American Institute of Mathematical Sciences

Advanced
February  2009, 3(1): 69-85. doi: 10.3934/ipi.2009.3.69

A greedy method for reconstructing polycrystals from three-dimensional X-ray diffraction data

Arun K. Kulshreshth 1, , Andreas Alpers 2, , Gabor T. Herman 1, , Erik Knudsen 2, , Lajos Rodek 1, and  Henning F. Poulsen 2,

1. 

Department of Computer Science, The Graduate Center, CUNY, NY 10016, United States, United States, United States
2. 

Center for Fundamental Research: ‘Metal Structures in Four Dimensions’, Risø DTU, Technical University of Denmark, DK-4000 Roskilde, Denmark, Denmark, Denmark

Received  April 2008 Revised  October 2008 Published  February 2009

An iterative search method is proposed for obtaining orientation maps inside polycrystals from three-dimensional X-ray diffraction (3DXRD) data. In each step, detector pixel intensities are calculated by a forward model based on the current estimate of the orientation map. The pixel at which the experimentally measured value most exceeds the simulated one is identified. This difference can only be reduced by changing the current estimate at a location from a relatively small subset of all possible locations in the estimate and, at each such location, an increase at the identified pixel can only be achieved by changing the orientation in only a few possible ways. The method selects the location/orientation pair indicated as best by a function that measures data consistency combined with prior information on orientation maps. The superiority of the method to a previously published forward projection Monte Carlo optimization is demonstrated on simulated data.
Keywords: 3DXRD, X-Ray Diffraction., Grain Map, Tomography, Reconstruction, Discrete Inverse Problem.
Mathematics Subject Classification: 94A08, 92F05, 74N15, 90C5.
Citation: Arun K. Kulshreshth, Andreas Alpers, Gabor T. Herman, Erik Knudsen, Lajos Rodek, Henning F. Poulsen. A greedy method for reconstructing polycrystals from three-dimensional X-ray diffraction data. Inverse Problems & Imaging, 2009, 3 (1) : 69-85. doi: 10.3934/ipi.2009.3.69
[1]

Zhenhua Zhao, Yining Zhu, Jiansheng Yang, Ming Jiang. Mumford-Shah-TV functional with application in X-ray interior tomography. Inverse Problems & Imaging, 2018, 12 (2) : 331-348. doi: 10.3934/ipi.2018015
[2]

Dan Jane, Gabriel P. Paternain. On the injectivity of the X-ray transform for Anosov thermostats. Discrete & Continuous Dynamical Systems - A, 2009, 24 (2) : 471-487. doi: 10.3934/dcds.2009.24.471
[3]

François Rouvière. X-ray transform on Damek-Ricci spaces. Inverse Problems & Imaging, 2010, 4 (4) : 713-720. doi: 10.3934/ipi.2010.4.713
[4]

Silvia Allavena, Michele Piana, Federico Benvenuto, Anna Maria Massone. An interpolation/extrapolation approach to X-ray imaging of solar flares. Inverse Problems & Imaging, 2012, 6 (2) : 147-162. doi: 10.3934/ipi.2012.6.147
[5]

Wenzhong Zhu, Huanlong Jiang, Erli Wang, Yani Hou, Lidong Xian, Joyati Debnath. X-ray image global enhancement algorithm in medical image classification. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1297-1309. doi: 10.3934/dcdss.2019089
[6]

Nuutti Hyvönen, Martti Kalke, Matti Lassas, Henri Setälä, Samuli Siltanen. Three-dimensional dental X-ray imaging by combination of panoramic and projection data. Inverse Problems & Imaging, 2010, 4 (2) : 257-271. doi: 10.3934/ipi.2010.4.257
[7]

Jakob S. Jørgensen, Emil Y. Sidky, Per Christian Hansen, Xiaochuan Pan. Empirical average-case relation between undersampling and sparsity in X-ray CT. Inverse Problems & Imaging, 2015, 9 (2) : 431-446. doi: 10.3934/ipi.2015.9.431
[8]

Alexander Balandin. The localized basis functions for scalar and vector 3D tomography and their ray transforms. Inverse Problems & Imaging, 2016, 10 (4) : 899-914. doi: 10.3934/ipi.2016026
[9]

Tim Kreutzmann, Andreas Rieder. Geometric reconstruction in bioluminescence tomography. Inverse Problems & Imaging, 2014, 8 (1) : 173-197. doi: 10.3934/ipi.2014.8.173
[10]

Henrik Garde, Kim Knudsen. 3D reconstruction for partial data electrical impedance tomography using a sparsity prior. Conference Publications, 2015, 2015 (special) : 495-504. doi: 10.3934/proc.2015.0495
[11]

Mila Nikolova. Model distortions in Bayesian MAP reconstruction. Inverse Problems & Imaging, 2007, 1 (2) : 399-422. doi: 10.3934/ipi.2007.1.399
[12]

Michael V. Klibanov. A phaseless inverse scattering problem for the 3-D Helmholtz equation. Inverse Problems & Imaging, 2017, 11 (2) : 263-276. doi: 10.3934/ipi.2017013
[13]

Christopher P. Grant. Grain sizes in the discrete Allen-Cahn and Cahn-Hilliard equations. Discrete & Continuous Dynamical Systems - A, 2001, 7 (1) : 127-146. doi: 10.3934/dcds.2001.7.127
[14]

Leonid Kunyansky. Fast reconstruction algorithms for the thermoacoustic tomography in certain domains with cylindrical or spherical symmetries. Inverse Problems & Imaging, 2012, 6 (1) : 111-131. doi: 10.3934/ipi.2012.6.111
[15]

Li Shen, Eric Todd Quinto, Shiqiang Wang, Ming Jiang. Simultaneous reconstruction and segmentation with the Mumford-Shah functional for electron tomography. Inverse Problems & Imaging, 2018, 12 (6) : 1343-1364. doi: 10.3934/ipi.2018056
[16]

Herbert Egger, Manuel Freiberger, Matthias Schlottbom. On forward and inverse models in fluorescence diffuse optical tomography. Inverse Problems & Imaging, 2010, 4 (3) : 411-427. doi: 10.3934/ipi.2010.4.411
[17]

Lacramioara Grecu, Constantin Popa. Constrained SART algorithm for inverse problems in image reconstruction. Inverse Problems & Imaging, 2013, 7 (1) : 199-216. doi: 10.3934/ipi.2013.7.199
[18]

Michael V. Klibanov, Dinh-Liem Nguyen, Loc H. Nguyen, Hui Liu. A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data. Inverse Problems & Imaging, 2018, 12 (2) : 493-523. doi: 10.3934/ipi.2018021
[19]

Jussi Korpela, Matti Lassas, Lauri Oksanen. Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation. Inverse Problems & Imaging, 2019, 13 (3) : 575-596. doi: 10.3934/ipi.2019027
[20]

Anatoli F. Ivanov. On global dynamics in a multi-dimensional discrete map. Conference Publications, 2015, 2015 (special) : 652-659. doi: 10.3934/proc.2015.0652

2018 Impact Factor: 1.469

Tools

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences