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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 15 — Jul. 19, 2010
  • pp: 16074–16089

Performance analysis of the attenuation-partition based iterative phase retrieval algorithm for in-line phase-contrast imaging

Aimin Yan, Xizeng Wu, and Hong Liu  »View Author Affiliations

Optics Express, Vol. 18, Issue 15, pp. 16074-16089 (2010)

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The phase retrieval is an important task in x-ray phase contrast imaging. The robustness of phase retrieval is especially important for potential medical imaging applications such as phase contrast mammography. Recently the authors developed an iterative phase retrieval algorithm, the attenuation-partition based algorithm, for the phase retrieval in inline phase-contrast imaging [1]. Applied to experimental images, the algorithm was proven to be fast and robust. However, a quantitative analysis of the performance of this new algorithm is desirable. In this work, we systematically compared the performance of this algorithm with other two widely used phase retrieval algorithms, namely the Gerchberg-Saxton (GS) algorithm and the Transport of Intensity Equation (TIE) algorithm. The systematical comparison is conducted by analyzing phase retrieval performances with a digital breast specimen model. We show that the proposed algorithm converges faster than the GS algorithm in the Fresnel diffraction regime, and is more robust against image noise than the TIE algorithm. These results suggest the significance of the proposed algorithm for future medical applications with the x-ray phase contrast imaging technique.

© 2010 Optical Society of America

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(340.7440) X-ray optics : X-ray imaging

ToC Category:
Image Processing

Original Manuscript: April 2, 2010
Revised Manuscript: June 11, 2010
Manuscript Accepted: July 9, 2010
Published: July 15, 2010

Virtual Issues
Vol. 5, Iss. 12 Virtual Journal for Biomedical Optics

Aimin Yan, Xizeng Wu, and Hong Liu, "Performance analysis of the attenuation-partition based iterative phase retrieval algorithm for in-line phase-contrast imaging," Opt. Express 18, 16074-16089 (2010)

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  1. A. Yan, X. Wu, and H. Liu, "An attenuation-partition based iterative phase retrieval algorithm for in-line phasecontrast imaging," Opt. Express 16, 13330 - 13341 (2008). [CrossRef]
  2. S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, "Phase-contrast imaging using polychromatic hard X-rays," Nature 384, 335 - 338 (1996). [CrossRef]
  3. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Shelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486 - 5492 (1995). [CrossRef]
  4. K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, "Quantitative Phase Imaging Using Hard X Rays," Phy. Rev. Lett. 77, 2961 - 2965 (1996). [CrossRef]
  5. A. Pogany, D. Gao, and S. Wilkins, "Contrast and resolution in imaging with a microfocus x-ray source," Rev. Sci. Instrum. 68, 2774 - 2782 (1997). [CrossRef]
  6. F. Arfelli, V. Bonvicini,  and et al, "Mammography with synchrotron radiation: phase-detected Techniques," Radiology 215, 286 - 293 (2000).
  7. D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, "Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object," J. Microsc. 206, 33 - 40 (2002). [CrossRef] [PubMed]
  8. S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Poganin, A. Pogany, A. Stevenson, and S. Wilkins, "X-ray phasecontrast microscopy and microtomography," Opt. Express 11, 2289 - 2302 (2003). [CrossRef] [PubMed]
  9. X. Wu and H. Liu, "A general theoretical formalism for X-ray phase contrast imaging," J. X-ray Sci. Tech.  11, 33 - 42 (2003).
  10. X. Wu and H. Liu, "Clinical implementation of phase-contrast x-ray imaging: Theoretical foundations and design considerations," Med. Phys. 30, 2169 - 2179 (2003). [CrossRef] [PubMed]
  11. X. Wu and H. Liu, "A new theory of phase-contrast x-ray imaging based on Wigner distributions," Med. Phys. 31, 2378 - 2384 (2004). [CrossRef] [PubMed]
  12. E. Donnelly, R. Price, and D. Pickens, "Experimental validation of the Wigner distributions theory of phasecontrast imaging," Med. Phys. 32, 928 - 931 (2005). [CrossRef] [PubMed]
  13. D. Zhang, M. Donvan, L. Fajardo, A. Archer, X. Wu, and H. Liu, "Preliminary feasibility study of an in-line phase contrast x-ray imaging prototype," IEEE Trans. Biomed. Eng. 55, 2249 - 2257 (2008). [CrossRef] [PubMed]
  14. X. Wu, H. Liu, and A. Yan, "X-ray phase-attenuation duality and phase retrieval," Opt. Lett. 30(4), 379 - 381 (2005). [CrossRef] [PubMed]
  15. X. Wu and H. Liu, "X-Ray cone-beam phase tomography formulas based on phase-attenuation duality," Opt. Express 13, 6000 - 6014 (2005). [CrossRef] [PubMed]
  16. P. Cloetens, R. Mache, M. Schlenker, and S. Lerbs-Mache, "Quantitative phase tomography of Arabidopsis seeds reveals intercellular void network," PNAS 103, 14,626 - 14,630 (2006). [CrossRef]
  17. X. Wu, H. Liu, and A. Yan, "Phase-Contrast X-Ray Tomography: Contrast Mechanism and Roles of Phase Retrieval," Eur. J. Radiology 68, S8 - S12 (2008). [CrossRef]
  18. D. Paganin and K. Nugent, "Noninterferometric Phase Imaging with Partially Coherent Light," Phy. Rev. Lett. 80, 2586 - 2589 (1998). [CrossRef]
  19. X. Wu and H. Liu, "A dual detector approach for X-ray attenuation and phase imaging," J. X-ray Sci. Tech. 12, 35-42 (2004).
  20. X. Wu and H. Liu, "Phase-space evolution of x-ray coherence in phase-sensitive imaging," Appl. Opt. 47, E44 - E52 (2008). [CrossRef] [PubMed]
  21. M. Teague, "Deterministic phase retrieval: a Green’s function solution," J. Opt. Soc. Am. 73, 1434 - 1441 (1983). [CrossRef]
  22. T. Gureyev, Y. Nesterets, D. Paganin, A. Pogany, and S. Wilkins, "Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination," Opt. Commun. 259, 569 - 580 (2006). [CrossRef]
  23. J. Guigay, M. Langer, R. Boistel, and P. Cloetens, "Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region," Opt. Lett. 32, 1617 - 1619 (2007). [CrossRef] [PubMed]
  24. X. Wu and A. Yan, "Phase Retrieval From One Single Phase Contrast X-Ray Image," Opt. Express  17, 11187 - 11196 (2009). [CrossRef]
  25. L. Allen and M. Oxley, "Phase retrieval from series of images obtained by defocus variation," Opt. Commun. 199, 65 - 75 (2001). [CrossRef]
  26. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of the phase from image and diffraction plane pictures," Optik 35, 237 - 246 (1972).
  27. J. Fienup, "Reconstruction of an object from the modulus of its Fourier Transform," Opt. Lett. 3, 27 - 29 (1978). [CrossRef] [PubMed]
  28. J. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758 - 2769 (1982). [CrossRef] [PubMed]
  29. N. Dyson, X-Rays in Atomic and Nuclear Physics (Longman Scientific and Technical, Essex, UK, 1973).
  30. X. Wu, A. Dean, and H. Liu, Biomedical Photonics Handbook, (CRC Press, Tampa, Fla., 2003) Chap. 26, pp. 26-1 - 26-34.
  31. J. H. Hubbell, W. I. Veigele, E. A. Briggs,  et al., "Atomic form factors, incohoerent scattering functions, and photon scattering cross sections," J. Phys. Chem. Ref. Data 4, 471-538 (1975). [CrossRef]
  32. L. Rudin, "Images, numerical analysis of singularities and shock filters," Report #TR:5250:87, Caltech, C,S, Dept. (1987).
  33. L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D 60, 259 - 268 (1992). [CrossRef]
  34. X. Wu, G. T. Barnes and D. M. Tucker, "Spectral dependence of glandular tissue dose in screen-film mammography," Radiology 179, 143 - 148 (1991). [PubMed]
  35. X. Wu, E. L. Gingold, G. T. Barnes and D. M. Tucker, "Normalized average glandular dose in Molybdenum target-Rhodium filter and Rhodium target-Rhodium filter mammography," Radiology 193, 83 - 89 (1994). [PubMed]
  36. J. Seldin and J. Fienup, "Numerical investigation of the uniqueness of phase retrieval," J. Opt. Soc. Am. A 7(3), 412 - 427 (1990). [CrossRef]
  37. F. Roddier and C. Roddier, "Wavefront reconstruction using Iterative Fourier transforms," Appl. Opt. 30, 1325 -1327 (1991). [CrossRef] [PubMed]
  38. C. Roddier and F. Roddier, "Wave-front reconstruction from defocused images and the testing of ground-based optical telescopes," J. Opt. Soc. Am. A 10, 2277 - 2287 (1993). [CrossRef]
  39. T. Gureyev, A. Roberts, and K. Nugent, "Partially coherent fields, the transport-of-intensity equation, and phase uniqueness," J. Opt. Soc. Am. A 12, 1942 - 1946 (1995). [CrossRef]
  40. T. Gureyev and K. Nugent, "Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination," J. Opt. Soc. Am. A 13, 1670 - 1682 (1996). [CrossRef]
  41. A. Tychonoff and V. Arsenin, Solution of Ill-posed Problems (Winston & Sons, Washington, 1977).

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