skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on October 31, 2020

Title: 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:
 [1];  [2];  [3];  [3]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Argonne National Lab. (ANL), Lemont, IL (United States)
  3. Carnegie Mellon Univ., Pittsburgh, PA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (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. doi: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. doi:10.1107/S1600576719013529.
@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 = {2019},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on October 31, 2020
Publisher's Version of Record

Save / Share:

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
  • DOI: 10.1287/ijoc.10.2.218

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
  • DOI: 10.1016/j.cam.2011.07.009

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
  • DOI: 10.1109/83.236536

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
  • DOI: 10.1109/TAC.2014.2354892

Parallel alternating direction multiplier decomposition of convex programs
journal, January 1994

  • Eckstein, J.
  • Journal of Optimization Theory and Applications, Vol. 80, Issue 1
  • DOI: 10.1007/BF02196592

A Splitting-Based Iterative Algorithm for Accelerated Statistical X-Ray CT Reconstruction
journal, March 2012


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
  • DOI: 10.1080/073033002100000182

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
  • DOI: 10.1063/1.1714396

High-order TVL1-based images restoration and spatially adapted regularization parameter selection
journal, June 2014


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
  • DOI: 10.1107/S002188980602468X

Entropy optimization in quantitative texture analysis
journal, August 1988

  • Schaeben, H.
  • Journal of Applied Physics, Vol. 64, Issue 4
  • DOI: 10.1063/1.341694

Compressed sensing
journal, April 2006


Orientation sampling for dictionary-based diffraction pattern indexing methods
journal, November 2016


Determination of the Orientation Distribution Function From One Pole-figure
journal, January 1982

  • Imhof, János
  • Textures and Microstructures, Vol. 5, Issue 2
  • DOI: 10.1155/TSM.5.73

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
  • DOI: 10.1088/0965-0393/22/7/075013

On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators
journal, April 1992

  • Eckstein, Jonathan; Bertsekas, Dimitri P.
  • Mathematical Programming, Vol. 55, Issue 1-3
  • DOI: 10.1007/BF01581204

A dual algorithm for the solution of nonlinear variational problems via finite element approximation
journal, January 1976


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
  • DOI: 10.1155/TSM.14-18.1203

Determination of the orientation distribution function from pole figures in arbitrarily defined cells
journal, April 1986


Texture Analysis with MTEX – Free and Open Source Software Toolbox
journal, February 2010


Three-dimensional maps of grain boundaries and the stress state of individual grains in polycrystals and powders
journal, November 2001

  • Poulsen, H. F.; Nielsen, S. F.; Lauridsen, E. M.
  • Journal of Applied Crystallography, Vol. 34, Issue 6
  • DOI: 10.1107/S0021889801014273

Analytical Methods for Representing Complex Textures by Biaxial Pole Figures
journal, August 1968

  • Williams, R. O.
  • Journal of Applied Physics, Vol. 39, Issue 9
  • DOI: 10.1063/1.1656969

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
  • DOI: 10.1107/S1600576717001157

Spherical harmonics in texture analysis
journal, July 2003


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
  • DOI: 10.1155/TSM.10.243