Maximum a posteriori estimation of crystallographic phases in X-ray difraction tomography

Doʇa Gürsoy*, Tekin Biçer, Jonathan D. Almer, Raj Kettimuthu, Stuart R. Stock, Francesco De Carlo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


A maximum a posteriori approach is proposed for X-ray diffraction tomography for reconstructing three-dimensional spatial distribution of crystallographic phases and orientations of polycrystalline materials. The approach maximizes the a posteriori density which includes a Poisson log-likelihood and an a priori term that reinforces expected solution properties such as smoothness or local continuity. The reconstruction method is validated with experimental data acquired from a section of the spinous process of a porcine vertebra collected at the 1-ID-C beamline of the Advanced Photon Source, at Argonne National Laboratory. The reconstruction results show significant improvement in the reduction of aliasing and streaking artefacts, and improved robustness to noise and undersampling compared to conventional analytical inversion approaches. The approach has the potential to reduce data acquisition times, and significantly improve beamtime efficiency.

Original languageEnglish (US)
Article number20140392
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2043
StatePublished - Jun 13 2015


  • Biomineralization
  • Crystalline phases
  • Difraction tomography
  • Image reconstruction
  • Maximum a posteriori estimation

ASJC Scopus subject areas

  • General Engineering
  • General Physics and Astronomy
  • General Mathematics


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