Deterministic versus stochastic level-set regularization in nonlinear phase contrast tomography

References

• Chappard C, Basillais A, Benhamou L, et al. 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
• Momose A, Takeda T, Tai Y, et al. Phase-contrast tomographic imaging using an X-ray interferometer. J. Synchrotron. Radiat. 1998;5:309–314.
   PubMed Web of Science ®Google Scholar
• Cloetens P, Pateyron-Salome M, Buffiere JY, et al. Observation of microstructure and damage in materials by phase sensitive radiography and tomography. J. Appl. Phys. 1997;81:5878–5886.
   Web of Science ®Google Scholar
• Langer M, Cloetens P, Pacureanu A, et al. X-ray in-line phase tomography of multimaterial objects. Opt. Lett. 2012;37:2151–2154.
   PubMed Web of Science ®Google Scholar
• Cloetens P, Ludwig PW, Baruchel J, et al. Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation X rays. Appl. Phys. Lett. 1999;5:2912–2914.
   Web of Science ®Google Scholar
• Sixou B, Davidoiu V, Langer M, et al. 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
• Langer M, Cloetens P, Guigay JP, et al. Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography. Med. Phys. 2008;35:4556–4565.
   PubMed 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
• Beltran MA, Paganin DM, Siu KKW, et al. Interface-specific x-ray phase retrieval tomography of complex biological organs. Phys. Med. Biol. 2011;56:7353–7369.
   PubMed Web of Science ®Google Scholar
• Paganin D, Mayo SC, Gureyev TE, et al. 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
• Beltran MA, Paganin DM, Uesugi K, et al. 2D and 3D X-ray phase retrieval of multi-material objects using a single defocus distance. Opt. Express. 2010;18:6423.
   PubMed Web of Science ®Google Scholar
• Cloetens Barrett PR, Baruchel J, Guigay JP, et al. Phase objects in synchrotron radiation hard X-ray imaging. J. Phys. D. 1996;29:133–146.
   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
• Paganin D. Coherent X-ray optics. New York (NY): Oxford University Press; 2006.
   Google Scholar
• Guigay JP, Langer M, Boistel R, et al. 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
• Sixou B. Reconstruction of the complex refractive index in nonlinear phase contrast tomography. Inverse Prob. Sci. Eng. 2014;23:901–912.
   Web of Science ®Google Scholar
• Engl H, Hanke M, Neubauer A. Regularization of inverse problems and its applications. Dordrecht: Kluwer; 1996.
   Google Scholar
• Sixou B, Davidoiu V, Langer M, et al. 2013. Level-set regularization for nonlinear absorption and phase retrieval in X-ray phase contrast tomography. In: IEEE international symposium biomedical imaging. San Francisco (CA). p. 1264–1267.
   Google Scholar
• Wang L, Sixou B, Peyrin F. Binary tomography reconstruction with stochastic level-set method. Signal Process. Lett. 2015;22:922–924.
   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
• Egger A, Leitao L. Nonlinear regularization for ill-posed problems with piecewise constant or strongly varying solutions. Inverse Prob. 2009;25:115014.
   Web of Science ®Google Scholar
• DeCezaro A, Leitao A, Tai XC. On multiple level-set regularization methods for inverse problems. Inverse Prob. 2009;25:035004
   Web of Science ®Google Scholar
• Scherzer O, Grasmair M, Grossauer H, et al. Variational methods in imaging. New York (NY): Springer; 2008.
   Google Scholar
• Kak AC, Slaney M. Principles of computerized tomographic imaging. New-York (NY): IEEE Press; 1988.
   Google Scholar
• Natterer F. The mathematics of computerized tomography. New-York: John Wiley and Sons; 1986.
   Google Scholar
• Herman GT. Image Reconstruction from Projections: the fundamentals of computerized tomography. New-York (NY): Academic Press; 1980.
   Google Scholar
• Kindermann S, Leitao A. Convergence rates for Kaczmarz-type regularization methods. Inverse Prob. Imaging. 2014;8:149–172.
   Web of Science ®Google Scholar
• Van der Doel K, Ascher M, Leitao A. Multiple level-set for piecewise constant surface reconstruction. J. Sci. Comput. 2010;4:44–66.
   Web of Science ®Google Scholar
• Sixou B. Binary tomography reconstruction with stochastic level-set methods. IEEE Signal Process. Lett. 2015;22:920–924.
   Web of Science ®Google Scholar
• Aubert G, Kornprobst P. Mathematical problems in image processing. Partial differential equations and the calculus of Variations. Applied Mathematical Sciences: Springer; 2006.
   Google Scholar
• Juan O, Keriven R, Postelnicu G. Stochastic motion and the level-set method in computer vision: stochastic active contours. Int. J. Comput. Vision. 2006;69:7–25.
   Web of Science ®Google Scholar
• Geman S, Hwang CR. Diffusion for global optimization. J. Control Optim. 1986;24:1031–1043.
   Web of Science ®Google Scholar
• Parpas P, Rustem B. Convergence analysis a a global optimization algorithm using stochastic differential equations. J. Control Optim. 2009;45:95–110.
   Web of Science ®Google Scholar
• Chow S, Yang T, Zhou H. Global optimization by intermittent diffusion. J. Control Optim. 2009;45:95–110.
   Google Scholar
• Chiang TS, Hwang CR, Sheu SJ. Diffusion for global optimization in Rn. SIAM J. Control Optim. 1987;25:737–753.
   Web of Science ®Google Scholar
• Da Prato G, Zabczyk J. Stochastic equations in infinite dimensions. Encyclopedia of mathematics and its applications, Cambridge: Cambridge University Press; 1992.
   Google Scholar
• Osher S, Fedkiw RP. The level-set method and dynamic implic surfaces. New York (NY): Springer; 1988.
   Google Scholar
• Burger Hackl B, Ring W. Incorporating topological derivatives into level-set methods. J. Comput. Phys. 2004;194:344–362.
   Web of Science ®Google Scholar
• Ramlau R, Ring W. A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data. J. Comput. Phys. 2007;221:539–557.
   Web of Science ®Google Scholar
• Jiang GS, Peng D. Weigthed ENO schemes for Hamilton--Jacobi equations. SIAM J. Control Optim. 2000;21:2126–2143.
   Google Scholar