OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 4, Iss. 10 — Oct. 2, 2009

Influence of imaging geometry on noise texture in quantitative in-line X-ray phase-contrast imaging

Cheng-Ying Chou and Mark A. Anastasio  »View Author Affiliations

Optics Express, Vol. 17, Issue 17, pp. 14466-14480 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (419 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Quantitative in-line X-ray phase-contrast imaging methods seek to reconstruct separate images that depict an object’s projected absorption and refractive properties. An understanding of the statistical properties of the reconstructed images can facilitate the identification of optimal imaging parameters for specific diagnostic tasks. However, the statistical properties of quantitative X-ray phase-contrast imaging remain largely unexplored. In this work, we derive analytic expressions that describe the second-order statistics of the reconstructed absorption and phase images. Concepts from statistical decision theory are applied to demonstrate how the statistical properties of images corresponding to distinct imaging geometries can influence signal detectability.

© 2009 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(110.4280) Imaging systems : Noise in imaging systems
(110.7440) Imaging systems : X-ray imaging
(170.3010) Medical optics and biotechnology : Image reconstruction techniques

ToC Category:
Imaging Systems

Original Manuscript: May 21, 2009
Revised Manuscript: July 23, 2009
Manuscript Accepted: July 24, 2009
Published: August 3, 2009

Virtual Issues
Vol. 4, Iss. 10 Virtual Journal for Biomedical Optics

Cheng-Ying Chou and Mark A. Anastasio, "Influence of imaging geometry on noise texture in quantitative in-line X-ray phase-contrast imaging," Opt. Express 17, 14466-14480 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, 2006). [CrossRef]
  2. X. Wu and H. Liu, "Clinical implementation of X-ray phase-contrast imaging: Theoretical foundations and design considerations," Med. Phys. 30, 2169-2179 (2003). [CrossRef] [PubMed]
  3. T. Davis, D. Gao, T. E. Gureyev, A. Stevenson, and S. Wilkins, "Phase-contrast imaging of weakly absorbing materials using hard X-rays," Nature (London) 373, 335-338 (1996).
  4. K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard x-rays," Phys. Rev. Lett. 77, 2961-2964 (1996). [CrossRef] [PubMed]
  5. A. Pogany, D. Gao, and S. W. Wilkins, "Contrast and resolution in imaging with a microfocus x-ray source," Rev. Sci. Instrum. 68, 2774-2782 (1997). [CrossRef]
  6. P. Cloetens, "Contribution to Phase Contrast Imaging, Reconstruction and Tomography with Hard Synchrotron Radiation: Principles, Implementation and Applications," Ph.D. thesis, Vrije Universiteit Brussel (1999).
  7. R. A. Lewis, "Medical phase contrast x-ray imaging: current status and future prospects," Phys. Med. Biol. 49(16), 3573-3583 (2004). URL http://stacks.iop.org/0031-9155/49/3573. [CrossRef]
  8. F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. D. Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Low-dose phase contrast x-ray medical imaging," Phys. Med. Biol. 43(10), 2845-2852 (1998). URL http://stacks.iop.org/0031-9155/43/2845. [CrossRef]
  9. D. M. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, "Quantitative phase retrieval using coherent imaging systems with linear transfer functions," Opt. Commun. 234, 87-105 (2004). [CrossRef]
  10. T. E. Gureyev, A. Pogany, D. M. Paganin, and S.W. Wilkins, "Linear algorithms for phase retrieval in the Fresnel region," Opt. Commun. 231, 53-70 (2004). [CrossRef]
  11. C.-Y. Chou, Y. Huang, D. Shi, and M. A. Anastasio, "Image reconstruction in quantitative X-ray phasecontrast imaging employing multiple measurements," Opt. Express 15(16), 10,002-10,025 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-16-10002.
  12. M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, "Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography," Med. Phys. 35(10), 4556-66 (2008). [CrossRef]
  13. T. E. Gureyev and K. A. Nugent, "Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination," J. Opt. Soc. Am. A 13(8), 1670-1682 (1996). URL http://josaa.osa.org/abstract.cfm?URI=josaa-13-8-1670. [CrossRef]
  14. A. Barty, K. Nugent, A. Roberts, and D. Paganin, "Quantitative phase tomography," Opt. Commun. 175(4), 329-336 (2000). [CrossRef]
  15. J.-P. Guigay, "Fourier transform analysis of Fresnel diffraction patterns and in-line holograms," Optik 49, 121-125 (1977).
  16. P. Cloetens, W. Ludwig, J. Baruchel, D. Dyck, J. Landuyt, J. P. Guigay, and M. Schlenker, "Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays," Appl. Phys. Lett. 75, 29,132 (1999). [CrossRef]
  17. D. Paganin, A. Barty, P. J. Mcmahon, and K. A. Nugent, "Quantitative phase-amplitude microscopy III. The effects of noise," J. Microsc. 214, 51-61 (2003). [CrossRef]
  18. E. F. Donnelly, R. R. Price, and D. R. Pickens, "Characterization of the phase-contrast radiography edgeenhancement effect in a cabinet x-ray system," Med. Phys. 30, 2292-2296 (2003). [CrossRef] [PubMed]
  19. B. D. Arhatari, A. P. Mancuso, A. G. Peele, and K. A. Nugent, "Phase contrast radiography: Image modelling and optimization," Rev. Sci. Instrum. 75, 5271-5276 (2004). [CrossRef]
  20. X. Wu, H. Liu, and A. Yan, "Optimization of X-ray phase-contrast imaging based on in-line holography," Nucl. Instrum. Meth. B 234, 563-572 (2005). [CrossRef]
  21. Y. Nesterets, S. Wilkins, T. Gureyev, A. Pogany, and A. Stevenson, "On the optimization of experimental parameters for x-ray in-line phase-contrast imaging," Rev. Sci. Instrum. 76(9) (2005).
  22. T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, "Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging," Opt. Express 16(5), 3223-3241 (2008). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-16-5-3223. [CrossRef]
  23. H. Barrett and K. Myers, Foundations of Image Science (Wiley Series in Pure and Applied Optics, 2004).
  24. H. H. Barrett, "Objective assessment of image quality: effects of quantum noise and object variability," J. Opt. Soc. Am. A 7, 1266-1278 (1990). [CrossRef] [PubMed]
  25. H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. 90, 9758-9765 (1993). [CrossRef] [PubMed]
  26. K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, and G. W. Seeley, "Effect of noise correlation on detectability of disk signals in medical imaging," J. Opt. Soc. Am. A 2, 1752-1759 (1985). [CrossRef] [PubMed]
  27. C. K. Abbey and M. P. Eckstein, "Classification images for simple detection and discrimination tasks in correlated noise," J. Opt. Soc. Am. A 24, B110-B124 (2007). [CrossRef]
  28. T. E. Gureyev, S. Mayo, S. W. Wilkins, D. Paganin, and A. W. Stevenson, "Quantitative In-Line Phase-Contrast Imaging with Multienergy X Rays," Phys. Rev. Lett. 86, 5827-5830 (2001). [CrossRef] [PubMed]
  29. D. Shi and M. A. Anastasio, "Intensity diffraction tomography with fixed detector plane," Opt. Eng.  46, 107003 (2007). [CrossRef]
  30. T. E. Gureyev, D. M. Paganin, A. W. Stevenson, S. Mayo, and S. Wilkins, "Generalized eikonal of partially coherent beams and its use in quantitative imaging," Phys. Rev. Lett. 93(6), 068103 (2004).
  31. A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes (McGraw Hill, 2002).
  32. S. Lowenthal and H. Arsenault, "Image formation for coherent diffuse objects: Statistical properties," J. Opt. Soc. Am. 60, 1478-1483 (1970). [CrossRef]
  33. W. D. Stanley, G. R. Dougherty, and R. Dougherty, Digital Signal Processing (Reston Publishing Company, Inc., 1984).
  34. A. R. Pineda and H. H. Barrett, "What does DQE say about lesion detectability in digital radiography?" in Proc. of SPIE, vol. 4320, pp. 561-569 (2001). [CrossRef]
  35. R. F. Wagner and D. G. Brown, "Unified SNR analysis of medical imaging systems," Phys. Med. Biol. 30(6), 489-518 (1985). URL http://stacks.iop.org/0031-9155/30/489. [CrossRef]
  36. W. E. Smith and H. H. Barrett, "Hotelling trace criterion as a figure of merit for the optimization of imaging systems," J. Opt. Soc. Am. A 3(5), 717-725 (1986). URL http://josaa.osa.org/abstract.cfm?URI=josaa-3-5-717. [CrossRef]
  37. M. Eckstein, J. Bartroff, C. Abbey, J. Whiting, and F. Bochud, "Automated computer evaluation and optimization of image compression of x-ray coronary angiograms for signal known exactly detection tasks," Opt. Express 11(5), 460-475 (2003). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-11-5-460. [CrossRef]
  38. A. H. Baydush, D. M. Catarious, C. K. Abbey, and C. E. Floyd, "Computer aided detection of masses in mammography using subregion Hotelling observers," Med. Phys. 30(7), 1781-1787 (2003). URL http://link.aip.org/link/?MPH/30/1781/1. [CrossRef]
  39. M. A. Anastasio, M. Kupinski, and X. Pan, "Noise properties of reconstructed images in ultrasound diffraction tomography," IEEE Trans. Nucl. Sci. 45, 2216-2223 (1998). [CrossRef]

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