Reconstruction of the complex refractive index in nonlinear phase contrast tomography

References

• Momose A, Takeda TT, Tai Y, Yoneyama A, Hirano K. Phase-contrast tomographic imaging using an X-ray interferometer. J. Synchrotron. Rad. 1998;5:309–314.
   PubMed Web of Science ®Google Scholar
• Davis GR, Wong SL. X-ray microtomography of bones and teeth. Physiol. Meas. 1996;17:121–146.
   PubMed Web of Science ®Google Scholar
• Salome M, Peyrin F, Cloetens P, Odet C, Laval-Jeantet AM, Baruchel J, Spanne P. A synchrotron radiation microtomography system for the analysis of trabecular bone samples. Med. Phys. 1999;26:2194–2204.
   PubMed Web of Science ®Google Scholar
• Nuzzo S, Peyrin F, Cloetens P, Baruchel J, Boivin G. Quantification of the degree of mineralization of bone in three dimensions using synchrotron radiation microtomograph. Med. Phys. 2002;29:2672–2681.
   PubMed Web of Science ®Google Scholar
• Bayat S, Apostol L, Boller E, Brochard T, Peyrin F. In vivo imaging of bone micro-architecture in mice with 3D synchrotron radiation micro-tomography. Nucl. Instrum. Methods Phys. Res. 2005;548:247–252.
   Web of Science ®Google Scholar
• Chappard C, Basillais A, Benhamou L, Bonassie A, Bonnet N, Brunet-Imbault B, Peyrin F. Comparison of synchrotron radiation and conventional X-ray microcomputed tomography for assessing trabecular bone microarchitecture of human femoral heads. Med. Phys. 2006;33:3568–3577.
   PubMed Web of Science ®Google Scholar
• Cloetens P, Ludwig PW, Baruchel J, Van Dyck D, Van Landuyt J, Guigay JP, Schlenker M. Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation X rays. Appl. Phys. Lett. 1999;75:2912–2914.
   Web of Science ®Google Scholar
• Langer M, Cloetens P, Pacureanu A, Peyrin F. X-ray in-line phase tomography of multimaterial objects. Opt. Lett. 2012;37:2151–2154.
   PubMed Web of Science ®Google Scholar
• Cloetens P, Barrett R, Baruchel J, Guigay JP, Schlenker M. Phase objects in synchrotron radiation hard X-ray imaging. J. Phys. D. 1996;29:133–146.
   Web of Science ®Google Scholar
• Langer M, Cloetens P, Guigay JP, Peyrin F. Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography. Med. Phys. 2008;35:4556–4565.
   PubMed Web of Science ®Google Scholar
• Langer M, Cloetens P, Peyrin F. Regularization of phase retrieval with phase attenuation duality prior for 3D holotomography. IEEE Trans. Image Process. 2010;19:2425–2436.
   Web of Science ®Google Scholar
• Davidoiu V, Sixou B, Langer M, Peyrin F. Nonlinear iterative phase retrieval based on Fréchet derivative. Opt. Express. 2011;23:22809–22819.
   Web of Science ®Google Scholar
• Guigay JP, Langer M, Boistel R, Cloetens P. A mixed contrast transfer and transport of intensity approach for phase retrieval in the Fresnel region. Opt. Lett. 2007;32:1617–1629.
   PubMed Web of Science ®Google Scholar
• Gureyev TE, Nugent KA. Phase retrieval with the transport of intensity equation: orthogonal series solution for non uniform illumination. Opt. Commun. 1996;13:1670–1682.
   Google Scholar
• Gureyev TE. Composite techniques for phase retrieval in the Fresnel region. Opt. Commun. 2003;220:49–58.
   Web of Science ®Google Scholar
• Nugent KA. Coherent methods in the X-rays science. Adv. Phys. 2010;59:1–99.
   Web of Science ®Google Scholar
• Paganin D, Mayo SC, Gureyev TE, Miller PR, Wilkins SW. Simulateneous phase and amplitude extraction from a single defocused image of a homogeneous object. J. Microsc. 2002;206:33–40.
   PubMed Web of Science ®Google Scholar
• Paganin D. Coherent X-ray optics. New York (NY): Oxford University Press; 2006.
   Google Scholar
• Moosmann J, Hofmann R, Bronnikov A, Baumbach T. Non-linear phase retrieval from single-distance radioagraph. Opt. Lett. 2010;18:25771–25785.
   Google Scholar
• Sixou B, Davidoiu V, Langer M, Peyrin F. Absorption and phase retrieval in phase contrast imaging with nonlinear Tikhonov regularization and joint sparsity constraint regularization. Inverse Prob. Imaging. 2013;7:267–282.
   Web of Science ®Google Scholar
• Beltran MA, Paganin DM, Uesugi Kand Kitchen MJ. 2D and 3D X-ray phase retrieval of multi-material objects using a single defocus distance. Opt. Express. 2010;18:6423–6436.
   PubMed Web of Science ®Google Scholar
• Beltran MA, Paganin DM, Siu KKW, Fouras A, Hooper SB, Reser DH, Kitchen MJ. Interface-specific X-ray phase retrieval tomography of complex biological organs. Phys. Med. Biol. 2011;56:7353–7369.
   PubMed Web of Science ®Google Scholar
• Born M, Wolf E. Principles of optics. Cambridge: Cambridge University Press; 1997.
   Google Scholar
• Goodman JW. Intoduction fo Fourier optics. Greenwood Village (CO): Roberts; 2005.
   Google Scholar
• Natterer F. The mathematics of computerized tomography. New York (NY): Wiley; 1986.
   Google Scholar
• Engl H, Kunisch K, Neubauer A. Convergence rates for Tikhonov regularization of nonlinear ill-posed problem. Inverse Prob. 1989;5:523–540.
   Web of Science ®Google Scholar
• Engl H, Hanke M, Neubauer A. Regularization of inverse problems and its applications. Dordrecht: Kluwer; 1996.
   Google Scholar
• Scherzer O, Grasmair M, Grossauer H, Haltmeier M, Lenzen F. Variational methods in imaging. New York (NY): Springer; 2008.
   Google Scholar
• Herman GT. Image reconstruction from projections: the fundamentals of computerized tomography. New York (NY): Academic Press; 1980.
   Google Scholar
• Kak AC, Slaney M. Principles of computerized tomographic imaging. New York (NY): IEEE Press; 1988.
   Google Scholar
• Daubechies I, Fornasier M, Loris I. Accelerated projected gradient method for linear inverse problems with sparsity constraints. JFAA. 2008;14:764–792.
   Web of Science ®Google Scholar
• Hanke M, Neubauer A, Scherzer O. A convergence analysis of the Landweber iteration for nonlinear ill-posed problems. Numer. Math. 1995;72:21–37.
   Web of Science ®Google Scholar