B. Littau, J. Tepe, G. Schober, S. Kremling, T. Hochrein and P. Heidemeyer, Entwicklung und Evaluierung der Potenziale von Terahertz-Tomografie-Systemen. SKZ - Das Kunststoffzentrum (Eds.), Shaker-Verlag, Aachen, 2016.
T. Schuster, B. Kaltenbacher, B. Hofmann and K. Kazimierski. Regularization Methods in Banach Spaces. In Radon Series on Computational and Applied Mathematics, deGruyter, Berlin, 2012.
T. Schuster. The Method of Approximate Inverse: Theory and Applications. In Lecture Notes in Mathematics, Vol. 1906, Springer, Berlin-Heidelberg-NewYork, 2007. DOI
R. Klein, T. Schuster and A. Wald. Sequential subspace optimization for recovering stored energy functions in hyperelastic materials from time-dependent data, submitted in Time-dependent problems in Imaging and Parameter Identification, B.~Kaltenbacher, T.~Schuster, A.~Wald (Eds.), Springer, 2019.
B. Kaltenbacher, T.T.N. Nguyen, A. Wald and T. Schuster. Parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging, submitted in Time-dependent problems in Imaging and Parameter Identification, B. Kaltenbacher, T. Schuster, A. Wald (Eds.), Springer, arXiv:1909.02912, 2019.
T. Schuster. The importance of the Radon transform in vector field tomography. In The first 100 years of the Radon Transform, R. Ramlau, O. Scherzer (Eds.), Springer, 2019.
A. Wald and T. Schuster. Tomographic terahertz imaging using sequential subspace optimization. In New Trends in Parameter Identification for Mathematical Models, B. Hofmann, A. Leitao, J. Zubelli (Eds.), Birkhäuser / Springer, 2018.
N. Kong, A. Sanders, M. Rösner, R. Friedrich, F. Dirksen, E. Bauma, T. Schuster, R. Lammering and J.P.~Wulfsberg. Functional integrated feed-units based on flexible mechanisms in small machine tools for small workpieces. In Small Machine Tools for Small Workpieces, J.P. Wulfsberg, A. Sanders (Eds.), Series: Lecture Notes in Production Engineering, Springer, 2017.
T. Schuster. 20 Years of Imaging in Vector Field Tomography: A Review. In Mathematical Methods in Biomedical Imaging and Intensity-Modulated Radiation Therapy (IMRT), Y. Censor, M. Jiang, A. K. Louis (Eds.), Series: Publications of the Scuola Normale Superiore, CRM Series , Vol. 7, Birkhäuser, 2008.
Articles with peer review
F. Heber, F. Schöpfer and T. Schuster. Acceleration of sequential subspace optimization in Banach spaces by orthogonal search directions. J. Comp. Appl. Math., 345:1-22, DOI:10.1016/j.cam.2018.05.049, 2019.
A. Wald. A fast subspace optimization method for nonlinear inverse problems in Banach spaces with an application in parameter identification. Inverse Problems, 34(8):27pp, DOI:10.1088/1361-6420/aac8f3, 2018.
S. Diebels, T. Schuster and A. Wewior. Identifying elastic and viscoelastic material parameters by Tikhonov regularization. Mathematical Problems in Engineering, DOI:10.1155/2018/1895208, Article ID 1895208, 11pp, 2018.
J. Seydel and T. Schuster. Identifying the stored energy of a hyperelastic structure from surface measurements by using an attenuated Landweber method. Inverse Problems. Special Issue: Dynamic Inverse Problems, Special Issue: Dynamic Inverse Problems, 33(12):31pp, DOI:10.1088/1361-6420/aa8d91, 2017.
A. Katsevich, D. Rothermel, and T. Schuster. An improved exact inversion formula for solenoidal fields in cone beam vector tomography. Inverse Problems, 33(6):19pp, Special issue: 100 Years of the Radon transform, DOI:10.1088/1361-6420/aa58d5, 2017.
C. Schorr, L. Dörr, M. Maisl and T. Schuster. Registration of a priori information for computed laminography. NDT&E International, 86:106-112, DOI:10.1016/j.ndteint.2016.12.005, 2017.
A. Wald and T. Schuster. Sequential subspace optimization for nonlinear inverse problems. J. Inv. Ill-Posed Prob., 25(1), DOI:10.1515/jiip-2016-0014, 2017.
J. Tepe, T. Schuster, and B. Littau. A modified algebraic reconstruction technique taking refraction into account with an application in terahertz tomography. Inverse Problems in Science and Engineering, 25:1448-1473, DOI:10.1080/17415977.2016.1267168, 2017.
U. Schröder and T. Schuster. A numerical algorithm to determine the refractive index of an inhomogeneous medium from time-of-flight measurements. Inverse Problems, 32(8):35pp, DOI:10.1088/0266-5611/32/8/085009, 2016.
J. Seydel and T. Schuster. On the linearization of identifying the stored energy function of a hyperelastic material from full knowledge of the displacement field. Math. Meth. Appl. Sci., DOI:10.1002/mma.3979, 2016.
F. Binder, F. Schöpfer and T. Schuster. PDE-based defect localization in fibre-reinforced composites from surface sensor measurements. Inverse Problems, 31(2):22pp, DOI:10.1088/0266-5611/31/2/025006, 2015.
A. Wöstehoff, T. Schuster. Uniqueness and stability result for Cauchy's equation of motion for a certain class of hyperelastic materials. Applicable Analysis, 94(8):1561-1593, DOI:10.1080/00036811.2014.940519, 2015.
T. Schuster, A. Wöstehoff. On the identifiable of the stored energy function of hyperelastic materials from sensor data at the boundary. Inverse Problems, 30(10):26pp, DOI:10.1088/0266-5611/30/10/105002, 2014.
I.E. Svetov, E.Y. Derevtsov, Y.S. Volkov, and T. Schuster. A numerical solver based on B-splines for 2D vector field tomography in a refracting medium. Mathematics and Computers in Simulation, 97:207-223, 2014. DOI:10.1016/j.matcom.2013.05.008
D. Kern, M. Rösner, E. Bauma, W. Seemann, R. Lammering and T. Schuster. Key features of exure hinges used as rotational joints. Forschung im Ingenieurwesen, DOI:10.1007/s10010-013-0169-z, 2013.
A. Katsevich and T. Schuster. An exact inversion formula for cone beam vector tomography. Inverse Problems, 29(6):13pp, 2013. DOI:10.1088/0266-5611/29/6/065013 Insights have been published to this article.
J.P. Wulfsberg, R. Lammering, T. Schuster, N. Kong, M. Rösner, E. Bauma, and R. Friedrich. A novel methodology for the development of compliant mechanisms with application to feed units. Production Engineering, DOI:10.1007/s11740-013-0472-4, 2013.
E. Derevtsov, V. Pickalov, and T. Schuster. Application of local operators for numerical reconstruction of the singular support of a vector field by its known ray transforms. Journal of Physics: Conference Series, IOP Publishing, Vol. 135, Article ID 012035, doi:10.1088/1742-6596/135/1/012035, 2008.
F. Schöpfer, T. Schuster, and A. K. Louis. Metric and Bregman projections onto affine subspaces and their computation via sequential subspace optimization methods. Journal of Inverse and Ill-Posed Problems, 16(5):479-506, 2008. DOI:10.1515/JIIP.2008.026
F. Schöpfer, T. Schuster, and A. K. Louis. An iterative regularization method for the solution of the split feasibility problem in Banach spaces. Inverse Problems, 24(5):20pp, 2008. DOI:10.1088/0266-5611/24/5/055008
T. Bonesky, K. Kazimierski, P. Maass, F. Schöpfer, and T. Schuster. Minimization of Tikhonov functionals in Banach spaces. Journal of Abstract and Applied Analysis, Article ID 192679, 19 pages, 2007. DOI:10.1155/2008/192679
T. Schuster. The formula of Grangeat for tensor fields of arbitrary order in n dimensions. International Journal of Biomedical Imaging, Article ID 12839, 4 pages, 2007. DOI:10.1155/2007/12839
E. Derevtsov, S. Kazantsev, and T. Schuster. Polynomial bases for subspaces of potential and solenoidal vector fields in the unit ball of R3. Journal of Inverse and Ill-Posed Problems, 15(1):19-55, 2007. DOI:10.1515/JIIP.2007.002
T. Schuster. Defect correction in vector field tomography: detecting the potential part of a field using BEM and implementation of the method. Inverse Problems, 21:75-91, 2005. DOI:10.1088/0266-5611/21/1/006
E. Derevtsov, A. K. Louis, and T. Schuster. Two approaches to the problem of defect correction in vector field tomography solving boundary value problems. Journal of Inverse and Ill-Posed Problems, 12:597-626, 2004. DOI:10.1515/1569394042545111
T. Schuster. A stable inversion scheme for the Laplace opterator using arbitrarily distributed data scanning points. Journal of Inverse and Ill-Posed Problems, 11:263-287, 2003. DOI:10.1515/156939403769237051
A. Rieder and T. Schuster. The approximate inverse in action II: convergence and stability. Mathematics of Computations, 72:1399-1415, 2003.DOI:10.1090/S0025-5718-03-01526-6
E. Derevtsov, R. Dietz, T. Schuster, and A. K. Louis. Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem. Journal of Inverse and Ill-Posed Problems, 8(2):161-191, DOI: 10.1515/jiip.2000.8.2.161, 2000.
A. Rieder and T. Schuster. The approximate inverse in action with an application to computerized tomography. SIAM Journal on Numerical Analysis, 37(6):1909-1929, 2000. DOI:10.1137/S0036142998347619
A. K. Louis and T. Schuster. A novel filter design technique in 2D computerized tomography. Inverse Problems, 12:685-696, 1996. DOI:10.1088/0266-5611/12/5/0112014
Articles in proceedings
E.Y. Derevtsov, Y.S. Volkov and T. Schuster. Differential equations and uniqueness theorems for the generalized attenuated ray transforms of tensor fields, Proceedings of the 3rd International Conference on Numerical Computations: Theory and Algorithms (NUMTA), Le Castella Village, Italy, 2019.
B. Littau, J. Tepe, S. Kremling, T. Schuster, T. Hochrein and P. Heidemeyer. Tomograsche Bildgebung mit vollelektronischen Terahertz-Systemen zur Prüfung von Kunststoff-Bauteilen. DACH-Jahrestagung 2015, 2015.
E. Bauma, T. Schuster. A novel hybrid method for optimal control problems and its application to trajectory optimization in micro manufacturing. Proceedings of the 4th International Conference on Engineering Optimization, Instituto Superior Tecnico, Lisbon, 8-11 September 2014, 2014.
E. Derevtsov, I. Svetov, Y. Volkov, and T. Schuster. Numerical B-spline solution of 2D emission and vector tomography problems for media with absoption and refraction. IEEE Proceedings 2008 Region 8 International Conference on Computational Technologies in Electrical and Electronics Engineering SIBIRCON-08, Novosibirsk Scientific Center, Novosibirsk, Russia, July 21-25, pp. 212-217, 2008.
T. Schuster. Advances and challenges in vector field tomography. In Report Nr. 34/2006 des Workshops Mathematical Methods in Tomography, Mathematisches Forschungsinstitut Oberwolfach, 2006.
T. Schuster. A novel mollifier inversion scheme for the Laplace transform. In Proceedings in Applied Mathematics and Mechanics (PAMM), 1(1), 2002.
M. Steffeck, T. Kluth, T. Knopp, P. Maaß, T. Schuster and A. Wald. A dictionary approach to include relaxation in magnetic particle imaging. Work in progress, 2019.
R. Klein, P. Sharma, A. Jung, S. Diebels, T. Schuster and A. Wald. Identification of material parameters for a viscoelastic model with ill-conditioned experimental data. Work in progress, 2019.
M. Burger, T. Schuster and A. Wald. Ill-posedness of time-dependent inverse problems in Lebesgue-Bochner spaces. Work in progress, 2019.
H. Hoffmann and Anne Wald. On parameter identification problems for elliptic boundary value problems in divergence form; Part I: An abstract framework. Work in progress, 2019.
H. Hoffmann and Anne Wald. On parameter identification problems for elliptic boundary value problems in divergence form; Part II: Examples and applications. Work in progress, 2019.
S. Blanke, B. Hahn and Anne Wald. Iterative reconstruction for inverse problems with an inexact forward operator with an application in dynamic imaging. Work in progress, 2019.
C. Bender, T. Hohage and T. Schuster. Nonlinear Landweber iteration with noisy forward operators for parameter identification in SDE's. Work in progress, 2019.