OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 7 — Jun. 25, 2012

Investigation of discrete imaging models and iterative image reconstruction in differential X-ray phase-contrast tomography

Qiaofeng Xu, Emil Y. Sidky, Xiaochuan Pan, Marco Stampanoni, Peter Modregger, and Mark A. Anastasio  »View Author Affiliations

Optics Express, Vol. 20, Issue 10, pp. 10724-10749 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (2572 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Differential X-ray phase-contrast tomography (DPCT) refers to a class of promising methods for reconstructing the X-ray refractive index distribution of materials that present weak X-ray absorption contrast. The tomographic projection data in DPCT, from which an estimate of the refractive index distribution is reconstructed, correspond to one-dimensional (1D) derivatives of the two-dimensional (2D) Radon transform of the refractive index distribution. There is an important need for the development of iterative image reconstruction methods for DPCT that can yield useful images from few-view projection data, thereby mitigating the long data-acquisition times and large radiation doses associated with use of analytic reconstruction methods. In this work, we analyze the numerical and statistical properties of two classes of discrete imaging models that form the basis for iterative image reconstruction in DPCT. We also investigate the use of one of the models with a modern image reconstruction algorithm for performing few-view image reconstruction of a tissue specimen.

© 2012 OSA

OCIS Codes
(100.3190) Image processing : Inverse problems
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
Image Processing

Original Manuscript: September 30, 2011
Revised Manuscript: January 3, 2012
Manuscript Accepted: January 9, 2012
Published: April 25, 2012

Virtual Issues
Vol. 7, Iss. 7 Virtual Journal for Biomedical Optics

Qiaofeng Xu, Emil Y. Sidky, Xiaochuan Pan, Marco Stampanoni, Peter Modregger, and Mark A. Anastasio, "Investigation of discrete imaging models and iterative image reconstruction in differential X-ray phase-contrast tomography," Opt. Express 20, 10724-10749 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13, 6296–6304 (2005). [CrossRef] [PubMed]
  2. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by x-ray talbot interferometry for biological imaging,” Jpn. J. Appl. Phys.45, 5254–5262 (2006). [CrossRef]
  3. A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase–contrast X–ray computed tomography for observing biological soft tissues,” Nat. Med.2, 473–475 (1996). [CrossRef] [PubMed]
  4. S. McDonald, F. Marone, C. Hintermuller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat.16, 562–572 (2009). [CrossRef] [PubMed]
  5. J. Brankov, M. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys.33, 278–289 (2006). [CrossRef] [PubMed]
  6. Z. Qi, J. Zambelli, N. Bevins, and G. Chen, “A novel method to reduce data acquisition time in differential phase contrast: computed tomography using compressed sensing,” in “Proc. SPIE,” 7258A1–A8 (2009)
  7. M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett.90, 224101 (2007). [CrossRef]
  8. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Phys.2, 258–261 (2006). [CrossRef]
  9. D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol.42, 2015–2025 (1997). [CrossRef] [PubMed]
  10. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys.42, 866–868 (2003). [CrossRef]
  11. G. Faris and R. Byer, “Three-dimensional beam-deflection optical tomography of a supersonic jet,” Appl. Opt.27, 5202–5212 (1988). [CrossRef] [PubMed]
  12. J. Stricker, “Analysis of 3-d phase objects by moiré deflectometry,” Appl. Opt.23, 3657–3659 (1984). [CrossRef] [PubMed]
  13. P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based x-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. USA107, 13576–13581 (2010). [CrossRef] [PubMed]
  14. Z. Huang, K. Kang, L. Zhang, Z. Chen, F. Ding, Z. Wang, and Q. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard x rays,” Phys. Rev. A79, 013815 (2009). [CrossRef]
  15. T. Köhler, B. Brendel, and E. Roessl, “Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. Phys.38, 4542–4545 (2011). [CrossRef] [PubMed]
  16. A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Meth. A352, 622–628 (1995). [CrossRef]
  17. A. Momose, “Phase-sensitive imaging and phase tomography using x-ray interferometers,” Opt. Express11, 2303–2314 (2003). [CrossRef]
  18. T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature373, 595–598 (1995). [CrossRef]
  19. M. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. Galatsanos, Y. Yang, J. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol.48, 3875–3895 (2003). [CrossRef]
  20. F. Dilmanian, Z. Zhong, B. Ren, X. Wu, L. Chapman, I. Orion, and W. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol.45, 933–946 (2000). [CrossRef] [PubMed]
  21. K. Pavlov, C. Kewish, J. Davis, and M. Morgan, “A new theoretical approach to x-ray diffraction tomography,” J. Phys. D Appl. Phys.33, 1596–1605 (2000). [CrossRef]
  22. S. Fiedler, A. Bravin, J. Keyriläinen, M. Fernández, P. Suortti, W. Thomlinson, M. Tenhunen, P. Virkkunen, and M. Karjalainen-Lindsberg, “Imaging lobular breast carcinoma: comparison of synchrotron radiation dei-ct technique with clinical ct, mammography and histology,” Phys. Med. Biol.49, 175–188 (2004). [CrossRef] [PubMed]
  23. A. Maksimenko, M. Ando, S. Hiroshi, and T. Yuasa, “Computed tomographic reconstruction based on x-ray refraction contrast,” Appl. Phys. Lett.86, 124105–124105-3 (2005). [CrossRef]
  24. I. Koyama, A. Momose, J. Wu, T. Lwin, and T. Takeda, “Biological imaging by x-ray phase tomography using diffraction-enhanced imaging,” Jpn. J. Appl. Phys.44, 8219–8221 (2005). [CrossRef]
  25. K. Creath, “Phase-measurement interferometry techniques,” Prog. Opt.26, 349–393 (1988). [CrossRef]
  26. Y. Takeda, W. Yashiro, Y. Suzuki, S. Aoki, T. Hattori, and A. Momose, “X-ray phase imaging with single phase grating,” Jpn. J. Appl. Phys.46, 89–91 (2007). [CrossRef]
  27. D. Paganin, Coherent X-ray Optics, (Oxford University Press, 2006). [CrossRef]
  28. M. A. Anastasio and X. Pan, “Region-of-interest imaging in differential phase-contrast tomography,” Opt. Lett.32, 3167–3169 (2007). [CrossRef] [PubMed]
  29. A. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Service Center, Piscataway, NJ, 1988).
  30. R. Siddon, “Fast calculation of the exact radiological path for a three-dimensional CT array,” Med. Phys.12, 252–255 (1985). [CrossRef] [PubMed]
  31. S. Lo, “Strip and line path integrals with a square pixel matrix: A unified theory for computational CT projections,” IEEE Trans. Med. Imag.7, 355–363 (1988). [CrossRef]
  32. J. Monaghan, “Smoothed particle hydrodynamics,” Rep. Prog. Phys.68, 1703–1760 (2005). [CrossRef]
  33. A. Chaniotis and D. Poulikakos, “High order interpolation and differentiation using b-splines,” J. Comput. Phys.197, 253–274 (2004). [CrossRef]
  34. R. Lewitt, “Multidimensional digital image representations using generalized Kaiser-Bessel window functions,” J. Opt. Soc. Am. A7, 1834–1846 (1990). [CrossRef] [PubMed]
  35. R. Lewitt, “Alternatives to voxels for image representation in iterative reconstruction algorithms,” Phys. Med. Biol.37, 705–716 (1992). [CrossRef] [PubMed]
  36. M. Bertero, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998). [CrossRef]
  37. R. Fatehi, M. Fayazbakhsh, and M. Manzari, “On discretization of second-order derivatives in smoothed particle hydrodynamics,” Proceedings of World Academy of Science, Engineering and Technology. 30 pp. 243–246 (2008).
  38. S. Matej and R. Lewitt, “Image representation and tomographic reconstruction using spherically-symmetric volume elements,” in Nuclear Science Symposium and Medical Imaging Conference, 1992., Conference Record of the 1992 IEEE, (IEEE, 1992), pp. 1191–1193.
  39. S. Matej and R. Lewitt, “Practical considerations for 3-D image reconstruction using spherically symmetric volume elements,” IEEE Trans. Med. Imag.15, 68–78 (1996). [CrossRef]
  40. T. Obi, S. Matej, R. Lewitt, and G. Herman, “2.5-D simultaneous multislice reconstruction by series expansion methods from fourier-rebinned pet data,” IEEE Trans. Med. Imag.19, 474–484 (2000). [CrossRef]
  41. D. Hanselman and B. Littlefield, Mastering Matlab 7 (Pearson Education, 2005).
  42. V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum.81, 073709 (2010). [CrossRef] [PubMed]
  43. T. Köhler, K. Engel, and E. Roessl, “Noise properties of grating-based x-ray phase contrast computed tomography,” Med. Phys.38, S106–S116 (2011). [CrossRef]
  44. J. Fessler, “Penalized weighted least-squares image reconstruction for positron emission tomography,” IEEE Trans. Med. Imag.13, 290–300 (1994). [CrossRef]
  45. H. Barrett, K. Myers, and S. Dhurjaty, Foundations of Image Science (Wiley-Interscience, 2003), 2nd ed.
  46. M. A. Anastasio, M. Kupinski, and X. Pan, “Noise propagation in diffraction tomography: Comparison of conventional algorithms with a new reconstruction algorithm,” IEEE Trans. Nucl. Sci.45, 2216–2223 (1998). [CrossRef]
  47. J. Zhang, M. A. Anastasio, P. La Rivière, and L. Wang, “Effects of different imaging models on least-squares image reconstruction accuracy in photoacoustic tomography,” IEEE Trans. Med. Imag.28, 1781–1790 (2009). [CrossRef]
  48. E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory52, 489–509 (2006). [CrossRef]
  49. E. Candes, J. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pur. Appl. Math.59, 1207–1223 (2006). [CrossRef]
  50. E. Y. Sidky, C. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” Journal of X-Ray Science and Technology14, 119–139 (2006).
  51. E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol.53, 4777–4807 (2008). [CrossRef] [PubMed]
  52. X. Han, J. Bian, D. Eaker, T. Kline, E. Y. Sidky, E. Ritman, and X. Pan, “Algorithm-enabled low-dose micro-CT imaging,” IEEE Trans. Med. Imag.30 pp. 606–620 (2011). [CrossRef]
  53. M. Abramovitz and I. Stegun, Handbook of Mathematical Functions (Dover Publications, 1972).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited