Books

  • B. Kaltenbacher, T. Schuster and A. Wald, Time-dependent problems in Imaging and Parameter Identification, Springer, Heidelberg, work in progress, 2020.
  • 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

Book sections

  • 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

2019

  • 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.

2018

  • 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 EngineeringDOI:10.1155/2018/1895208, Article ID 1895208, 11pp, 2018.

2017

  • 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.

2016

  • 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.

2015

  • 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.

2014

  • 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

2013

  • 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.

2012

2011

2010

2009

2008

  • 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

2007

  • 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

2006

  • T. Schuster. Error estimates for defect correction methods in Doppler tomography.
    Journal of Inverse and Ill-Posed Problems
    , 14:83-106, 2006. DOI:10.1515/156939406776237465

2005

  • 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

2004

  • 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

2003

  • 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

2001

2000

  • 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

1996

  • 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.

Preprints

  • 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.