Articles with peer review

2022

• C. Meiser, A. Wald and T. Schuster. Learned anomaly detection with terahertz radiation in inline process monitoring. Sensing and Imaging, 23:30, 2022.

• L. Vierus and T. Schuster. Well-defined forward operators in dynamic diffractive tensor tomography using viscosity solutions of transport equations. Electronic Transactions on Numerical Analysis, 57:80-100, 2022.

• R. Rothermel, W. Panlenko, P. Sharma, A. Wald, T. Schuster, A. Jung and S. Diebels. A method for determining the parameters in a rheological model for viscoelastic materials by minimizing Tikhonov functionals. Applied
  Mathematics in Science and Engineering, 30(1):141-165, 2022.

2021

• D. Rothermel, T. Schuster, R. Schorr and M. Peglow. Determination of the temperature-dependent thermal material properties in the cooling process of steel plates. Mathematical Problems in Engineering,
  DOI:10.1155/2021/6653388, Article ID 6653388, 2021.

• D. Rothermel and T. Schuster. Solving an inverse heat convection problem with an implicit forward operator by using a projected quasi-Newton method. Inverse Problems, 37(4):36pp, 2021.

2020

• S.E. Blanke, B.N. Hahn and A. Wald. Inverse Problems with inexact forward operator: iterative regularization and application in dynamic imaging. Inverse Problems, to appear, 2020.

• E.Y. Derevtsov, Y.S. Volkov and T. Schuster. Generalized attenuated ray transforms and their integral angular moments. Applied Mathematics and Computation, DOI:10.1016/j.amc.2020.125494, 2020.

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 Engineering,  DOI: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.

• F. Schöpfer, F. Binder, A. Wöstehoff, T. Schuster, S. v. Ende, S. Föll, and R. Lammering. Accurate determination of dispersion curves of guided waves in plates by applying the matrix pencil method to laser vibrometer measurement data. CEAS Aeronautical Journal, 2013. Article ID 10.1007/s13272-012-0055-7, 2013.

2012

• T. Schuster, A. Rieder and F. Schöpfer. The approximate inverse in action IV: semi-discrete equations in a Banach space setting.
  Inverse Problems, 28:19pp, 2012.

2011

• S. Kazantsev and T. Schuster. Asymptotic inversion formulas in 3D vector field tomography for different geometries.
  Journal of Inverse and Ill-Posed Problems, 19:769-799, 2011

• E.Y. Derevtsov, A. Efimov, A.K. Louis and T. Schuster. Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography.
  Journal of Inverse and Ill-Posed Problems, 19:689-715, 2011.

• E. T. Quinto, A. Rieder, and T. Schuster. Local inversion of the sonar transform regularized by the approximate inverse. Inverse Problems, 27:18pp, 2011.

• T. Pfitzenreiter, and T. Schuster. Tomographic reconstruction of the curl and divergence of 2D vector fields taking refractions into account. SIAM Journal on Imaging Sciences, 4:40-56, 2011.

2010

• F. Schöpfer, F. Binder, A. Wöstehoff, and T. Schuster. A mathematical analysis of the strip- element method for the computation of dispersion curves of guided waves in anisotropic layered media.
  Mathematical Problems in Engineering, Article ID 924504, 17 pp, 2010.

• T. Schuster and F. Schöpfer. Solving linear operator equations in Banach spaces non-iteratively by the method of approximate inverse. Inverse Problems, 26(8):19pp, 2010.

2009

• B. Kaltenbacher, F. Schöpfer, and T. Schuster. Iterative methods for nonlinear ill-posed problems in Banach spaces: convergence and applications to parameter identification problems.
  Inverse Problems, 25(6):19pp, 2009. DOI:10.1088/0266-5611/25/6/065003

• T. Schuster, D. Theis, and A. K. Louis. A reconstruction approach for imaging in 3D cone beam vector field tomography. International Journal of Biomedical Imaging, Article ID 174283, 17 pages, 2009. DOI:10.1155/2008/174283

• F. Schöpfer and T. Schuster. Fast regularizing sequential subspace optimization in Banach spaces.Inverse Problems, 25(1):22p, 2009. DOI:10.1088/0266-5611/25/1/015013

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 and J. Weickert. On the application of projection methods for computing optical flow fields.
  Inverse Problems and Imaging, 1(4):673-690, 2007.

• 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

• F. Schöpfer, A. K. Louis, and T. Schuster. Nonlinear iterative methods for linear ill-posed problems in Banach spaces.
  Inverse Problems, 22(1):311-329, 2006. DOI:10.1088/0266-5611/22/1/017

• 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

• M. Haltmeier, T. Schuster, and O. Scherzer. Filtered backprojection for thermoacoustic computed tomography in spherical geometry.
  Mathematical Methods in The Applied Sciences, 28:1919-1937, 2005. DOI:10.1002/mma.648

• T. Schuster and E. T. Quinto. On a regularization scheme for linear operators in distribution spaces with an application to the spherical Radon transform.
  SIAM Journal on Applied Mathematics, 65:1369-1387, 2005. DOI:10.1137/S003613990343879X

• 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

• A. Rieder and T. Schuster. The approximate inverse in action III: 3D-Doppler tomography.
  Numerische Mathematik, 97:353-378, 2004. DOI:10.1007/s00211-003-0512-7

2003

• T. Schuster, J. Plöger, and A .K. Louis. Depth-resolved residual stress evaluation from X-ray diffraction measurement data using the approximate inverse method.
  Zeitschrift fuer Metallkunde, 94:934-937, 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

• T. Schuster. An efficient mollifier method for 3D vector tomography: convergence analysis and implementation.
  Inverse Problems, 17:739-766, 2001. DOI:10.1088/0266-5611/17/4/312

2000

• T. Schuster. The 3D Doppler transform: elementary properties and computation of reconstruction kernels.
  Inverse Problems, 16(3):701-723, 2000. DOI:10.1088/0266-5611/16/3/311

• A. Rieder, R. Dietz, and T. Schuster. Approximate inverse meets local tomography.
  Mathematical Methods in The Applied Sciences, 23(15):1373-1387, DOI: 10.1002/1099-1476(200010)23:15<1373::AID-MMA170>3.0.CO;2-A, 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