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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 12185–12196

Total variation minimization approach in in-line x-ray phase-contrast tomography

Alexander Kostenko, K. Joost Batenburg, Andrew King, S. Erik Offerman, and Lucas J. van Vliet  »View Author Affiliations

Optics Express, Vol. 21, Issue 10, pp. 12185-12196 (2013)

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The reconstruction problem in in-line X-ray Phase-Contrast Tomography is usually approached by solving two independent linearized sub-problems: phase retrieval and tomographic reconstruction. Both problems are often ill-posed and require the use of regularization techniques that lead to artifacts in the reconstructed image. We present a novel reconstruction approach that solves two coupled linear problems algebraically. Our approach is based on the assumption that the frequency space of the tomogram can be divided into bands that are accurately recovered and bands that are undefined by the observations. This results in an underdetermined linear system of equations. We investigate how this system can be solved using three different algebraic reconstruction algorithms based on Total Variation minimization. These algorithms are compared using both simulated and experimental data. Our results demonstrate that in many cases the proposed algebraic algorithms yield a significantly improved accuracy over the conventional L2-regularized closed-form solution. This work demonstrates that algebraic algorithms may become an important tool in applications where the acquisition time and the delivered radiation dose must be minimized.

© 2013 OSA

OCIS Codes
(100.5070) Image processing : Phase retrieval
(100.6950) Image processing : Tomographic image processing
(110.7440) Imaging systems : X-ray imaging

ToC Category:
Image Processing

Original Manuscript: February 11, 2013
Revised Manuscript: March 29, 2013
Manuscript Accepted: March 30, 2013
Published: May 10, 2013

Virtual Issues
Vol. 8, Iss. 6 Virtual Journal for Biomedical Optics

Alexander Kostenko, K. Joost Batenburg, Andrew King, S. Erik Offerman, and Lucas J. van Vliet, "Total variation minimization approach in in-line x-ray phase-contrast tomography," Opt. Express 21, 12185-12196 (2013)

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