Maximum a posteriori estimation of crystallographic phases in X-ray diffraction tomography.
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.
X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Lemont, IL, USA dgursoy@aps.anl.gov.
Doĝa
D
Gürsoy
Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL, USA.
Tekin
T
Biçer
X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Lemont, IL, USA.
Jonathan D
JD
Almer
Mathematics and Computer Science Division, Argonne National Laboratory, Lemont, IL, USA.
Raj
R
Kettimuthu
Department of Cell and Molecular Biology, Feinberg School of Medicine, Northwestern University, Chicago, IL, USA.
Stuart R
SR
Stock
X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Lemont, IL, USA.
Francesco
F
De Carlo
D000465:Algorithms; D016477:Artifacts; D003198:Computer Simulation; D003461:Crystallography / Q000379:methods*; D015233:Models, Statistical; D044367:Phase Transition; D016012:Poisson Distribution; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014961:X-Ray Diffraction / Q000379:methods*
biomineralization; crystalline phases; diffraction tomography; image reconstruction; maximum a posteriori estimation