This project was funded by an Advanced Grant from the European Research Council

Follow this link to learn more about the project and its objectives. Additional information is available in the Midway Report, and a summary of the project and the scientific results is available in the Final Activity Report.

Summary of the Achievements of the Project

It is of vital importance that the images are as sharp, detailed and reliable as possible, so scientists, engineers, doctors etc. can make the correct decisions. To achieve high-definition tomography - sharper images with more reliable details - we must use prior information consisting of accumulated knowledge about the object.

Overall Outcome: Insight and Framework
Previous efforts were often based on ad-hoc techniques and naive algorithms with limited applications and ill-defined results. This project focused on obtaining deeper insight and developing a rigorous framework. We carefully analyzed the underlying mathematical problems and algorithms, and we developed new theory that provides better understanding of their challenges and possibilities. This insight allowed us to develop a solid framework for precisely formulated CT algorithms that compute much more well-defined results. We laid the groundwork for the next generation of rigorously defined algorithms that will further optimize the use of prior information.

The road to this insight involved specific case studies related to the formulation and use of prior information, involving such applications as X-ray phase-contrast tomography, fusion plasma physics, and underwater pipeline inspection. Below we list the highlights of these cases.

Understanding of Sparsity for Low-Dose CT
We characterize how the prior information that an object is "simple" - in mathematical terms, sparse - allows us to compute reliable images from very limited data, and we show that the sufficient amount of CT data depends in a simple way on the sparsity. This is essential in medical and engineering CT where one must minimize the X-ray dose and shorten measurement time.

Superior Localization in Electrical Impedance Tomography
By incorporation the prior information that the details stand out from the background, we can now compute images with superior localization and contrast. Moreover we developed new theory that, for the first time, precisely describes the obtainable resolution and the optimal measurement configuration. This is essential in industrial process monitoring where measurement constraints often limit the amount of data.

Superior Use of Textural Training Images
For textural images, we developed a new mathematical and computational framework that is superior to other methods for limited-data. It is particularly suited for computing reliable segmentations of these images. To do this we use prior information in the form of training images that the computed image must resemble.

Novel Convergence Analysis of Iterative Methods
We developed novel theoretical insight into the advantages and limitations of the iterative methods that are required for 3D tomography computations. This insight guided the development of new software suited for many-core and GPU computers, as well as public-domain software with model implementations of these algorithms.

Correct Handling of Noise
We formulate correct mathematical models for the measurement noise and we develop new computational algorithms especially suited for using prior information about non-Gaussian noise. We show that these noise priors improve both the algorithms and the images, compared to the standard algorithms that are based on cruder models.

Novel Use of Prior Information about Structure
Structural prior information states that the image contains visual structures, e.g., texture along certain directions. Incorporation of this kind of information prompted us to develop new anisotropic higher-order techniques that avoid the unwanted artifacts of traditional methods (such as total variation).

Motion Modeling for Dynamic Tomography
The precised motion behavior of an object is unknown, and therefore we jointly perform motion estimation and image reconstruction. We derive a motion model to handle the challenging task of representing formation and closing af cracks in the object.

Permanent Team Members All members are from the Scientific Computing section. Professor Per Christian Hansen - Principal Investigator Associate Professor Kim Knudsen Associate Professor Yiqiu Dong Associate Professor Martin S. Andersen

Associated Members

• Professor Anders Bjorholm Dahl, DTU Compute.
• Kristoffer Hoffmann, now with Sven Ole Hansen ApS. PhD project: Reconstruction Methods for Inverse Problems with Partial Data (finished 2014).
• Associate Professor Mirza Karamehmedovic, DTU Compute.
• Federica Sciacchitano, now with University of Genoa. PhD project at DTU Compute: Image Reconstruction Under Non-Gaussian Noise (September 2013 - October 2016), PhD Thesis.
• Angeliki Xenaki, now with Center for Maritime Research and Experimentation (CMRE). PhD project: High-Resoluiton Imaging Methods in Arrays Signal Processing (finished 2015).
• Jürgen Frikel, now with University of Regensburg. H.C. Ørsted Post Doc with DTU Compute (April 2015 - August 2016).
• Ivan G. Kazantsev, DTU Compute and DTU Physics (project ended June 2015).

Other Members of the Team

• Post Doc Jakob Sauer Jørgensen, now with Manchester University. Project: Computations with Sparse Representations (September 1, 2013 - July 31, 2017)
• Sara Soltani, now with 3Shape A/S. PhD project: Training Sets in Large-Scale Reconstruction Methods (September 1, 2012 - August 31, 2015), PhD Thesis
• Mikhail (Mike) Romanov, PhD project: Statistical Priors in Variational Reconstruction Methods (November 1, 2012 - October 31, 2015), PhD Thesis
• Henrik Garde, now with Aalborg University. PhD project: Prior Information in Inverse Boundary Problems (March 1, 2013 - February 29, 2016), PhD Thesis
• Rasmus Dalgas Kongskov, now with 3Shape A/S. PhD project: Segmentation-Driven Tomographic Reconstruction (started September 1, 2014), PhD Thesis.
• Hari Om Aggrawal, now with University of Lübeck. PhD project: Priors for Temporal Tomographic Image Reconstruction (April 1, 2015 - May 31, 2018).
• Post Doc Lauri Harhanen, now with KaVo Kerr, Finland. Project: Formulation and Application of Priors in Spectral CT (May 1, 2015 - July 31, 2016).
• Post Doc Hans Martin Kjer, now with DTU Compute and the Danish Research Centre for Magentic Resonance. Project: Joint CT Reconstruction and Segmentation (January 1, 2016 - July 31, 2017).

Visiting and Honorary Professors Professor Bill Lionheart from Manchester University was visiting professor at DTU Compute and associated with this project. He was funded by a visiting professor scholarship from the Otto Mønsted Fonden. He visited us in October 2013 and again in June and July 2014, and traveled to Copenhagen on his boat Tui. Professor Samuli Siltanen from University of Helsinki is adjunct professor at DTU and was also associated with this project. Professor Todd Quinto from Tufts University was Otto Mønsted Visiting Professor at DTU Compute in the fall and winter of 2016.

Related Research Projects

• Improved Impedance Tomography with Hybrid Data is another research project in the Scientific Computing section, funded by a grant from the Danish Council for Independent Research | Natural Sciences.
• CINEMA: Alliance for Imaging and Modelling of Energy Applications has members from DTU Compute and several other departments as well as industrial collaborators; it is funded by a grant from the Danish Council for Strategic Research.

Activities - Scientific Publications, Visitors, etc.

Software and Data

• AIR Tools II, a Matlab package of algebraic iterative reconstruction methods - improved implementation.
• IR Tools, a Matlab pacage of iterative regularization methods and test problems for large-scale linear inverse problems.
• DLCT-Toolbox, a Matlab package for the dictionary learning approach to tomograhic image reconstruction, written by Sara Soltani: zip file and manual.
• DTGV-Reg, a Matlab package for Directional Total Variation (DTV) and Directional Total Generalized Variation (DTGV) regularization, written by Rasmus Dalgas Kongskov: zip file and readme file.
• Matlab software for handling non-Gaussian noise: available from the homepage of Yiqiu Dong.
• Software for kernel regularization and ring reduction: available from the homepage of Martin S. Andersen.
• SparseBeads Dataset for benchmarking of sparsity-regularized reconstruction methods (Jakob Sauer Jørgensen et al.).

Accepted and Published Papers

1. H. O. Aggrawal, M. S. Andersen, S. Rose, and E. Y. Sidky, A convex reconstruction model for X-ray tomographic imaging with uncertaint flat-fields, IEEE Trans. Comput. Imaging, 4 (2018), pp. 17-31, DOI: 10.1109/TCI.2017.2723246 (open access).
2. H. O. Aggrawal, M. S. Andersen, and J. Modersitzki, An image registration framework for discontinuous mappings along cracks; in Ž. Špiclin, J. McClelland, J. Kybic, and O. Goksel (Eds), Biomedical Image Registration. WBIR 2020, Lecture Notes in Computer Science, vol 12120, Springer, 2020, DOI: 10.1007/978-3-030-50120-4_16 (open access). This paper received the '1st best paper award' at the WBIR 2020 conference.
3. M. S. Andersen and P. C. Hansen, Generalized row-action methods for tomographic imaging, Numerical Algorithms, 67 (2013), pp. 121-144; DOI: 10.1007/s11075-013-9778-8.
4. G. Bal, K. Hoffmann, and K. Knudsen, Propagation of singularities for linearized hybrid data impedance tomography, Inverse Problems, 34 (2917), 024001 (19pp); DOI: 10.1088/1361-6420/aa0d78.
5. L. Borg, J. Frikel, J. S. Jørgensen, and E. T. Quinto, Analyzing reconstruction artifacts from arbitrary incomplete X-ray CT data, SIAM J. Imaging Sciences, 11 (2018), pp.2786-2814; DOI: 10.1137/18M1166833
6. L. Borg, J. S. Jørgensen, J. Frikel, and J. Sporring, Reduction of variable-truncation artifacts from beam occlusion during in situ X-ray tomography, Meas. Sci. Technol., 28 (2017), 124004 (19pp); DOI: 10.1088/1361-6501/aa8c27.
7. D. Chen, M. E. Kilmer, and P. C. Hansen, "Plug-and-play" edge-preserving regularization, Electronic Transactions on Numerical Analysis, 41 (2014), pp. 465-477 (open access).
8. T. Chen, M. S. Andersen, L. Ljung, A. Chiuso, and G. Pillonetto, System identification via sparse multiple kernel-based regularization using sequential convex optimization techniques, IEEE Trans. on Automatic Control, 59 (2014), pp. 2933-2945. DOI: 10.1109/TAC.2014.2351851.
9. V. A. Dahl, A. B. Dahl, and P. C. Hansen, Computing segmentations directly from X-ray projection data via parametric deformable curves, Meas. Sci. Technol., 29 (2018), 014003 (16pp); DOI: 10.1088/1361-6501/aa950e. Software available at: github.com/vedrana/tomography-snake.
10. F. Delbary and K. Knudsen, Numerical nonlinear complex geometrical optics for the 3D Calderón problem, Inverse Problems and Imaging, 8 (2014), pp. 991-1012; DOI: 10.3934/ipi.2014.8.991.
11. Y. Dong, H. Garde, and P. C. Hansen, R³GMRES: including prior information in GMRES-type methods for discrete inverse problems, Electronic Transactions on Numerical Analysis, 42 (2014), pp. 136-146 (open access).
12. Y. Dong, T. Görner, and S. Kunis, An algorithm for total variation regularized photoacoustic imaging, Adv. Comput. Math., June 2014; DOI: 10.1007/s10444-014-9364-1
13. Y. Dong, P. C. Hansen, M. E. Hochstenbach, and N. A. B. Riis, Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojection, SIAM J. Sci. Comput., 40 (2019), pp. A1822-A1839. doi: 10.1137/18M1206448
14. Y. Dong, P. C. Hansen, and H. M. Kjer, Joint CT reconstruction and segmentation with discriminative dictionary learning, IEEE Trans. Computational Imaging, 4 (2018), pp. 528-536; doi: 10.1109/TCI.2018.2858139.
15. Y. Dong and T. Zeng, A convex variational model for restoring blurred images with multiplicative noise, SIAM J. Imaging Sci., 6 (2013), pp. 1598-1625; DOI: 10.1137/120870621.
16. Y. Dong and T. Zeng, New hybrid variational recovery model for blurred images with multiplicative noise, East Asian Journal on Appl. Math., 3 (2013), pp. 263-282; DOI: 10.4208/eajam.240713.120813a.
17. T. Elfving and P. C. Hansen, Unmatched projector/backprojector pairs: perturbation and convergence analysis, SIAM J. Sci. Comp., 40 (2018), pp. A573-A591; DOI: 10.1137/17M1133828.
18. T. Elfving, P. C. Hansen, and T. Nikazad, Convergence analysis for column-action methods in image reconstruction, Numerical Algorithms, 74 (2016), DOI: 10.1007/s11075-016-0176-x. Erratum (Fig. 3 was incorrect): DOI: 10.1007/s11075-016-0232-6.
19. T. Elfving, P. C. Hansen, and T. Nikazad, Semi-convergence properties of Kaczmarz's method, Inverse Problems, 30 (2014), DOI: 10.1088/0266-5611/30/5/055007. This paper was selected to be part of the journal's Highlights Collection
20. H. Garde, Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations, Inverse Problems in Science and Engineering, 26 (2018), pp. 33-50. DOI: 10.1080/17415977.2017.1290088.
21. H. Garde and K. Knudsen, Distinguishability revisited: depth dependent bounds on reconstruction quality in electrical impedance tompography SIAM J. Appl. Math., 77 (2017); DOI: 10.1137/16M1072991.
22. H. Garde and K. Knudsen, Sparsity prior for electrical impedance tomography with partial data, Inverse Problems in Science and Engineering, 24 (2016), pp. 524-541; DOI: 10.1080/17415977.2015.1047365.
23. H. Garde and S. Staboulis, The regularized monotonicity method: detecting irregular indefinite inclusions, Inverse Problems and Imaging, 13 (2019), pp. 93-116. DOI: 10.3934/ipi.2019006.
24. H. Garde and S. Staboulis, Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography, Numer. Math., 135 (2017), pp. 1221-1251; DOI: 10.1007/s00211-016-0830-1.
25. S. Gazzola, P. C. Hansen, and J. G. Nagy, IR Tools - A MATLAB package of iterative regularization methods and large-scale test problems, Numerical Algorithms, 81 (2019), pp. 773-811. doi: 10.1007/s11075-018-0570-7.
26. P. C. Hansen, Y. Dong, and K. Abe, Hybrid enriched bidiagonalization for discrete ill-posed problems, Numer. Linear Algebra Appl., 26 (2019), e2230; DOI: 10.1002/nla.2230.
27. P. C. Hansen and J. S. Jørgensen, AIR Tools II: algebraic iterative reconstruction methods, improved implementation, Numerical Algorithms, 79 (2018), pp. 107-137; DOI: 10.1007/s11075-017-0430-x.
28. P. C. Hansen, J. G. Nagy, and K. Tigkos, Rotational image deblurring with sparse matrices, BIT Numerial Mathematics, 54 (2014), pp. 649-671, DOI: 10.1007/s10543-013-0464-y
29. K. Hoffmann and K. Knudsen, Iterative reconstruction methods for hybrid inverse problems in impedance tomography, Sensing and Imaging, 15 (2014), pp. 1-27; DOI: 10.1007/s11220-014-0096-6
30. J. S. Jørgensen, S. B. Coban, W. R. B Lionheart, S. A. McDonald, and P. J. Withers, SparseBeads data: benchmarking sparsity-regularized computed tomography, Meas. Sci. Technol., 28 (2017), 124005 (18pp); DOI: 10.1088/1361-6501/aa8c29
31. J. S. Jørgensen, C. Kruschel, and D. Lorenz, Testable uniqueness conditions for empirical assessment of undersampling levels in total variation-regularized x-ray CT, Inverse Problems in Science and Engineering, 23 (2014), pp. 1283-1305; DOI: 10.1080/17415977.2014.986724
32. J. S. Jørgensen and E. Y. Sidky, How little data is enough? Phase-diagram analysis of sparsity-regularized X-ray CT, Phil. Trans. Royal Soc. A, 373 (2015), 20140387 (special issue "X-ray tomographic reconstruction for materials science"); DOI: 10.1098/rsta.2014.0387. Data and code to reproduce the results are available from DOI: 10.5061/dryad.3jg57.
33. J. S. Jørgensen, E. Y. Sidky, P. C. Hansen, and X. Pan, Empirical average-case relation between undersampling and sparsity in X-ray CT, Inverse Problems and Imaging, 9 (2015), pp. 431-446; DOI: 10.3934/ipi.2015.9.431 (open access).
34. M. Karamehmedovic and K. Knudsen, Inclusion estimation from a single electrostatic boundary measurement, Inverse Problems, 29 (2013); DOI: 10.1088/0266-5611/29/2/025005.
35. R. D. Kongskov and Y. Dong, Tomographic reconstruction methods for decomposing directional components, Inverse Problems and Imaging, 12 (2018), pp. 1429-1442. DOI: 10.3934/ipi.2018060.
36. R. D. Kongskov, Y. Dong, and K. Knudsen, Directional total generalized variation regularization, BIT Numerical Mathematics, 59 (2019), pp. 903-928. DOI: 10.1007/s10543-019-00755-6
37. R. D. Kongskov, J. S. Jørgensen, H. F. Poulsen, and P. C. Hansen, Noise robustness of a combined phase retrieval and reconstruction method for phase-contrast tomography, J. Optical Society of America A, 33 (2016), pp. 447-454; DOI: 10.1364/JOSAA.33.000447.
38. J.-J. Mei, Y. Dong, T.-Z. Huang, and W. Yin, Cauchy noise removal by nonconvex ADMM with convergence guarantees, J. Sci. Comput., 74 (2018), pp. 743-766. DOI: 10.1007/s10915-017-0460-5.
39. S. K. Pakazad, M. S. Andersen, and A. Hansson, Distributed solutions for loosely coupled feasibility problems using proximal splitting methods, Optimization Methods and Software, 30 (2015), pp. 128-161; DOI: 10.1080/10556788.2014.902056.
40. V. Paoletti, P. C. Hansen, M. F. Hansen, and M. Fedi, A computationally efficient tool for assessing the depth resolution in large-scale potential-field inversion, Geophysics, 79 (2014), pp. A33-A38; DOI: 10.1190/geo2014-0017.1.
41. T. Ramos, J. S. Jørgensen, and J. W. Andreasen, Automated angular and translational tomographic alignment and application to phase-contrast imaging, J. Optical Society of America A, 34 (2017), pp. 1830-1843; DOI: 10.1364/JOSAA.34.001830.
42. N. A. B. Riis, J. Frøsig, Y. Dong, and P. C. Hansen, Limited-data X-ray CT for underwater pipeline inspection, Inverse Problems, 34 (2018), 034002 /16pp); DOI: 10.1088/1361-6420/aaa49c.
43. M. Romanov, A. B. Dahl, Y. Dong, and P. C. Hansen, Simultaneous tomographic reconstruction and segmentation with class priors; Inverse Problems in Science and Engineering, 24 (2015), pp. 1432-1453; DOI: 10.1080/17415977.2015.1124428.
44. S. Rose, E. Y. Sidky, X. Pan, and M. S. Andersen, Noise properties of CT images reconstructed by use of constrained total-variation, data-discrepancy minimization, Medical Physics, 42 (2015), pp. 2690-2698; DOI: 10.1118/1.4914148
45. M. Salewski, B. Geiger, A. Jacobsen, P. C. Hansen + 12, High-definition velocity-space tomography of fast-ion dynamics, Nuclear Fusion, 56 (2016), DOI: 10.1088/0029-5515/56/10/106024.
46. M. F. Schmidt, M. Benning, and C.-B. Schönlieb, Inverse scale space decomposition, Inverse Problems, 34 (2018), 045008 (34pp); DOI: 10.1088/1361-6420/aab0ae.
47. F. Sciacchitano, Y. Dong, and M. S. Andersen, Total variation based parameter-free model for Impulse noise removal, Numerical Mathematics: Theory, Methods and Applications, 10 (2017), pp. 186-204, DOI: 10.4208/nmtma.2017.m1613
48. F. Sciacchitano, Y. Dong, and T. Zeng, Variational approach for restoring blurred images with Cauchy noise, SIAM J. Imaging Sc., 8 (2015), pp. 1896-1922, DOI: 10.1137/140997816
49. S. Soltani, M. S. Andersen, and P. C. Hansen, Tomographic image reconstruction using training images, Journal of Computational and Applied Mathematics, 313 (2017), pp. 243-258; DOI: 10.1016/j.cam.2016.09.019.
50. S. Soltani, M. E. Kilmer, and P. C. Hansen, A tensor-based dictionary learning approach to tomographic image reconstruction, BIT Numerical Mathematics, 56 (2016), pp. 1425-1454; DOI: 10.1007/s10543-016-0607-z. This paper is mentioned on the front page of SIAM News Vol. 50 Issue 6, 2017: A Computationally Efficient Solution of Large-Scale Image Reconstruction Problems.
51. Y. Sun, M. S. Andersen, and L. Vandenberghe, Decomposition in conic optimization with partially separable structure, SIAM J. Optimiz., 24 (2014), pp. 873-897; DOI: 10.1137/130926924.
52. H. H. B. Sørensen and P. C. Hansen, Multicore performance of block algebraic iterative reconstruction methods, SIAM J. Sci. Comp, 36 (2014), pp. C524-C546. DOI: 10.1137/130920642.
53. P. Weiss, P. Escande, G. Bathie, and Y. Dong, Contrast invariant SNR and isotonic regressions, International Journal of Computer Vision, published online 2019. DOI: 10.1007/s11263-019-01161-9

Refereed Conference Proceedings

• H. Garde and K. Knudsen, 3D reconstruction for partial data electrical impedance tomography using a sparsity prior, Dynamical Systems, Differential Equations and Applications - AIMS Proceedings (2015), pp. 495-504; open access DOI: 10.3934/proc.2015.0495.
• J. S. Jørgensen, S. B. Coban, W. R. B. Lionheart, and P. J. Withers, Effect of sparsity and exposure on total variation regularized X-ray tomography from few projections, Proc. 4th International Conference on Image Formation in X-Ray Computed Tomography, Bamberg, Germany, 2016, pp. 279-282.
• I. G. Kazantsev, U. L. Olsen, H. F. Poulsen, and P. C. Hansen, A spectral geometrical model for Compton scatter tomography based on the SSS approximation, Proceedings of the 4th International Conference on Image Formation in X-Ray Computed Tomography, July 18-22, Bamberg, Germany, pp. 577-580.
• H. M. Kjer, Y. Dong, and P. C. Hansen, User-friendly simultaneous tomographic reconstruction and segmentation with class priors, Proc. SSVM 2017, pp. 260-270, Springer, 2017; DOI: 10.1007/978-3-319-58771-4_21.
• R. D. Kongskov and Y. Dong, Directional total generalized variation regularization for impulse noise removal, Proc. SSVM 2017, pp. 221-231, Springer, 2017; DOI: 10.1007/978-3-319-58771-4_18.
• S. Rose, M. S. Andersen, E. Y. Sidky, and X. Pan, Application of incremental algorithms to CT reconstruction for sparse-view, noisy data, Proc. 3rd International Conference on Image Formation in X-Ray Computed Tomography, 2014, pp. 351-354.

Technical Reports

• L. Borg, J. S. Jørgensen, and J. Sporring, Towards characterizing and reducing artifacts caused by varying projection truncation, Technical Report 2017/1, Department of Computer Science, University of Copenhagen, 2017.
• M. Burger, Y. Dong, and F. Sciacchitano, Bregman cost for non-Gaussian noise, DTU Compute Technical Report 2016-8.
• P. C. Hansen and K. Abe, LBAS: Lanczos bidiagonalization with subspace augmentation for discrete inverse problems, Technical Report 2017-03.
• M. Romanov, A. B. Dahl, Y. Dong, and P. C. Hansen, Relaxed Simultaneous Tomographic Reconstruction and Segmentation with Class Priors for Poisson Noise, DTU Compute Technical Report 2015-6.
• M. Romanov, P. C. Hansen, and A. B. Dahl, A Parameter Choice Method for Simultaneous Reconstruction and Segmentation, DTU Compute Technical Report 2015-5.
• S. Soltani, Studies of Sensitivity in the Dictionary Learning Approach to Computed Tomography: Simplifying the Reconstruction Problem, Rotation, and Scale, DTU Compute Technical Report 2015-4, July 2, 2015.

Visitors

• Kuniyoshi Abe, Gifu Shotoku Gakuen University.
• Joost Batenburg, CWI, Amsterdam.
• Martin Benning, Univ. of Cambridge
• Marta Betcke, UCL.
• Raymond Chan, Chinese Univ. of Hong Kong.
• Julianne Chung, Virginia Tech.
• Fabrice Delbary, Univ. of Genova.
• Tommy Elfving, Linkoping Univ.
• Oliver G. Ernst, TU Chemnitz.
• David Franck, TU Munich.
• Jürgen Frikel, TU Munich.
• Silvia Gazzola, Univ. of Bath.
• Sarah Hamilton, Helsinki University.
• Andreas Hauptmann, Helsinki University.
• Michiel Hochstenbach, Technische Universiteit Eindhoven.
• Yinyi (Larry) Hu, Emory Univ.
• Simon Hubmer, Johannes Kepler University, Linz.
• Daniil Kazantsev, Manchester Univ.
• Ivan Kazantsev, Novisibirsk Scientific Centre.
• Ville Kolehmainen, Univ. of Eastern Finland.
• Tobias Lasser, Technische Universität München.
• Julia Mrongowius, Univ. of Lübeck.
• James G. Nagy, Emory University.
• Touraj Nikazad, Iran Univ. of Science and Technology.
• Mila Nikolova, Universite Paris-Saclay.
• Willem Jan Palenstijn, CWI, Amsterdam.
• Valeria Paoletti, Univ, of Naples Federico II.
• Stefania Petra, Univ. of Heidelberg.
• Martin Plesinger, Technical Univ. of Liberec, Czech Republic.
• David Rigie, University of Chicago.
• Carola-Bibiane Schönlieb, Univ. of Cambridge.
• Ekatarina Sherina, Tomsk State Univ.
• Gabriele Steidl, Univ. of Kaiserslautern.
• Gabriele Stocchino, Univ. of Padua.
• Tristan van Leeuwen, Universiteit Utrecht.
• Pierre Weiss, Institut des Technologies Avancées du Vivant.
• Matthias Wieczovek, Technische Universität München.
• Tieyong Zeng, Hong Kong Baptist University.
• Xiaoqun Zhang, Shanghai Jiao Tong University.

Seminars, Workshops, PhD Courses, etc.

• Training School: Algebraic Reconstruction Methods in Tomography, April 4-6, 2016, as part of the EXTREMA COST Action MP1207.
• Training School Scientific Computing for X-Ray Computed Tomography, January 2017, as part of the EXTREMA COST Action MP1207.
• Mini-workshop: Insights and Algorithms for Incomplete Data Tomography, September 14, 2016:
  • Todd Quinto, Tufts University, What you can see in limited data tomography.
  • Leise Borg, Copenhagen University, Characterizing and reducing artefacts.
  • Jürgen Frikel, Ostbayerische Technische Hochschule, Regensburg, On the use of highly directional representations in incomplete data tomography.
  • Jakob Lemvig, DTU, A frame theoretic view on inverse problems.
• Workshop: HD-Tomo Days, April 6-8, 2016. The program with abstracts is available here.
• Workshop: Sparse Tomo Days, March 26-28, 2014. The abstracts are available here.
• Three seminars on Microlocal characterization in limited-angle tomography Jürgen Frikel:
  • Introduction to the mathematics of computerized tomography.
  • Introduction to the basic concepts of microlocal analysis.
  • Microlocal analysis of limited angle reconstruction in tomography.
• Five seminars by Prof. Bill Lionheart, October 2013 and July 2014:
  • Sufficient Data for Stable Reconstruction,
  • Ray Transforms,
  • EIT for Beginners,
  • Rich Tomography,
  • Inverse Problems in Security Screening.
• Online short-course: Algebraic Iterative Reconstruction Methods.
• MSc course Introduction to Inverse Problems (at DTU).
• PhD course Scientific Computing for X-Ray Computed Tomography (at DTU).
• PhD course Measurement Techniques and Mathematical Modeling in Tomography in the spring of 2014.
• Weekly seminars by project members, visitors, and invited speakers.

Bachelor and Master Projects

• Sparsity Regularization for Electrical Impedance Tomography (MSc), 2013; this thesis by H. Garde won the special award by the Danish Mathematical Society.
• Sparsity Regularization for Inverse Problems using Curvelets (MSc), 2013.
• Magnetic Resonance Electrical Impedance Tomography for Anisotropic Conductivity Distribution (MSc), 2013.
• Characterization and Modeling of Structured Noise in Seismic Reflection Data (MSc), 2013.
• Shape Optimization for Electrical Impedance Tomography (MSc), 2013.
• Computational Methods for Multi-Spectral Tomography (BSc), July 2014.
• Multi-Spectral Tomography: Models and Computational Methods (BSc), July 2014
• Frequency Dependent Stability for Inverse Boundary Value Problems (MSc), 2014.
• Image Denoising and Tomography for Non-Linear Diffusion (MSc), 2014.
• Simulated Phase Contrast Tomography Experiments Using Total Variation Regularization (MSc), June 2014; joint with DTU Physics.
• Block Algebraic Methods for 3D Image Reconstructions on GPUs (MSc), August 2014.
• Robust Computed Tomography with Incomplete Data (BSc), 2015; joint with School of Mathematics, Manchester University.
• GPU Implementation of a Toolbox for Tomographic Reconstruction (BSc), July 2015.
• Linearized Acousto-Electric Impedance Tomography (MSc), 2015.
• Material Decomposition Using Spectral Tomography (BSc), 2016.
• Hybrid Data Impedance Tomogarphy with the Complete Electrode Model (MSc), 2016.
• Preconditioning for PDE-Constrained Optimization Problems (MSc), 2016.
• Computational Methods for Hybrid Impedance Tomography (MSc), 2016.
• High-Performance Computing for Block-Iterative Tomography Reconstructions (MSc), July 2016.
• Iterative Tomographic Reconstruction with Priorconditioning (BSc), January 2017.
• Computed Tomography for Region-of-Interest Problems with Limited Data (MSc), February 2017.