An iterative reconstruction algorithm for pole figure inversion using total variation regularization
Abstract
This paper describes a new discrete method for inverting X-ray pole figures to estimate the orientation distribution function (ODF). The method employs the equal-volume `cubochoric' representation for uniform discretization of orientation space, SO(3). The forward-projection model is combined with an anisotropic total variation term to iteratively determine the ODF. Here, the efficacy of the new method is evaluated with both model and experimental data and compared with existing discrete and series expansion methods.
- Authors:
-
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Argonne National Lab. (ANL), Lemont, IL (United States)
- Carnegie Mellon Univ., Pittsburgh, PA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1575870
- Report Number(s):
- LLNL-JRNL-767546
Journal ID: ISSN 1600-5767; JACGAR; 957917
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Applied Crystallography (Online)
- Additional Journal Information:
- Journal Name: Journal of Applied Crystallography (Online); Journal Volume: 52; Journal Issue: 6; Journal ID: ISSN 1600-5767
- Publisher:
- International Union of Crystallography
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; pole figure inversion; orientation distribution function; total variation regularization; texture
Citation Formats
Singh, Saransh, Kc, Prabhat, Sridhar, Shivram Kashyap, and De Graef, Marc. An iterative reconstruction algorithm for pole figure inversion using total variation regularization. United States: N. p., 2019.
Web. doi:10.1107/S1600576719013529.
Singh, Saransh, Kc, Prabhat, Sridhar, Shivram Kashyap, & De Graef, Marc. An iterative reconstruction algorithm for pole figure inversion using total variation regularization. United States. https://doi.org/10.1107/S1600576719013529
Singh, Saransh, Kc, Prabhat, Sridhar, Shivram Kashyap, and De Graef, Marc. Thu .
"An iterative reconstruction algorithm for pole figure inversion using total variation regularization". United States. https://doi.org/10.1107/S1600576719013529. https://www.osti.gov/servlets/purl/1575870.
@article{osti_1575870,
title = {An iterative reconstruction algorithm for pole figure inversion using total variation regularization},
author = {Singh, Saransh and Kc, Prabhat and Sridhar, Shivram Kashyap and De Graef, Marc},
abstractNote = {This paper describes a new discrete method for inverting X-ray pole figures to estimate the orientation distribution function (ODF). The method employs the equal-volume `cubochoric' representation for uniform discretization of orientation space, SO(3). The forward-projection model is combined with an anisotropic total variation term to iteratively determine the ODF. Here, the efficacy of the new method is evaluated with both model and experimental data and compared with existing discrete and series expansion methods.},
doi = {10.1107/S1600576719013529},
journal = {Journal of Applied Crystallography (Online)},
number = 6,
volume = 52,
place = {United States},
year = {Thu Oct 31 00:00:00 EDT 2019},
month = {Thu Oct 31 00:00:00 EDT 2019}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Operator-Splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control
journal, May 1998
- Eckstein, Jonathan; Ferris, Michael C.
- INFORMS Journal on Computing, Vol. 10, Issue 2
Uniform spherical grids via equal area projection from the cube to the sphere
journal, October 2011
- Roşca, Daniela; Plonka, Gerlind
- Journal of Computational and Applied Mathematics, Vol. 236, Issue 6
A generalized Gaussian image model for edge-preserving MAP estimation
journal, July 1993
- Bouman, C.; Sauer, K.
- IEEE Transactions on Image Processing, Vol. 2, Issue 3
Optimal Parameter Selection for the Alternating Direction Method of Multipliers (ADMM): Quadratic Problems
journal, March 2015
- Ghadimi, Euhanna; Teixeira, Andre; Shames, Iman
- IEEE Transactions on Automatic Control, Vol. 60, Issue 3
A novel pole figure inversion method: specification of the MTEX algorithm
journal, November 2008
- Hielscher, R.; Schaeben, H.
- Journal of Applied Crystallography, Vol. 41, Issue 6
On the Reproduction of the Orientation Distribution Function of Texturized Samples from Reduced Pole Figures Using the Conception of a Conditional Ghost Correction
journal, August 1982
- Matthies, S.; Vinel, G. W.
- physica status solidi (b), Vol. 112, Issue 2
Electron Backscatter Diffraction in Materials Science
book, January 2009
- Schwartz, Adam J.; Kumar, Mukul; Adams, Brent L.
Parallel alternating direction multiplier decomposition of convex programs
journal, January 1994
- Eckstein, J.
- Journal of Optimization Theory and Applications, Vol. 80, Issue 1
A Splitting-Based Iterative Algorithm for Accelerated Statistical X-Ray CT Reconstruction
journal, March 2012
- Ramani, S.; Fessler, J. A.
- IEEE Transactions on Medical Imaging, Vol. 31, Issue 3
Pole Figure Inversion Using Finite Elements Over Rodrigues Space
journal, January 2002
- Barton, Nathan R.; Boyce, Donald E.; Dawson, Paul R.
- Textures and Microstructures, Vol. 35, Issue 2
Description of Crystallite Orientation in Polycrystalline Materials. III. General Solution to Pole Figure Inversion
journal, June 1965
- Roe, Ryong‐Joon
- Journal of Applied Physics, Vol. 36, Issue 6
High-order TVL1-based images restoration and spatially adapted regularization parameter selection
journal, June 2014
- Liu, Gang; Huang, Ting-Zhu; Liu, Jun
- Computers & Mathematics with Applications, Vol. 67, Issue 10
A novel optimization-based pole-figure inversion method: comparison with WIMV and maximum entropy methods
journal, September 2006
- Bernier, Joel V.; Miller, Matthew P.; Boyce, Donald E.
- Journal of Applied Crystallography, Vol. 39, Issue 5
Entropy optimization in quantitative texture analysis
journal, August 1988
- Schaeben, H.
- Journal of Applied Physics, Vol. 64, Issue 4
Compressed sensing
journal, April 2006
- Donoho, D. L.
- IEEE Transactions on Information Theory, Vol. 52, Issue 4
Orientation sampling for dictionary-based diffraction pattern indexing methods
journal, November 2016
- Singh, S.; De Graef, M.
- Modelling and Simulation in Materials Science and Engineering, Vol. 24, Issue 8
Determination of the Orientation Distribution Function From One Pole-figure
journal, January 1982
- Imhof, János
- Textures and Microstructures, Vol. 5, Issue 2
A new method of constructing a grid in the space of 3D rotations and its applications to texture analysis
journal, October 2014
- Roşca, D.; Morawiec, A.; De Graef, M.
- Modelling and Simulation in Materials Science and Engineering, Vol. 22, Issue 7
A dual algorithm for the solution of nonlinear variational problems via finite element approximation
journal, January 1976
- Gabay, Daniel; Mercier, Bertrand
- Computers & Mathematics with Applications, Vol. 2, Issue 1
popLA - An Integrated Software System for Texture Analysis
journal, January 1991
- Kallend, John S.; Kocks, U. F.; Rollett, A. D.
- Textures and Microstructures, Vol. 14
Determination of the orientation distribution function from pole figures in arbitrarily defined cells
journal, April 1986
- Pawlik, K.
- physica status solidi (b), Vol. 134, Issue 2
Texture Analysis with MTEX – Free and Open Source Software Toolbox
journal, February 2010
- Bachmann, F.; Hielscher, Ralf; Schaeben, Helmut
- Solid State Phenomena, Vol. 160
Analytical Methods for Representing Complex Textures by Biaxial Pole Figures
journal, August 1968
- Williams, R. O.
- Journal of Applied Physics, Vol. 39, Issue 9
Three-dimensional texture visualization approaches: theoretical analysis and examples
journal, March 2017
- Callahan, Patrick G.; Echlin, McLean; Pollock, Tresa M.
- Journal of Applied Crystallography, Vol. 50, Issue 2
Spherical harmonics in texture analysis
journal, July 2003
- Schaeben, Helmut; van den Boogaart, K. Gerald
- Tectonophysics, Vol. 370, Issue 1-4
Properties of Projection Lines in the Space of the Orientation Distribution Function
journal, January 1989
- Morawiec, A.; Pospiech, J.
- Textures and Microstructures, Vol. 10, Issue 3