Preprints

• Optimality of Cross-validation in Scattered Data Approximation (pdf)
  F. Bartel, R. Hielscher: arXiv:2105.13790, 2021.
  


• Approximating the Derivative of Manifold-valued Functions (pdf)
  R. Hielscher, L. Lippert: arXiv:2102.12562, 2021.
  


• Parent grain reconstruction from partially or fully transformed microstructures in MTEX (pdf)
  F. Niessen, T. Nyyssönen, A. A. Gazder, R. Hielscher: arXiv:2104.14603, 2021.
  

Publications in Journals (Publications and Citations in Google Scholar)

• Isometric Embeddings of Quotients of the Rotation Group Modulo Finite Symmetries (pdf)
  R. Hielscher, L. Lippert: Journal of Multivariate Analysis 185, 104764, 2021.
  


• Fast Cross-validation in Harmonic Analysis (pdf)
  F. Bartel, R. Hielscher and D. Potts: Applied and Computational Harmonic Analysis 49(2), 2020.
  


• Approximant-based orientation determination of quasicrystals using electron backscatter diffraction
  C. Grzegorz, G. Nolze, A. Winkelmann, T. Tokarski, R. Hielscher, R. Strzałka, I. Bugański, J. Wolny and P. Bała: Ultramicroscopy 218, 2020.
  


• EBSD orientation analysis based on experimental Kikuchi reference patterns
  A. Winkelmann, G. Cios, T. TokarskiShow, G. Nolze, R. Hielscher and T. Kozieł: Acta Materialia 188, 2020.
  


• Optimized reconstruction of the crystallographic orientation density function based on a reduced set of orientations
  A. Biswas, N. Vajragupta, R. Hielscher and A. Hartmaier: Journal of Applied Crystallography 53(1), 2020.
  


• Visualization of texture components using MTEX
  G. Rafailov, E. N. Caspi, R. Hielscher, E. Tiferet, R. Schneck and C. Vogel: J. Appl. Cryst. 53, 2020
  


• Gazing at crystal balls - Electron backscatter diffraction indexing and cross correlation on a sphere (pdf)
  R. Hielscher, B. Britton and F. Bartel: Ultramicroscopy, 2019.
  


• Denoising of Crystal Orientation Maps (pdf)
  R. Hielscher, C. Silbermann, E. Schmidl, J. Ihlemann: Journal of Applied Crystallography 52, 2019.
  


• An analytical finite-strain parametrization for texture evolution in deforming olivine polycrystals (pdf)
  N. M. Ribe, R. Hielscher and O. Castelnau: Geophysical Journal International 216, 486–514, 2019.
  


• The cone-beam transform and spherical convolution operators (pdf)
  M. Quellmalz, R. Hielscher und A. K. Louis: Inverse Problems 34 (2018) 105006, 2018.
  


• An SVD in Spherical Surface Wave Tomography (pdf)
  R. Hielscher, D. Potts and M. Quellmalz: In: Bernd Hofmann, Antonio Leitao and Jorge P. Zubelli (Eds.). New Trends in Parameter Identification for Mathematical Models, Birkhäuser Basel, 2018.
  


• On three-dimensional misorientation spaces (pdf)
  R. Krakow, R. J. Bennett, D. N. Johnstone, Z. Vukmanovic, W. Solano-Alvarez, S. J. Laine, J. F. Einsle, P. A. Midgley, C. M. F. Rae, R. Hielscher: Proceedings of the Royal Society A, 473, 2017.


• Electron Backscatter Diffraction beyond the mainstream (pdf)
  G. Nolze, R. Hielscher, A. Winkelmann: Crystal Research & Technolog, 25(1), 2017.
  


• Orientations - perfectly colored (pdf)
  G. Nolze, R. Hielscher: Journal of Applied Crystallography, 49, 1786-1802, 2016.
  


• Reconstructing a Function on the Sphere from Its Means Along Vertical Slices (pdf)
  R. Hielscher, M. Quellmalz: Inverse Problems and Imaging, 10 (3), 711-739, 2016.
  


• Restoration of Manifold-Valued Images by Half-Quadratic Minimization (pdf)
  R. Bergmann, R. H. Chan, R. Hielscher, J. Persch, G. Steidl, Inverse Problems and Imaging, 10 (2), 281-304, 2016.
  


• Optimal molifiers for spherical deconvolution (pdf)
  R. Hielscher, M. Quellmalz: Inverse Problems, 31, art. no. 085001, 2015.
  


• Global optimization on the torus, the sphere and the rotation group (pdf)
  M. Gräf, R. Hielscher: SIAM J. Optim., 25, 540 - 564, 2015.
  


• Calculating anisotropic piezoelectric properties from texture data using the MTEX open source package (pdf)
  D. Mainprice, F. Bachmann, R. Hielscher, H. Schaeben: Geological Society, London, Special Publications, 409, 2014.
  
  
• Descriptive tools for the analysis of texture projects with large datasets using MTEX: strength, symmetry and components (pdf)
  D. Mainprice, F. Bachmann, R. Hielscher, H. Schaeben: Geological Society, London, Special Publications, 409, 2014.
  
  
• Numerical Inversion of the Funk transform on the Rotation Group (pdf)
  R. Hielscher: Inverse Problems, 29, art. no. 125014, 2013.
  
  
• Kernel Density Estimation on the Rotation Group and its Application to Crystallographic Texture Analysis (pdf)
  R. Hielscher: J. Multivariate Anal., 119, 119 - 143, 2013.
  
  
• Efficient and accurate computation of spherical mean values at scattered center points (pdf)
  T. Görner, R. Hielscher, S. Kunis: Inverse Prob. Imaging, 6, 645 - 661, 2012.
  
  
• Optimizing the experimental design of texture goniometry (pdf)
  F.Bachmann, R. Hielscher, H. Schaeben: J. Appl. Cryst., 45, 1173-1181, 2012.
  
  
• Grain detection from 2d and 3d EBSD data - Specification of the MTEX algorithm (pdf)
  F.Bachmann, R. Hielscher, H. Schaeben: Ultramicroscopy, 111, 1720-1733, 2011.
  
  
• Calculating anisotropic physical properties from texture data using the MTEX open source package (pdf)
  D.Mainprice, R. Hielscher, H. Schaeben: Prior, D.J., Rutter, E.H., Tatham, D. J. (eds) Deformation Mechanisms, Rheology and Tectonics: Microstructures, Mechanics and Anisotropy. Geological Society, London, Special Publications, 360, 175-192, 2011.
  
  
• Inferential statistics of electron backscatter diffraction data from within individual crystalline grains (pdf)
  F. Bachmann, R. Hielscher, P. E. Jupp, W. Pantleon, H. Schaeben, E. Wegert: J. Appl. Cryst. 43, 1338-1355, 2010.
  
  
• Fast summation of functions on the rotation group (pdf)
  R. Hielscher, J. Prestin, A. Vollrath, Math. Geosci., 42, 773-794, 2010.
  
  
• Texture analysis with MTEX- Free and open source software toolbox (pdf)
  F. Bachmann, R. Hielscher, H. Schaeben: Solid State Phenomena, 160, 63-68, 2010.
  
  
• Orientation Distribution Within a Single Hematite Crystal (pdf)
  R. Hielscher, H. Schaeben, H. Siemes: Math. Geosci., 42, 395-375, 2010.
  
  
• Reconstruction from circular and spherical mean data (pdf)
  F. Filbir, R. Hielscher, W.R. Madych: Appl. Comput. Harmon. Anal., 29, 111 - 120, 2010.
  
  
• The generalized totally geodesic Radon transform and its application to texture analysis (pdf)
  S. Bernstein, R. Hielscher, H. Schaeben: Math. Methods Appl. Sci., 32, 379 - 394, 2009.
  
  
• A novel pole figure inversion method: specification of the MTEX algorithm (pdf)
  R. Hielscher, H. Schaeben: J. Appl. Cryst. 41, 1024-1037, 2008
  
  
• The radon transform on SO(3): a Fourier slice theorem and numerical inversion (pdf)
  R. Hielscher, D. Potts, J. Prestin, H. Schaeben, M. Schmalz: Inverse Problems 24, 025011 - 025032, 2008
  
  
• Multi-scale texture modeling (pdf)
  R. Hielscher, H. Schaeben: Math. Geosci., 40, 63 - 82, 2008
  
  
• On the calibration of fission-track annealing models (pdf)
  S. Guedes, R. Jonckheere, P.A.F.P. Moreira, R. Hielscher: Chem. Geol., 248, 1-13, 2007
  
  
• Orientation density function-controlled pole probability density function measurements: automated adaptive control of texture goniometers. (pdf)
  H. Schaeben, R. Hielscher, J. J. Fundenberger, D. Potts and J. Prestin: J. Appl. Cryst., 40, 570-579, 2007.
  
  
• On the entropy to texture index relationship in quantitative texture analysis (pdf)
  R. Hielscher, H. Schaeben, D. Chateigner: J. Appl. Cryst., 40, 371-375, 2007.
  
  
• Kernel-based methods for inversion of the Radon transform on SO(3) and their applications to texture analysis (pdf)
  K. van den Boogaart, R. Hielscher, J. Prestin, H. Schaeben: J. Comp. Appl. Math., 199, 122-140, 2006.
  
  

Proceedings Papers and Book Chapters

• Structures: Orientation Texture
  S. Wright, R. Hielscher: Elsevier Reference Module in Materials Science and Materials Engineering, 2016, accepted.
  


• Material Behavior: Texture and Anisotropy (pdf)
  R. Hielscher, D. Mainprice, H. Schaeben: in Handbook of Geomathematics, W. Freeden, M. Z. Nashed, T, Sonar (eds.), Springer, 2010.
  
  
• Quantifying rock fabrics - a test of independence of the spatial distribution of crystals
  J.R. McKenzie, Egozcue, R. Heilbronner, R. Hielscher, A. Mueller, H. Schaeben: CoDaWork 2008, Girona, Spain, May 27-30, 2008
  
  
• Determination of an ODF from Diffraction Measurements Based on Optimal Smoothing Splines (pdf)
  K.G. van den Boogaart, R. Hielscher: Materials Science Forum, 495-497, 267-272, 2005.
  
  
• Common Basics of Mathematical Texture Analysis (pdf)
  S. Bernstein, R. Hielscher, H. Schaeben Materials Science Forum, 495-497, 277-282, 2005.
  
  
• PDF-to-ODF Inversion by Approximation with Spherical Radial Basis Functions (pdf)
  R. Hielscher, S. Bernstein, H. Schaeben, K.G. van den Boogaart, J. Beckmann, J. Prestin: K.G. van den Boogaart, R. Hielscher: Materials Science Forum, 495-497, 313-318, 2005.
  
• High Resolution Texture Analysis with Spherical Wavelets (pdf)
  H. Schaeben, S. Bernstein, R. Hielscher, J. Beckmann, J. Keiner, J. Prestin: Materials Science Forum, 495-497, 245-254, 2005.

Dissertation

• The Radon Transform on the Rotation Group - Inversion and Application to Texture Analysis (pdf)
  R. Hielscher, Thesis, Freiberg, 2007.

Patents

• Verfahren zum Steuern eines Texturgoniometers im Rahmen eines texturanalytischen Untersuchung einer Probe und Vorrichtung zum Steuern eines Texturgoniometers im Rahmen eines texturanalytischen Untersuchung einer Probe (pdf)
  H. Schaeben, R. Hielscher, J. Prestin, D. Potts, Deutsches Patent und Markenamt, DE 10 2006 053 433 B3 (2008).