Tobias Kluth

Dr.- Ing. Tobias Kluth

Postdoc, Center for Industrial Mathematics, University of Bremen

Contact Me

About Me

I am a mathematician by training and finished my PhD in computer science related to neuroscience. Currently I am a postdoc in the Center for Industrial Mathematics at the University of Bremen focusing on applied inverse problems. I am fascinated by the idea to connect abstract mathematical results with various applications like, for example, tomography, image processing, aspects of human vision, etc.. My research interests are covered by the fields of

  • (nonlinear) inverse problems, parameter identification
  • mathematical modeling and simulation
  • algorithmic solutions, scientific computing
  • neural networks/deep learning

and applications in

  • imaging modalities, magnetic particle imaging, electrical impedance tomography
  • image processing/encoding
  • computer/human vision (neural behavior)

Short CV

Higher education

2015 Dr.-Ing. in Scientific Computing/Computer Science, University of Bremen.
Title: "Intrinsic dimensionality in vision: Nonlinear filter design and applications."
Supervisor: Dr. Christoph Zetzsche.
2011 Diploma in Industrial Mathematics, University of Bremen
Title: "3D Electrical Impedance Tomography with Sparsity Constraints."

Professional appointment

since 2016 Postdoc, ZeTeM, AG Technomathematik, University of Bremen
2011-2015 Research scientist/PhD student, Cognitive Neuroinformatics, University of Bremen

Projects

In the following you can find a selection of third-party funded projects I'm involved in:

Postdoc project in RTG 2224/1 (10/2016 - 04/2020) - Magnetic Particle Imaging

RTG 2224 This project is embedded in the framework of the Research Training Group π3 on parameter identification funded by the DFG and allows me to investigate different aspects of parameter identification in the context of magnetic particle imaging (MPI). The problem of modeling magnetic particle imaging, with respect to finding the correct integral kernel/system function, remains an unsolved problem. Existing model-based reconstruction techniques incorporate particle behavior based on the theory of paramagnetism. Methods based on ideal magnetic fields and on realistic magnetic fields are promising but have not yet reached the necessary quality of measured system functions.

Find out more about the RTG

Project MPI2 "Model-based parameter identification in magnetic particle imaging" (12/2016 - 05/2020)

RTG 2224 In the collaborative research project MPI2 funded by the BMBF model-based methods and their efficient realizations in algorithms are investigated since the beginning of 2017. Besides the university partners from University of Bremen (Prof. Dr. Peter Maass, Dr. Tobias Kluth), the  Aschaffenburg University of Applied Sciences (Prof. Dr. Hans-Georg Stark), Medical Center Hamburg-Eppendorf (Prof. Dr. Tobias Knopp) and  Saarland University (Prof. Dr. Thomas Schuster), industrial partners complement the consortium. SCiLS, a branch of Bruker Daltonik GmbH, and the Center for Radiology and Endoscopy of the UKE Hamburg-Eppendorf, as well as Bruker BioSpin, the manufacturer of the first commercially distributed MPI device, support the joint project.

Find out more

Project D-MPI "Dynamic inverse problems in Magnetic Particle Imaging" (since 05/2020)

Magnetic particle imaging is currently in the preclinical phase. However, several crucial dynamic aspects have been left out of consideration so far to simplify modeling, data acquisition and reconstruction. In this collaborative project with Prof. Dr. Bernadette Hahn (University of Würzburg) and me, we address three dynamic aspects of MPI resulting in a variety of dynamic inverse problems: (i) concentration dynamics, (ii) magnetic field dynamics, and (iii) particle magnetization dynamics. The project is funded by the DFG.

Project DELETO "Machine learning with correlative MR and high-throughput NanoCT" (since 04/2020)

Machine Learning (ML) and in particular the learning of large Neural Networks (NN), the so-called Deep Learning (DL), are currently among the most viral and widely discussed scientific topics, which have applications in many research areas. In the joint project DELETO (jointly with FAU Erlangen (Prof. Dr. Martin Burger) and Saarland University (Prof. Dr. Thomas Schuster)) funded by the BMBF, the mathematical research of DL in the solution of inverse problems is to be decisively advanced in order to make the reconstruction methods based on structural priorities and motion correction in the field of correlative MR and high-throughput NanoCT, which are computationally demanding due to the large amounts of data, more accurate and efficient. The goal is to integrate these methods into next generation devices. To this end, we are working closely with corresponding industrial partners. For the first time, model-based and data-driven methods will be applied in the big data technologies of correlative magnetic resonance imaging and high-throughput NanoCT, thus leading to improved next-generation devices. We participate in DELETO with the sub-project "Invertable Residual Networks", which aims at theoretical investigations of the regularization properties of certain network architectures, invertible residual networks (IRN).

More on my institutional webpage

Publications

Preprints

[3]   H. Albers, T. Kluth, T. Knopp.  A simulation framework for particle magnetization dynamics of large ensembles of single domain particles: Numerical treatment of Brown/Néel dynamics and parameter identification problems in magnetic particle imaging. arXiv:2010.07772, 2020.

[2]   S. Dittmer, T. Kluth, M. Henriksen, P. Maass.  Deep image prior for 3D magnetic particle imaging: A quantitative comparison of regularization techniques on Open MPI dataset. arXiv:2007.01593, 2020.

[1]   T. Kluth, B. Jin.  Exploiting heuristic parameter choice rules for one-click image reconstruction in magnetic particle imaging. Preprint can be provided upon request, 2020.

Journal

[14]   T. Kluth, B. Jin.  L1 data fitting for robust numerical reconstruction in magnetic particle imaging: quantitative evaluation on Open MPI dataset. arXiv:2001.06083 [math.NA], 2020. Accepted at International Journal on Magnetic Particle Imaging.

[13]   T. Kluth, C. Bathke, M. Jiang, P. Maass.  Joint super-resolution image reconstruction and parameter identification in imaging operator: Analysis of bilinear operator equations, numerical solution, and application to magnetic particle imaging. arXiv:2004.13091 [math.NA], 2020. Accepted at Inverse Problems.

[12]   T. Kluth, P. Szwargulski, T. Knopp.  Towards accurate modeling of the multidimensional magnetic particle imaging physics. In New Journal of Physics, 21(10):103032, 2019.

[11]   S. Dittmer, T. Kluth, P. Maass, D. Otero Baguer.  Regularization by architecture: A deep prior approach for inverse problems. In Journal of Mathematical Imaging and Vision, 2019.

[10]   T. Kluth, B. Jin.  Enhanced reconstruction in magnetic particle imaging by whitening and randomized SVD approximation. In Physics in Medicine & Biology, 64(12):125026, 2019.

[9]   J. Clemens, T. Kluth, T. Reineking.  β-SLAM: Simultaneous Localization and Grid Mapping With Beta Distributions. Information Fusion, 52:62-75, 2019

[8]   T. Kluth, B. Jin, G. Li.  On the Degree of Ill-Posedness of Multi-Dimensional Magnetic Particle Imaging. In Inverse Problems, 34(9): 095006, 2018

[7]   T. Kluth.  Mathematical models for magnetic particle imaging. In Inverse Problems, 34(8): 083001, 2018

[6]   T. Kluth, P. Maass.  Model uncertainty in magnetic particle imaging: Nonlinear problem formulation and model-based sparse reconstruction. In International Journal on Magnetic Particle Imaging, Article ID 1707004, 3(2), 10 pages, 2017.

[5]   C. Bathke, T. Kluth, C. Brandt, P. Maass.  Improved image reconstruction in magnetic particle imaging using structural a priori information. In International Journal on Magnetic Particle Imaging, Article ID 1703015, 3(1), 10 pages, 2017.

[4]   J. Clemens, T. Reineking, T. Kluth. An evidential approach to SLAM, path planning, and active exploration. In International Journal of Approximate Reasoning, 73:1-26, 2016.

[3]   T. Kluth, C. Zetzsche. Numerosity as a topological invariant. In Journal of Vision, 16(3):30, 1-39, 2016.

[2]  M. Gehre, T. Kluth, C. Sebu, P. Maass. Sparse 3D reconstructions in Electrical Impedance Tomography using real data. In Inverse Problems in Science and Engineering, 22(1):31-44, 2014.

[1]  M. Gehre, T. Kluth, A. Lipponen, B. Jin, A. Seppaenen, J. P. Kaipio, P. Maass. Sparsity Reconstruction in Electrical Impedance Tomography: An Experimental Evaluation. In Journal of Computational and Applied Mathematics,, 236(8):2126-2136, 2012.

Conference articles (full paper, peer-reviewed)

[7]   S. Dittmer, T. Kluth, D. Otero Baguer, and P. Maass. A deep prior approach to magnetic particle imaging. In F. Deeba, P. Johnson, T. Würfl, and J. Ye, editors, Machine Learning for Medical Image Reconstruction , pages 113–122. Springer International Publishing, 2020.

[6]   T. Reineking, T. Kluth, D. Nakath. Adaptive information selection in images: Efficient naive bayes nearest neighbor classification. In G. Azzopardi and N. Petkov, editors, Computer Analysis of Images and Patterns, volume 9256 of Lecture Notes in Computer Science, pages 350-361. Springer International Publishing, 2015.

[5]  T. Kluth, D. Nakath, T. Reineking, C. Zetzsche, K. Schill. Affordance-based object recognition using interactions obtained from a utility maximization principle. In Computer Vision-ECCV 2014 Workshops, volume 8926 of Lecture Notes in Computer Science, pages 406-412. Springer International Publishing, 2014.

[4]  T. Kluth, C. Zetzsche. Spatial numerosity: A computational model based on a topological invariant. In C. Freksa, B. Nebel, M. Hegarty, and T. Barkowsky, editors, Spatial Cognition IX, volume 8684 of Lecture Notes in Computer Science, pages 237-252. Springer International Publishing, 2014.

[3]  D. Nakath, T. Kluth, T. Reineking, C. Zetzsche, K. Schill. Active sensorimotor object recognition in three-dimensional space. In C. Freksa, B. Nebel, M. Hegarty, and T. Barkowsky, editors, Spatial Cognition IX, volume 8684 of Lecture Notes in Computer Science, pages 312-324. Springer International Publishing, 2014.

[2]  C. Zetzsche, K. Gadzicki, T. Kluth. Statistical Invariants of Spatial Form: From Local AND to Numerosity. In Proceedings of the Second Interdisciplinary Workshop The Shape of Things, pp. 163-172, 2013.

[1]  S. Eberhardt, T. Kluth, C. Zetzsche, K. Schill. From Pattern Recognition to Place Detection. In Proceedings of the International Workshop on Place-related Knowledge Acquisition Research (P-KAR), pp. 39-44, 2012.

Conference proceedings (short contributions, peer-reviewed)

[7]   H. Albers, T. Kluth, T. Knopp. MNPDynamics: A computational toolbox for simulating magnetic moment behavior of ensembles of nanoparticles. International Journal on Magnetic Particle Imaging, 6(2 Suppl. 1):ID 2009020, 3 pages, 2020.

[6]   T. Kluth, P. Szwargulski, T. Knopp. Towards accurate modeling of the multidimensional MPI physics. International Journal on Magnetic Particle Imaging, 6(2 Suppl. 1):ID 2009004, 3 pages, 2020.

[5]   M. Möddel, F. Griese, T. Kluth, T. Knopp. Estimating orientation using multi-contrast MPI. International Journal on Magnetic Particle Imaging, 6(2 Suppl. 1):ID 2009023, 3 pages, 2020.

[4]   T. Kluth, B. Hahn, C. Brandt. Spatio-temporal concentration reconstruction using motion priors in magnetic particle imaging. In T. Knopp and T. M. Buzug, editors, 9th International Workshop on Magnetic Particle Imaging 2019, pages 23-24. Infinite Science Publishing, 2019.

[3]   T. Kluth, B. Jin. Exploiting ill-posedness in magnetic particle imaging - system matrix approximation via randomized SVD. In T. Knopp and T. M. Buzug, editors, 8th International Workshop on Magnetic Particle Imaging 2018, pages 127-128. Infinite Science Publishing, 2018.

[2]   J. Flötotto, T. Kluth, M. Möddel, T. Knopp, P. Maass.  Improving generalization properties of measured system matrices by using regularized total least squares reconstruction in MPI. In T. Knopp and T. M. Buzug, editors, 8th International Workshop on Magnetic Particle Imaging 2018, pages 53-54. Infinite Science Publishing, 2018.

[1]   C. Bathke, T. Kluth, P. Maass. MPI reconstruction using structural prior information and sparsity. In T. Knopp and T. M. Buzug, editors, 8th International Workshop on Magnetic Particle Imaging 2018, pages 129-130. Infinite Science Publishing, 2018.

Misc

[5]   T. Kluth and P. Maass.  Model uncertainty in magnetic particle iamging: Motivating nonlinear problems by model-based sparse reconstruction. In T. Knopp and T. M. Buzug, editors, 7th International Workshop on Magnetic Particle Imaging 2017, page 83. Infinite Science Publishing, 2017.

[4]   C. Bathke, T. Kluth, C. Brandt, P. Maass.  Improved image reconstruction in magnetic particle imaging using structural a priori information. In T. Knopp and T. M. Buzug, editors, 7th International Workshop on Magnetic Particle Imaging 2017, page 85. Infinite Science Publishing, 2017.

[3]   T. Kluth, C. Zetzsche.  Visual numerosity: A computational model based on a topological invariant. In Perception ECVP, volume 43, page 163, 2014.

[2]   T. Kluth, D. Nakath, T. Reineking, C. Zetzsche, K. Schill.  Sensorimotor integration using an information gain strategy in application to object recognition tasks. In Perception ECVP, volume 42, page 223, 2013.

[1]   S. Eberhardt, T. Kluth, M. Fahle, C. Zetzsche.  The role of nonlinearities in hierarchical feed-forward models for pattern recognition. In Perception ECVP, volume 41, page 241, 2012.

Talks and other scientific contributions

[26]  T. Kluth. Model-based to data-driven methods for imaging in application to magnetic particle imaging. Talk at Imaging meets computational PDEs Workshop, virtual conference (Bath, UK), 2020. Slides upon request.

[25]  T. Kluth, P. Szwargulski, T. Knopp. Towards accurate modeling of the multidimensional MPI physics. Talk at 10th International Workshop on Magnetic Particle Imaging, virtual conference, 2020. Slides upon request.

[24]  T. Kluth. Modeling of the Magnetic Particle Imaging Physics - Theoretical insights and image reconstruction. Talk at 2nd IMA Conference On Inverse Problems From Theory To Application, London, UK, 2019. Slides upon request.

[23]  T. Kluth. Deep image priors for magnetic particle imaging. Invited talk at International Congress on Industrial and Applied Mathematics (ICIAM), Valencia, Spain, 2019. Slides upon request.

[22]  T. Kluth. Enhanced Reconstruction in Magnetic Particle Imaging by Whitening and Randomized SVD Approximation. Invited talk at 10th Applied Inverse Problems Conference, Grenoble, France, 2019. Slides upon request.

[21]   T. Kluth, B. Hahn, C. Brandt.  Spatio-temporal concentration reconstruction using motion priors in magnetic particle imaging. Talk at 9th International Workshop on Magnetic Particle Imaging, New York, USA, 2019. Slides upon request.

[20]  T. Kluth. The model-based reconstruction problem in magnetic particle imaging. Invited talk at International Conference on Sensing and Imaging, Liuzhou, China, 2018. Slides upon request.

[19]  T. Kluth. Spatio-temporal concentration estimation in magnetic particle imaging using a priori motion information. Invited talk at IFIP TC 7 Conference on System Modelling and Optimization, Essen, Germany, 2018. Slides upon request.

[18]  T. Kluth. Modeling of magnetic particle imaging. Invited talk at Universitaet Hamburg-Harburg (invited by Prof. Dr. Christina Brandt), Hamburg, Germany, 2018. Slides upon request.

[17]  T. Kluth. Mathematical models in magnetic particle imaging. Talk at SIAM Conference on Imaging Science, Bologna, Italy, 2018. Slides upon request.

[16]  T. Kluth, B. Jin. Exploiting ill-posedness in magnetic particle imaging - system matrix approximation via randomized SVD. Talk at 8th International Workshop on Magnetic Particle Imaging, Hamburg, Germany, 2018. Slides upon request.

[15]  T. Kluth. Modeling of magnetic particle imaging. Invited tutorial talk at 8th International Workshop on Magnetic Particle Imaging (invited by Prof. Dr. Thorsten Buzug, Prof. Dr. Tobias Knopp), Hamburg, Germany, 2018. Slides upon request.

[14]  T. Kluth. Model-based magnetic particle imaging. Invited talk at WIAS Berlin (invited by Prof. Dr. Michael Hintermueller), Berlin, Germany, 2018. Slides upon request.

[13]  T. Kluth. Model-based magnetic particle imaging. Invited talk at Oberseminar Wissenschaftliches Rechnen, Julius-Maximilians-Universitaet Wuerzburg (invited by Prof. Dr. Bernadette Hahn), Wuerzburg, Germany, 2017. Slides upon request.

[12]  T. Kluth. Operator uncertainty in model-based magnetic particle imaging. Invited talk at Inverse Problems Seminar, University College London (invited by Dr. Bangti Jin), London, UK, 2017. Slides upon request.

[11]  T. Kluth. Nonlinear parameter identification problems for model-based magnetic particle imaging (joint work with P. Maass). Talk at 9th Applied Inverse Problems Conference, Hangzhou, China, 2017. Slides upon request.

[10]  T. Kluth, P. Maass. Model Uncertainty in Magnetic Particle Imaging. Talk at the 7th International Workshop on Magnetic Particle Imaging, Prague, 2017. Slides upon request.

[9]  C. Bathke, T. Kluth, C. Brandt, P. Maass. Magnetic Particle Imaging: Improved image reconstruction using structural a priori information. Talk at the 22nd Inverse Days, Kuopio, 2016. Slides upon request.

[8]  T. Kluth. 3D electrical impedance tomography with sparsity constraints. Invited talk at the workshop Compressive Sensing and Sparsity: Theory and Applications in Tomography, Manchester, 2015.

[7]   T. Reineking, T. Kluth, D. Nakath. Adaptive information selection in images: Efficient naive bayes nearest neighbor classification. Poster at 16th International Conference on Computer Analysis of Images and Patterns, Valletta, 2015.

[6]  T. Kluth. Intrinsic dimensionality in vision: Nonlinear filter design and applications. Talk at my Doctorate Defense, Bremen, 2015.

[5]  T. Kluth, C. Zetzsche. Spatial numerosity: A computational model based on a topological invariant. Talk at International Conference on Spatial Cognition, Bremen, 2014.

[4]  T. Kluth, C. Zetzsche. Visual numerosity: A computational model based on a topological invariant. Poster at ECVP, Belgrade, 2014.

[3]  T. Kluth, C. Zetzsche. Numerical cognition in vision based on a topological invariant. Poster at OCCAM, Osnabrueck, 2014.

[2]  T. Kluth, D. Nakath, T. Reineking, C. Zetzsche, K. Schill. Sensorimotor integration using an information gain strategy in application to object recognition tasks. Poster at ECVP, Bremen, 2013.

[1]  T. Kluth, S. Eberhardt, M. Fahle, C. Zetzsche. Slow features between invariance and selectivity. Poster at OCCAM, Osnabrueck, 2012.