Center of Optimization and Approximation and associated with the Institute for Biomedical Imaging at the University hospital Hamburg Eppendorf (UKE).
My actual research covers large-scale inverse problems in biological and medical applications such as for example fluorescence microscopy, photo acoustic tomography and magnetic particle imaging. More precisely, I am working on variational regularization methods, dynamic inverse problems, Bayesian inversion, and approximation error modelling.
Members of the research group
- Christiane Schmidt
- Julian Muldoon
- Inga Glöckner
- Lisa Schönrock
- Amol Bains
Former members of the research group
- Dawit Hailu
- Aoxiang Geng
- Ivan Pabon
- Dennis Hamann, Bsc
- Ikram Jumakulyyev, Msc
- Lina Nawwas, Msc
- Thomas Yu, Msc
- Frederico Lucchesi, Msc
News
PhD position
We are looking for a PhD candidate within the DASH graudate school. The topic are inverse problems in X-ray science and will be supervised jointly with Prof. Rohringer from the department of physics. Apply here .
Upcoming conferences
I will attend the Oberwolfach workshop "Tomographic Inverse Problems: Theory and Applications" from 27.1.-2.2.19 and the API conference in July 2019.
Our project "Multi-messenger x-ray science - Solving inverse problems of x-ray crystallography with constraints by x-ray emission spectra" has been accepted for funding from the DESY Strategy Fond.
We are looking for a PostDoc for our project. More information your can find here.
My research
Article
Erb, W.; Weinmann, A.; Ahlborg, M.; Brandt, C.; Bringout, G.; Buzug, T.M.; Frikel, J.; Kaethner, C.; Knopp, T.; März, T.; Möddel, M.; Storath, M.; Weber, A.: Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging. Inverse Problems, 34(5):2018.doi:10.1088/1361-6420/aab8d1
Bathke, C.; Kluth, T.; Brandt, C. & Maaß, P.: Improved image reconstruction in magnetic particle imaging using structural a priori information. International Journal On Magnetic Particle Imaging, 3(1):2017.
online availble here
Storath, M.; Brandt, C.; Hofmann, M.; Knopp, T.; Salamon, J.; Weber, A. & Weinmann, A.: Edge preserving and noise reducing reconstruction for magnetic particle imaging. IEEE Transactions on Medical Imaging, 36(1):74-85, 2017.
doi:10.1109/TMI.2016.2593954
Brandt, C., Maass, P., Piotrowska-Kurczewski, I., Schiffler, S., Riemer,O., and Brinksmeier, E.: Mathematical methods for optimizing high precision cutting operations. International Journal of Nanomanufacturing, 8(4):306–325, 2012.
doi:10.1504/IJNM.2012.048580.
Brandt, C., Niebsch, J., Ramlau, R., and Maass, P.: Modeling the influence of unbalances for ultra-precision cutting processes. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 91(10):795–808, 2011.
doi:10.1002/zamm.201000155.
Piotrowska, I., Brandt, C., Karimi, H. R., and Maass, P.: Mathematical model of micro turning process The International Journal of Advanced Manufacturing Technology, Volume 45(1):33–40, 2009.
doi:10.1007/s00170-009-1932-z.
Brandt,C., Niebsch, J., and Vehmeyer, J.: Modelling of ultra-precision turning process in consideration of unbalances. Advanced Materials Research, 223:839–848, 2011.
doi:10.4028/www.scientific.net/AMR.223.839
Gossiaux, P.B., Aichelin, J., Brandt, C., Gousset, T., and Peigné, S.: Energy loss of a heavy quark produced in a finite-size quark-gluon plasma. Journal of Physics G: Nuclear and Particle Physics, 34(8):S817, 2007.
doi:10.1088/0954-3899/34/8/S103.
Gossiaux, P.B., Peigné, S., Brandt, C., and Aichelin, J.: Energy loss of a heavy quark produced in a finite size medium. Journal of High Energy Physics, 4(04):012, 2007.
doi:10.1088/1126-6708/2007/04/012.
Thesis
Brandt, C.: Regularization of Inverse Problems for Turning Processes. Ph.D. thesis, University of Bremen, Logos, 2012available by Logos
Book chapter
Andres, M., Blum, H., Brandt, C., Carstensen, C., Maass, P., Niebsch, J., Rademacher, R., Ramlau, R., Schröder, A., Stephan, E.-P., and Wiedemann, S.: Process Machine Interactions, Adaptive finite elements and mathematical optimization methods. Lectures Notes in Production Engineering. Springer, 2013.doi:DOI:10.1007/978-3-642-32448-2.
Brandt, C., Krause, A., Niebsch, J., Vehmeyer, J., Brinksmeier, E., Maass, P., and Riemer, O.: Process Machine Interactions, Surface Generation Process with Consideration ot the Balancing State in Diamond Machining. Lectures Notes in Production Engineering. Springer, 2013.
doi:DOI: 10.1007/978-3-642-32448-2.
Piotrowska-Kurczewski, I., Brandt, C., Maass, P., and Riemer, O.: Micro Metal Forming, chapter Simulation technologies - Inverse Modelling, pages 368–379. Springer, 2013.
Brandt, C., Piotrowska, I., Karimi, H., Niebsch, J., Ramlau, R., Krause, A., Riemer, O., and Maass, P.: Process machine interaction model for turning processes. International Journal of Control Theory and Applications, 1(2):145–153, 2008.
Conference proceedings (reviewed)
Kluth, T.; Hahn, B.N. and Brandt, C.: Spatio-temporal concentration reconstruction using motion priors in magnetic particle imaging. Proceedings of the International Workshop on Magnetic Particle Imaging 2019, March 17-19. 2016, New York, USA, 2019.Brandt, C. and Hauptmann, A.: Fast temporal regularized reconstructions for magnetic particle imaging. Proceedings of the International Workshop on Magnetic Particle Imaging 2019, March 17-19. 2016, New York, USA, 2019.
Storath, M., Brandt, C., Hofmann, M., Knopp, T. , Weber, A., Weinmann, A.: Fused lasso regularization for magnetic particle imaging. Proceedings of the International Workshop on Magnetic Particle Imaging 2016, March 16-18. 2016, Lübeck, Germany, 2016.
Brandt, C., Niebsch, J., and Vehmeyer, J.: Modelling of ultra-precision turning process in consideration of unbalances. In Outeiro, J.C., editor, Proceedings of the 13th CIRP Conference on Modeling of Machining Operations, May 12-13. 2011, Sintra, Portugal, volume 223, pages 839–848. 2011. www.scientific.net/AMR.223.839>
Niebsch, J., Ramlau, R., and Brandt, C.: On the interaction of unbalances and surface quality in ultra-precision cutting machinery. In SIRM 2011, Darmstadt, Germany. 2011.
Brandt, C., Niebsch, J., Maass, P., and Ramlau, R.: Simulation of process machine interaction for ultra precision turning. In Proceedings of the 2nd International Conference on Process Machine Interactions, June 10-11, 2010, Vancouver, Canada. 2010.
Brandt, C., Krause, A., Brinksmeier, E., and Maass, P.: Force modelling in diamond machining with regard to the surface generation process. In Proceedings of the 9th International Conference and Exhibition on Laser Metrology, machine tool, CMM and robotic performance, LAMDAMAP 2009, London, 30.06.-02.07.2009, pages 377–386. 2009.
Gossiaux, P.B., Peigné, S., Brandt, C., and Aichelin, J.: Energy loss of a heavy quark produced in a finite-size quark-gluon plasma
doi:10.1088/0954-3899/34/8/S103. QM2006 Proceedings; 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (QM2006), Shanghai, China, November 14-20, 2006.
2019
Tomographic inverse problems: theory and application
Oberwolfach 2019, 27.1-2.2.2019
SIAM conference on computational science and engineering, 25.2-1.3.2019
Spokane, USA
Invited by Samuli Siltanen and Tatiana Bubba
2018
EUCCO 2018, 10.-12.6.2018
Trier, Germany
Plenary talk
Siam Imaging 2018, 5.-8.6.2018
Bologna, Italy
Invited by Traufiquar Khan and Cristiana Sebu
GAMM, March 2018, 19.-23.3.2018
München, Germany
Invited by Felix Krahmer and Benedict Wirth
2017
Conference on Applied Inverse Problems, May 2017
Hangzhou, China
2016
Imaging with modulated/incomplete data, 22.-24.9.2016
Graz, Austria
Inverse problems seminar at Helsinki University, 15.6.2016
Helsinki, Finland
Invited by Samuli Siltanen
SIAM Imaging 2016
23.-26.5.2016, Albuquerque, USA
Invited by Cecile Louchet
International Workshop on Magnetic Particle Imaging IWMPI 2016
16.-18.3.2016, Lübeck, Germany
2015
Inverse Days 2015, 8.-10.12.2015
Lappeenranta, Finland
Mini-symposium on "Mathematical Methods for MPI" at the DMV 2015, 21.-25.9.2015,Hamburg
Invited by Wolfgang Erb
Applied Inverse Problems 2015
May 2015, Helsinki, Finland
2014
Seminar AG Imaging, University Münster,
3.12.2014
Invited by Martin Burger
DSR seminar at the Helmholtz Institut München
7.7.2014
Invited by Frank Filbir
Sparse Image Reconstruction for Photoacoustic Tomography Using Shearlets
Workshop "Wavelets and Applications"
22.5.2014, Université Libre de Bruxelles, Belgium
Invited by Christine de Mol
SIAM Conference on Imaging Science
12-14.5.2014, Hongkong, China
Mecklenburger Workshop "Approximationsmethoden und schnelle Algorithmen, 17-20.03.2014, Hasenwinkel
2013
Advances In Mathematical Image Processing, 30.09.-2.10.2013, Annweiler
Applied Inverse Problems Conference AIP 2013, 1.-5.07.2013, Daejeon, Korea
2012
Inverse Problems: Modelling and Simulation 2012, 21.-26.05.2012, Antalya, Turkey
Oberseminar Analysis Universität Osnabrück, 14.05.2013, Osnabrück
(invited talk)
Winterseminar der AG Technomathematik der Universität Bremen, 2012, 28.-29.2.2912, Ganderkesee
Magnetic Particle Imaging (MPI) is a novel imaging modality for biomedical diagnostics that determines the spatial distribution of magnetic nanoparticles by measuring the non-linear magnetization response of the particles to an applied magnetic field. The advantages of MPI are the high dynamic spatial and temporal resolution and that it does not employ any ionizing radiation.
Actual research projects on MPI
Flow estimation with a priori edge information for MPI/MRI data , joint work with Ikram Jumakulyyev and Tobias Kluth
Joint reconstruction in multi-color MPI, joint work with Martin Storath, Martin Hofmann and Tobias Knopp
Approximation error modelling for model-based MPI, joint work with Aku Seppänen
Time based regularization for 4D MPI, joint work Andreas Hauptmann
It is a joint research within of the scientific network "Mathematical methods for Magnetic Particle Imaging (MIEM). The network funded by the DFG consists of 9 researchers and it is lead by Dr. Wolfgang Erb from the University of Lübeck. For more information, see the official MIEM homepage.
The main objective of this research is the development of mathematical methods for three imaging modalities in biological and medical applications: fluorescence microscopy (FM), photo-acoustic tomography (PAT) and magnetic particle imaging (MPI). All imaging applications have in common that the desired object such as in PAT and MPI the cancer cell in the human body is not directly observable but can be measured only indirectly.
In order to reconstruct the desired object, one has to solve the so-called inverse problem. In this project, mathematical methods for solving inverse problems are developed which consider modelling errors and uncertainties of the underlying models in the inversion. It is expected that the image reconstruction quality will be increased significantly in all three applications. In particular, the improvements are assumed to contribute to the development of PAT and MPI as medical imaging techniques in clinical practice.
This project is founded by the Academy of Finland.
Related Publications:
Brandt, C.; Seppänen, A. : Recovery from errors due to domain truncation in magnetic particle imaging -- approximation error modeling approach. Journal of Mathematical Imaging and Vision, 2018.10.1007/s10851-018-0807-z
Novel X-ray sources (in particular FELs) allow for the first time to study complex chemical reactions and catalysis in time-dependent manner. While x-ray diffraction gives access to the structure of the underlying system (atomic position), x-ray emission spectroscopy is a complementary technique, to gain chemical knowledge (such as, for example the spin and oxidation state of a particular reaction center). The time-dependent observation of the breaking and formation of electronic bonds is, however, still a delicate task and relies on the interpretation of experimental data based on models.
At the current stage, a few pioneering groups perform x-ray scattering and x-ray emission spectroscopy within one experimental set up and build models to interpret these data. The data analysis and the reconstruction of the underlying physical quantities (determination of the electron density by solving the phase problem of crystallography) are, however, performed independently and separately for each method. In this project, we aim for the next rigorous step, by developing a common data analysis, reconstruction and model building approach combining x-ray diffraction and emission spectroscopy. This novel holistic approach has the potential to strongly improve on the resolution of the chemically-relevant valence electronic density and their current densities.
This project is founded by the DESY Strategy Fund. It is a joint project with Prof. N. Rohringer and Prof. S. Techert from DESY.
10.1007/s10851-018-0807-z
Brandt, C.; Hauptmann, A.: Real time reconstruction for 4D Magnetic Particle Imaging.
More generally my research interests are :
- Medical and biological imaging
- Modelling and simulation
- Regularization with sparsity constraints
- Dynamic inverse problems
- Bayesian inversion and approximation error modelling
Collaborations
Prof. Martin Storath
Hochschule Würzburg-SchweinfurtProf. Tobias Knopp, Dr. Martin Hofmann
Universitätsklinikum Hamburg-EppendorfSektion für Biomedizinische Bildgebung
Institut für Biomedizinische Bildgebung
Technische Universität Hamburg
Dr. Wolfgang Erb
Università degli Studi di PadovaItaly
Prof.P. Maass, Dr. Tobias Kluth
Center for Industrial MathematicsUniversity of Bremen
Dr. Andreas Hauptmann
University College LondonGreat Britain
Dr. Aku Seppänen
University of Eastern FinlandKuopio, Finland
Prof. Nina Rohringer
Deutsches Elektron-Synchrotonand Universiät Hamburg
Prof. Simone Techert
Deutsches Elektron-Synchrotonand Universiät Göttingen
Teaching
Actual courses
Convex optimization
I will give a course on convex optimization during summer semester 2019. The course will cover a introduction to convex optimization in infinite dimensional spaces and modern splitting approaches for minimization.
Mathematik in der Medizin
Lothar Collatz Seminar (together with Stefan Heitmann) (Summer semester 2019)
Supervision of theses
I am offering topics for thesis such that inverse problems, image reconstruction, optimization methods and Bayesian inversion related to applications in bio/medical imaging. There is also the possibility to have a joint project with the Medical university center Eppendorf (UKE). Current theses are:- Amol Bains, Variationelle Tikhonov-Regulariserungsverfahren für Entfaltungsprobleme, Bsc University of Hamburg
- Julian Muldoon, Radon basierte Rekontruktion für Lasterinterferometrie Msc, University of Hamburg, supervision together with Dr. Rene Wernder (UKE HH Eppendorf)
- Ina Glöckner, Reconstruction methods for multi-color magnetic particle imaging, Msc, University of Hamburg, supervision together with Dr. Martin Möddel (UKE HH Eppendorf)
Previous Courses
Inverse problems
Master course on inverse problems. We will treat the classical theory of linear inverse problems. (Winter semester 2018/19)
Computer tomography
Master course on computer tomography. This is the first part of the inverse problems course. (Winter semester 2018/19)
Optimierung
Bachelor course on optimization (Summer semester 2018)
Wirkung sucht Ursache - Inverse Probleme in den Naturwissenschaften
Lothar Collatz Seminar (together with Stefan Heitmann) (Summer semester 2018)
Computer tomography
Course on computer tomography
and short introduction to inverse problems (Winter semester 2017/18)
Optimization
Course on convex optimization
in infinite dimesions (Summer semester 2017)
Inverse Problems
Exercises on inverse problems (Winter semester 2016/27)
Inverse Problems
course together with Prof. Kunis (Summer semester 2014)
Mathematics I for production engineering
2 tutorials (winter semester 2012/13)
Analysis II
2 tutorials ( summer semester 2012 )
Supervised theses and projects
- Dawit Hailu, Reconstructions for dynamic x-ray data with help of shearlets, Msc, University of Hamburg
- Aoxiang Geng, Improving calibration measurements in magnetic particle imaging by compressed sensing, Msc, University of Hamburg, superivision together with Dr. Martin Möddel (UKE HH Eppendorf)
- Ivan Pabon, Adaptive spatio-temporal regularization for robust nonlinear registration in artifact-affected 4D medical images, Msc, University of Hamburg, supervision together with Dr. Rene Werner (UKE HH Eppendorf)
- Dennis Hamann, Non-convex stochastic optimization, Bsc 2018, University of Hamburg
- Ikram Jumakulyyev, Joint motion estimation and image reconstruction by incorporating a priori edge information, Msc 2018, University of Hamburg
- Lina Nawwas, Bias-reduction for sparsity promoting regularization in magnetic particle imaging, Msc 2018, University of Gdansk/University of Hamburg
- Thomas Yu, Optimization for HDR brachytherapy, Msc 2017, University of Hamburg, supervision together with Prof. Schlaefer, TUHH
- Federico Lucchesi, Adversarial domain adaption for semantic segmentation Msc 2017, Unversity of Hamburg, supervision together with Prof. Vazquez, Universitat Autònoma de Barcelona
- Tuukka Heiskanen, Superresolution in microscopy, Bsc 2017, University of Eastern Finland
- Arun Pandey and Ikram Jumakulyyev, Optical flow estimation, Summer project 2017, University of Hamburg
- Tuukka Heiskanen, Deconvolution in fluorescence microscopy, Summer trainee 2016, University of Eastern Finland
- Phil Gralla, Mathematical methods for controlling ultra precise processes of machining, Bsc 2012, Supervision together with Dr. I. Piotrowska, University of Bremen.
- Philipp Welz, Regenerative chattering for micro cutting processes, Bsc 2011, supervision together with Prof. P. Maass, University of Bremen.
- Florian Dollinger, A continuous model for determination of dwell periods for a form corrective polishing process, Diploma thesis 2010 , supervision together with Dr. I. Piotrowska, University of Bremen.
- Thi Bach, Mathematical optimization of micro polishing, Student project (12 month) 2010, supervision together with Dr. I. Piotrowska, University Bremen.
Short CV
Academic positions
Since 03 2017
Assistant professor at the University of Hamburg.
Research group: Mathematical and computational methods in medical imaging
09/2015 - 02 2017
Academy post-doctoral researcher in the Inverse Problems group at the Eastern University of Finland in Kuopio.
- Academy of Finland project "Approximation error modelling in large scale inverse problems in imaging" (2015-2018)
04/2013 - 08/2015
Post-doctoral researcher in the research group "Applied and Numerical Analysis" at the University Osnabrück working within the
- Helmholtz young investigator group "Fast algorithms for biomedical imaging" (Helmholtz Zentrum München)
01/2008 - 04/2013
Research assistant in the at the WG Industrial Mathematics at the Center for Industrial Mathematics at the University Bremen, working within the
- DFG priority program SPP1180, project "Mathematical methods for precision balancing of machine tool" (2008-2011)
- SFB "Micro cold forming" (2012-2013)
11/2007 - 12/2007
Research assistant in the research group "Solid physics" at the University Rostock, working within the SFB 652, project B1 Exciton matter in mesoscopic potentials
- Tasks: Implementation of a phase retrieval algorithm for ultrashort laser pulses
Education
2008 - 2012
Doctoral studies in the research group "Industrial mathematics" at the University Bremen
2012: Doctorate degree in mathematics, University Bremen
- Thesis: "Regularization of Inverse Problems for Turning Processes"
- Supervisor: Prof Peter Maass
10/2001 - 08/2007
08/2007
Diploma studies in mathematics , University Rostock
Diploma degree in mathematics, University Rostock
- Thesis: "Numerical phase reconstruction" (Numerical phase retrieval)
- Supervisor: Prof Manfred Tasche
10/2002 - 08/2007
10/2006 - 07/2006
08/2007
Diploma studies in physics, University Rostock
Master studies in physics, Erasmus exchange program, University Nantes
Master degree in physics, University Nantes (France)
- Master thesis: "Energy loss of a parton in a quark-gluon-plasma"
- Supervisor: Stéphane Peigné
Contact me
Office adress
Universität HamburgDepartment of Mathematics
Bundesstraße 55
20146 Hamburg
Office: Geomatikum 104
Phone: +49 -40 42838 4076
Mail: Christina.Brandt(ad)uni-hamburg.de
Postal address
Universität HamburgFachbereich Mathematik
Bundesstraße 55
20146 Hamburg
Germany