Regularization of phase retrieval with phase-attenuation duality prior for 3-D holotomography

IEEE Transactions on Image Processing

Volumn 19, Issue 9, 2010, Pages 2428-2436

  Langer, Max ^a,b   Cloetens, Peter ^a   Peyrin, Françoise ^a,b  

^a EUROPEAN SYNCHROTRON RADIATION FACILITY   (France)

^b UNIVERSITÉ DE LYON   (France)

Author keywords

Inverse problems; phase retrieval; regularization; synchrotron radiation; X ray tomography

Indexed keywords

REFRACTIVE INDEX; SYNCHROTRON RADIATION; SYNCHROTRONS; TOMOGRAPHY;

EUROPEAN SYNCHROTRON RADIATION FACILITIES; FRESNEL DIFFRACTION PATTERNS; PHASE RETRIEVAL; PHASE-ATTENUATION DUALITY; REFRACTIVE-INDEX DISTRIBUTION; REGULARIZATION; TOMOGRAPHIC RECONSTRUCTION; X-RAY TOMOGRAPHY;

INVERSE PROBLEMS;

ALGORITHM; ARTICLE; COMPUTER ASSISTED TOMOGRAPHY; HOLOGRAPHY; IMAGE PROCESSING; IMAGE QUALITY; METHODOLOGY;

ALGORITHMS; HOLOGRAPHY; IMAGE PROCESSING, COMPUTER-ASSISTED; PHANTOMS, IMAGING; TOMOGRAPHY, X-RAY COMPUTED;

EID: 77955828919     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2010.2048608     Document Type: Article

References (38)

1. A. Momose and J. Fukuda, "Phase-contrast radiographs of nonstained rat cerebellar specimen," Med. Phys., vol.22, pp. 375-379, 1995.
2. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of X-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum., vol.66, p. 5486, 1995.
3. J. P. Guigay, "Fourier transform analysis of Fresnel diffraction patterns and in-line holograms," Optik, vol.46, pp. 121-125, 1977.
4. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre- sized non-crystalline specimens," Nature, vol.400, pp. 342-344, 1999.
5. S. Marchesini, H. N. Chapman, S. P. Hau-Riege, R. A. London, A. Szoke, H. Me, M. R. Howells, H. Padmore, R. Rosen, J. C. H. Spence, and U. Weierstall, "Coherent X-ray diffractive imaging: Applications and limitations," Opt. Exp., vol.11, pp. 2344-2353, 2003.
6. R. W. Gerchberg and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik, vol.35, pp. 237-246, 1972.
7. J. R. Fienup, "Phase retrieval algorithms: A comparison," Appl. Opt., vol.21, pp. 2758-2769, 1982.
8. V. Elser, "Phase retrieval by iterated projections," J. Opt. Soc. Amer. A, vol.20, pp. 40-55, 2003.
9. L. D. Turner, B. B. Dhal, J. P. Hayes, K. A. Nugent, D. Paterson, R. E. Scholten, C. Q. Tran, and A. G. Peele, "X-ray phase imaging: Demonstration of extended conditions with homogeneous objects," Opt. Express, vol.12, p. 2916, 2004.
10. P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, "Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X rays," Appl. Phys. Lett., vol.75, pp. 2912-2914, 1999.
11. P. Cloetens, W. Ludwig, E. Boller, L. Helfen, L. Salvo, R. Mache, and M. Schlenker, "Quantitative phase contrast tomography using coherent synchrotron radiation," Proc. SPIE, vol.4503, pp. 82-91, 2002.
12. S. Zabler, P. Cloetens, J. P. Guigay, J. Baruchel, and M. Schlenker, "Optimization of phase contrast imaging using hard X rays," Rev. Sci. Instrum., vol.76, pp. 1-7, 2005.
13. M. R. Teague, "Irradiance moments: Their propagation and use for unique retrieval of phase," J. Opt. Soc. Amer., vol.72, pp. 1199-1209, 1982.
14. K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard X rays," Phys. Rev. Lett., vol.77, pp. 2961-2964, 1996. (Pubitemid 126624182)
15. D. Paganin and K. A. Nugent, "Noninterferrometric phase imaging with partially coherent light," Phys. Rev. Lett., vol.80, pp. 2586-2589, 1998.
16. T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, "Hard X-ray quantitative non-interferrometric phase-contrast microscopy," J. Phys. D, Appl. Phys., vol.32, pp. 563-567, 1999.
17. D. M. Paganin, Coherent X-Ray Optics, ser. Oxford series on synchrotron radiation. London, U.K.: Oxford Univ. Press, 2006, vol.6.
18. A. V. Bronnikov, "Theory of quantitative phase-contrast computed tomography," J. Opt. Soc. Amer. A, vol.19, pp. 472-480, 2002.
19. T. E. Gureyev, A. Pogany, D. M. Paganin, and S. W. Wilkins, "Linear algorithms for phase retrieval in the Fresnel region," Opt. Comm., vol.231, pp. 53-70, 2004.
20. X. Wu and H. Liu, "A general theoretical formalism for X-ray phase contrast imaging," J. X-Ray Sci. Tech., vol.11, pp. 33-42, 2003.
21. J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, "Mixed contrast transfer and transport of intensity approach for phase retrieval in the Fresnel region," Opt. Lett., vol.32, pp. 1617-1619, 2007.
22. B. D. Arhatari, F. De Carlo, and A. G. Peele, "Direct quantitative tomographic reconstruction for weakly absorbing homogeneous phase objects," Rev. Sci. Instrum., vol.78, p. 053701, 2007.
23. M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, "Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography," Med. Phys., vol.35, pp. 4556-4566, 2008.
24. A. Groso, R. Abela, and M. Stampanoni, "Implementation of a fast method for high resolution phase contrast tomography," Opt. Exp., vol.14, pp. 8103-8110, 2006.
25. A. N. Tikhonov and V. A. Arsenin, Solution of Ill-Posed Problems. Washington, DC: Winston, 1977.
26. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W.Wilkins, "Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object," J. Microsc., vol.206, pp. 33-40, 2002.
27. X.Wu, H. Liu, and A. Yan, "X-ray phase-attenuation duality and phase retrieval," Opt. Lett., vol.30, pp. 379-381, 2005.
28. P. C. Hansen, "Analysis of discrete ill-posed problems by means of the L-curve," SIAM Rev., vol.34, pp. 561-580, 1992.
29. P. C. Hansen and D. P. O'Leary, "The use of the L-curve in the regularization of discrete ill-posed problems," SIAM J. Sci. Comput., vol.14, pp. 1487-1503, 1993.
30. G. H. Golub, M. Heath, and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge parameter," Technometrics, vol.21, pp. 215-223, 1979.
31. D. Gabor, "A new microscopic principle," Nature, vol.161, pp. 777-778, 1948.
32. M. Born and E.Wolf, Principles of Optics, 7th ed. Cambridge, U.K.: Cambridge Univ. Press, 1997.
33. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. Greenwood Village, CO: Roberts, 2005.
34. L. J. Allen and M. P. Oxley, "Phase retrieval from series of images obtained by defocus variation," Opt. Comm., vol.199, pp. 65-75, 2001.
35. A. Groso, M. Stampanoni, R. Abela, P. Schneider, S. Linga, and R. Müller, "Phase contrast tomography: An alternative approach," Appl. Phys. Lett., vol.88, p. 214104, 2006.
36. M. Beleggia, M. A. Schofield, V. V. Volkov, and Y. Zhu, "On the transport of intensity technique for phase retrieval," Ultramicroscopy, vol.102, pp. 37-49, 2004.
37. R. Ali, M. Gooding, M. Christlieb, and M. Brady, "Advanced phasebased segmentation of multiple cells from brightfield microscopy images," in Proc. 4th IEEE Int. Symp. Biomedical Imaging: From Nano to Macro, 2008, pp. 181-184.
38. J.-C. Labiche, O. Maton, S. Pascarelli, M. A. Newton, G. C. Ferre, C. Curfs, G. Vaughan, A. Homs, and D. F. Carreiras, "The FReLoN camera as a versatile X-ray detector for time resolved dispersive exafs and diffraction studies of dynamic problems in materials science, chemistry, and catalysis," Rev. Sci. Instrum., vol.78, p. 091301, 2007.