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Phase retrieval in in-line x-ray phase contrast imaging based on total variation minimizationAlexander Kostenko, K. Joost Batenburg, Heikki Suhonen, S. Erik Offerman, and Lucas J. van Vliet »View Author Affiliations
Alexander Kostenko,1,*
K. Joost Batenburg,2
Heikki Suhonen,3
S. Erik Offerman,4
and Lucas J. van Vliet1
1Department of Imaging Science & Technology, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands 2Scientific Computing group, Centrum Wiskunde & Informatica, Science Park 123, NL-1098XG Amsterdam, The Netherlands 3European Synchrotron Radiation Facility, 6 rue Jules Horowitz, Grenoble, France 4Department of Materials Science & Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands *Corresponding author: a.kostenko@tudelft.nl |
Optics Express, Vol. 21, Issue 1, pp. 710-723 (2013)
http://dx.doi.org/10.1364/OE.21.000710
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Abstract
State-of-the-art techniques for phase retrieval in propagation based X-ray phase-contrast imaging are aiming to solve an underdetermined linear system of equations. They commonly employ Tikhonov regularization – an L2-norm regularized deconvolution scheme – despite some of its limitations. We present a novel approach to phase retrieval based on Total Variation (TV) minimization. We incorporated TV minimization for deconvolution in phase retrieval using a variety of the most common linear phase-contrast models. The results of our TV minimization was compared with Tikhonov regularized deconvolution on simulated as well as experimental data. The presented method was shown to deliver improved accuracy in reconstructions based on a single distance as well as multiple distance phase-contrast images corrupted by noise and hampered by errors due to nonlinear imaging effects.
© 2012 OSA
OCIS Codes
(100.3190) Image processing : Inverse problems
(100.5070) Image processing : Phase retrieval
(110.7440) Imaging systems : X-ray imaging
ToC Category:
Image Processing
History
Original Manuscript: September 10, 2012
Revised Manuscript: October 1, 2012
Manuscript Accepted: October 4, 2012
Published: January 7, 2013
Citation
Alexander Kostenko, K. Joost Batenburg, Heikki Suhonen, S. Erik Offerman, and Lucas J. van Vliet, "Phase retrieval in in-line x-ray phase contrast imaging based on total variation minimization," Opt. Express 21, 710-723 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-710
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References
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Appel, A. A.
Argunova, T.
Baker, R.
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- A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision20, 89–97 (2004). [CrossRef]
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- P. Weiss, L. Obadia, D. Magne, X. Bourges, C. Rau, T. Weitkamp, I. Khairoun, J.M. Bouler, D. Chappard, O. Gauthier, and G. Daculsi, “Synchrotron x-ray microtomography (on a micron scale) provides three dimensional imaging representation of bone ingrowth in calcium phosphate biomaterials,” Biomat.24, 4591 (2003). [CrossRef]
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- J. Xu, A. W. Stevenson, D. Gao, M. Tykocinski, D. Lawrence, S. W. Wilkins, G. M. Clark, E. Saunders, and R. S. Cowan, “The role of radiographic phase-contrast imaging in the development of intracochlear electrode arrays,” Otology and Neur.22, 862–868 (2001). [CrossRef]
- R. Barrett, R. Baker, P. Cloetens, Y. Dabin, C. Morawe, H. Suhonen, R. Tucoulou, A. Vivo, and L. Zhang. “Dynamically-figured mirror system for high-energy nanofocusing at the ESRF, Proc. SPIE12, 813904 (2011). [CrossRef]
- P. Weiss, L. Obadia, D. Magne, X. Bourges, C. Rau, T. Weitkamp, I. Khairoun, J.M. Bouler, D. Chappard, O. Gauthier, and G. Daculsi, “Synchrotron x-ray microtomography (on a micron scale) provides three dimensional imaging representation of bone ingrowth in calcium phosphate biomaterials,” Biomat.24, 4591 (2003). [CrossRef]
- J. Dahl, P. C. Hansen, S. H. Jensen, and T. L. Jensen, “Algorithms and software for total variation image reconstruction via first-order methods,” Num. Alg.53, 67–92 (2010). [CrossRef]
- A. Kostenko, H. Sharma, E. G. Dere, A. King, W. Ludwig, W. van Oel, S. Stallinga, L. J. van Vliet, and S. E. Offerman, “Three-dimensional morphology of cementite in steel studied by x-ray phase-contrast tomography,” Scr. Mater.67, 261–264 (2012). [CrossRef]
- E. C. Ismaila, W. Kaabara, D. Garritya, O. Gundogdua, O. Bunkb, F. Pfeifferb, M. J. Farquharsond, and D. A. Bradleya, “X-ray phase contrast imaging of the bone-cartilage interface,” Appl. Rad. and Isot.68, 767–771 (2010). [CrossRef]
- L.I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D.60, 259–268 (1992). [CrossRef]
- J. Xu, A. W. Stevenson, D. Gao, M. Tykocinski, D. Lawrence, S. W. Wilkins, G. M. Clark, E. Saunders, and R. S. Cowan, “The role of radiographic phase-contrast imaging in the development of intracochlear electrode arrays,” Otology and Neur.22, 862–868 (2001). [CrossRef]
- E. C. Ismaila, W. Kaabara, D. Garritya, O. Gundogdua, O. Bunkb, F. Pfeifferb, M. J. Farquharsond, and D. A. Bradleya, “X-ray phase contrast imaging of the bone-cartilage interface,” Appl. Rad. and Isot.68, 767–771 (2010). [CrossRef]
- A. A. Appel, J. C. Larson, S. Somo, Z. Zhong, P. P. Spicer, F. K. Kasper, A. B. Garson, A. M. Zysk, A. G. Mikos, M. A. Anastasio, and E. M. Brey, “Imaging of poly(α-hydroxy-ester) scaffolds with x-ray phase-contrast microcomputed tomography,” Tissue Eng. Part C18, (2012).
- P. Weiss, L. Obadia, D. Magne, X. Bourges, C. Rau, T. Weitkamp, I. Khairoun, J.M. Bouler, D. Chappard, O. Gauthier, and G. Daculsi, “Synchrotron x-ray microtomography (on a micron scale) provides three dimensional imaging representation of bone ingrowth in calcium phosphate biomaterials,” Biomat.24, 4591 (2003). [CrossRef]
- O. Coindreau, C. Mulat, C. Germain, J. Lachaud, and G. L. Vignoles, “Benefits of x-ray CMT for the modeling of C/C composites,” Adv. Eng. Mat.13, 178–185 (2011). [CrossRef]
- P. Coan, F. Gruener, C. Glaser, T. Schneider, A. Bravin, M. Reiser, and D. Habs, “Phase contrast medical imaging with compact x-ray sources at the Munich-centre for advance photonics,” Nucl. Instr. and Meth. Phys. Res. A608, S44–S46 (2009). [CrossRef]
- P. Coan, F. Gruener, C. Glaser, T. Schneider, A. Bravin, M. Reiser, and D. Habs, “Phase contrast medical imaging with compact x-ray sources at the Munich-centre for advance photonics,” Nucl. Instr. and Meth. Phys. Res. A608, S44–S46 (2009). [CrossRef]
- 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.75, 2912–2914 (1999). [CrossRef]
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- E. C. Ismaila, W. Kaabara, D. Garritya, O. Gundogdua, O. Bunkb, F. Pfeifferb, M. J. Farquharsond, and D. A. Bradleya, “X-ray phase contrast imaging of the bone-cartilage interface,” Appl. Rad. and Isot.68, 767–771 (2010). [CrossRef]
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- P. Coan, F. Gruener, C. Glaser, T. Schneider, A. Bravin, M. Reiser, and D. Habs, “Phase contrast medical imaging with compact x-ray sources at the Munich-centre for advance photonics,” Nucl. Instr. and Meth. Phys. Res. A608, S44–S46 (2009). [CrossRef]
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- T. Argunova, M. Gutkin, J. H. Je, E. Mokhov, S. Nagalyuk, S. Sergey, and Y. Hwu, “SR phase-contrast imaging to address the evolution of defects during SiC growth,” Phys. Status Solid. A Appl. Mat.208, 819–824 (2011). [CrossRef]
- E. C. Ismaila, W. Kaabara, D. Garritya, O. Gundogdua, O. Bunkb, F. Pfeifferb, M. J. Farquharsond, and D. A. Bradleya, “X-ray phase contrast imaging of the bone-cartilage interface,” Appl. Rad. and Isot.68, 767–771 (2010). [CrossRef]
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- P. Weiss, L. Obadia, D. Magne, X. Bourges, C. Rau, T. Weitkamp, I. Khairoun, J.M. Bouler, D. Chappard, O. Gauthier, and G. Daculsi, “Synchrotron x-ray microtomography (on a micron scale) provides three dimensional imaging representation of bone ingrowth in calcium phosphate biomaterials,” Biomat.24, 4591 (2003). [CrossRef]
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- M. Herbig, A. King, P. Reischig, H. Proudhon, E. M. Lauridsen, J. Marrow, J. -Y. Buffire, and W. Ludwig, “3-D growth of a short fatigue crack within a polycrystalline microstructure studied using combined diffraction and phase-contrast x-ray tomography,” Acta Mater.59, 590–601 (2011). [CrossRef]
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- Q. Tao, D. li, L. Zhang, and S. Luo, “Using x-ray in-line phase-contrast imaging for the investigation of nude mouse hepatic tumors,” PLoS ONE7, e39936, (2012). [CrossRef] [PubMed]
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- Q. Tao, D. li, L. Zhang, and S. Luo, “Using x-ray in-line phase-contrast imaging for the investigation of nude mouse hepatic tumors,” PLoS ONE7, e39936, (2012). [CrossRef] [PubMed]
- P. Weiss, L. Obadia, D. Magne, X. Bourges, C. Rau, T. Weitkamp, I. Khairoun, J.M. Bouler, D. Chappard, O. Gauthier, and G. Daculsi, “Synchrotron x-ray microtomography (on a micron scale) provides three dimensional imaging representation of bone ingrowth in calcium phosphate biomaterials,” Biomat.24, 4591 (2003). [CrossRef]
- R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffire, “Nanoscale zoom tomography with hard x-rays using Kirkpatrick-Baez optics, Appl. Phys. Lett.90, 144104 (2007). [CrossRef]
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- 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]
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- T. Argunova, M. Gutkin, J. H. Je, E. Mokhov, S. Nagalyuk, S. Sergey, and Y. Hwu, “SR phase-contrast imaging to address the evolution of defects during SiC growth,” Phys. Status Solid. A Appl. Mat.208, 819–824 (2011). [CrossRef]
- P. Weiss, L. Obadia, D. Magne, X. Bourges, C. Rau, T. Weitkamp, I. Khairoun, J.M. Bouler, D. Chappard, O. Gauthier, and G. Daculsi, “Synchrotron x-ray microtomography (on a micron scale) provides three dimensional imaging representation of bone ingrowth in calcium phosphate biomaterials,” Biomat.24, 4591 (2003). [CrossRef]
- A. Kostenko, H. Sharma, E. G. Dere, A. King, W. Ludwig, W. van Oel, S. Stallinga, L. J. van Vliet, and S. E. Offerman, “Three-dimensional morphology of cementite in steel studied by x-ray phase-contrast tomography,” Scr. Mater.67, 261–264 (2012). [CrossRef]
- L.I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D.60, 259–268 (1992). [CrossRef]
- 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]
- M. Langer, P. Cloetens, and F. Peyrin, “Fourier-wavelet regularization of phase retrieval in x-ray in-line phase tomography,” J. Opt. Soc. Am. A26, 1876–1881 (2009). [CrossRef]
- M. Langer, F. Peyrin, P. Cloetens, and J. -P. Guigay, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.35, 4556 (2008). [CrossRef] [PubMed]
- E. C. Ismaila, W. Kaabara, D. Garritya, O. Gundogdua, O. Bunkb, F. Pfeifferb, M. J. Farquharsond, and D. A. Bradleya, “X-ray phase contrast imaging of the bone-cartilage interface,” Appl. Rad. and Isot.68, 767–771 (2010). [CrossRef]
- T. Q. Pham, L. J. van Vliet, and K. Schutte, “Robust super-resolution by minimizing a gaussian-weighted l2 error norm,” J. Phys.: Conf.124, 012037 (2008). [CrossRef]
- M. Herbig, A. King, P. Reischig, H. Proudhon, E. M. Lauridsen, J. Marrow, J. -Y. Buffire, and W. Ludwig, “3-D growth of a short fatigue crack within a polycrystalline microstructure studied using combined diffraction and phase-contrast x-ray tomography,” Acta Mater.59, 590–601 (2011). [CrossRef]
- P. Weiss, L. Obadia, D. Magne, X. Bourges, C. Rau, T. Weitkamp, I. Khairoun, J.M. Bouler, D. Chappard, O. Gauthier, and G. Daculsi, “Synchrotron x-ray microtomography (on a micron scale) provides three dimensional imaging representation of bone ingrowth in calcium phosphate biomaterials,” Biomat.24, 4591 (2003). [CrossRef]
- M. Herbig, A. King, P. Reischig, H. Proudhon, E. M. Lauridsen, J. Marrow, J. -Y. Buffire, and W. Ludwig, “3-D growth of a short fatigue crack within a polycrystalline microstructure studied using combined diffraction and phase-contrast x-ray tomography,” Acta Mater.59, 590–601 (2011). [CrossRef]
- P. Coan, F. Gruener, C. Glaser, T. Schneider, A. Bravin, M. Reiser, and D. Habs, “Phase contrast medical imaging with compact x-ray sources at the Munich-centre for advance photonics,” Nucl. Instr. and Meth. Phys. Res. A608, S44–S46 (2009). [CrossRef]
- E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory52, 489–509 (2006). [CrossRef]
- L.I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D.60, 259–268 (1992). [CrossRef]
- J. Xu, A. W. Stevenson, D. Gao, M. Tykocinski, D. Lawrence, S. W. Wilkins, G. M. Clark, E. Saunders, and R. S. Cowan, “The role of radiographic phase-contrast imaging in the development of intracochlear electrode arrays,” Otology and Neur.22, 862–868 (2001). [CrossRef]
- 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.75, 2912–2914 (1999). [CrossRef]
- P. Coan, F. Gruener, C. Glaser, T. Schneider, A. Bravin, M. Reiser, and D. Habs, “Phase contrast medical imaging with compact x-ray sources at the Munich-centre for advance photonics,” Nucl. Instr. and Meth. Phys. Res. A608, S44–S46 (2009). [CrossRef]
- A. W. M. van Eekeren, K. Schutte, and L. J. van Vliet, “Multiframe super-resolution reconstruction of small moving objects,” IEEE Trans. Im. Proc.19, 2901–2912 (2010). [CrossRef]
- T. Q. Pham, L. J. van Vliet, and K. Schutte, “Robust super-resolution by minimizing a gaussian-weighted l2 error norm,” J. Phys.: Conf.124, 012037 (2008). [CrossRef]
- T. Argunova, M. Gutkin, J. H. Je, E. Mokhov, S. Nagalyuk, S. Sergey, and Y. Hwu, “SR phase-contrast imaging to address the evolution of defects during SiC growth,” Phys. Status Solid. A Appl. Mat.208, 819–824 (2011). [CrossRef]
- A. Kostenko, H. Sharma, E. G. Dere, A. King, W. Ludwig, W. van Oel, S. Stallinga, L. J. van Vliet, and S. E. Offerman, “Three-dimensional morphology of cementite in steel studied by x-ray phase-contrast tomography,” Scr. Mater.67, 261–264 (2012). [CrossRef]
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- A. A. Appel, J. C. Larson, S. Somo, Z. Zhong, P. P. Spicer, F. K. Kasper, A. B. Garson, A. M. Zysk, A. G. Mikos, M. A. Anastasio, and E. M. Brey, “Imaging of poly(α-hydroxy-ester) scaffolds with x-ray phase-contrast microcomputed tomography,” Tissue Eng. Part C18, (2012).
- A. Kostenko, H. Sharma, E. G. Dere, A. King, W. Ludwig, W. van Oel, S. Stallinga, L. J. van Vliet, and S. E. Offerman, “Three-dimensional morphology of cementite in steel studied by x-ray phase-contrast tomography,” Scr. Mater.67, 261–264 (2012). [CrossRef]
- J. Xu, A. W. Stevenson, D. Gao, M. Tykocinski, D. Lawrence, S. W. Wilkins, G. M. Clark, E. Saunders, and R. S. Cowan, “The role of radiographic phase-contrast imaging in the development of intracochlear electrode arrays,” Otology and Neur.22, 862–868 (2001). [CrossRef]
- R. Barrett, R. Baker, P. Cloetens, Y. Dabin, C. Morawe, H. Suhonen, R. Tucoulou, A. Vivo, and L. Zhang. “Dynamically-figured mirror system for high-energy nanofocusing at the ESRF, Proc. SPIE12, 813904 (2011). [CrossRef]
- Q. Tao, D. li, L. Zhang, and S. Luo, “Using x-ray in-line phase-contrast imaging for the investigation of nude mouse hepatic tumors,” PLoS ONE7, e39936, (2012). [CrossRef] [PubMed]
- E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory52, 489–509 (2006). [CrossRef]
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- R. Barrett, R. Baker, P. Cloetens, Y. Dabin, C. Morawe, H. Suhonen, R. Tucoulou, A. Vivo, and L. Zhang. “Dynamically-figured mirror system for high-energy nanofocusing at the ESRF, Proc. SPIE12, 813904 (2011). [CrossRef]
- J. Xu, A. W. Stevenson, D. Gao, M. Tykocinski, D. Lawrence, S. W. Wilkins, G. M. Clark, E. Saunders, and R. S. Cowan, “The role of radiographic phase-contrast imaging in the development of intracochlear electrode arrays,” Otology and Neur.22, 862–868 (2001). [CrossRef]
- 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.75, 2912–2914 (1999). [CrossRef]
- A. W. M. van Eekeren, K. Schutte, and L. J. van Vliet, “Multiframe super-resolution reconstruction of small moving objects,” IEEE Trans. Im. Proc.19, 2901–2912 (2010). [CrossRef]
- 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.75, 2912–2914 (1999). [CrossRef]
- A. Kostenko, H. Sharma, E. G. Dere, A. King, W. Ludwig, W. van Oel, S. Stallinga, L. J. van Vliet, and S. E. Offerman, “Three-dimensional morphology of cementite in steel studied by x-ray phase-contrast tomography,” Scr. Mater.67, 261–264 (2012). [CrossRef]
- A. Kostenko, H. Sharma, E. G. Dere, A. King, W. Ludwig, W. van Oel, S. Stallinga, L. J. van Vliet, and S. E. Offerman, “Three-dimensional morphology of cementite in steel studied by x-ray phase-contrast tomography,” Scr. Mater.67, 261–264 (2012). [CrossRef]
- A. W. M. van Eekeren, K. Schutte, and L. J. van Vliet, “Multiframe super-resolution reconstruction of small moving objects,” IEEE Trans. Im. Proc.19, 2901–2912 (2010). [CrossRef]
- T. Q. Pham, L. J. van Vliet, and K. Schutte, “Robust super-resolution by minimizing a gaussian-weighted l2 error norm,” J. Phys.: Conf.124, 012037 (2008). [CrossRef]
- O. Coindreau, C. Mulat, C. Germain, J. Lachaud, and G. L. Vignoles, “Benefits of x-ray CMT for the modeling of C/C composites,” Adv. Eng. Mat.13, 178–185 (2011). [CrossRef]
- R. Barrett, R. Baker, P. Cloetens, Y. Dabin, C. Morawe, H. Suhonen, R. Tucoulou, A. Vivo, and L. Zhang. “Dynamically-figured mirror system for high-energy nanofocusing at the ESRF, Proc. SPIE12, 813904 (2011). [CrossRef]
- P. Weiss, L. Obadia, D. Magne, X. Bourges, C. Rau, T. Weitkamp, I. Khairoun, J.M. Bouler, D. Chappard, O. Gauthier, and G. Daculsi, “Synchrotron x-ray microtomography (on a micron scale) provides three dimensional imaging representation of bone ingrowth in calcium phosphate biomaterials,” Biomat.24, 4591 (2003). [CrossRef]
- P. Weiss, L. Obadia, D. Magne, X. Bourges, C. Rau, T. Weitkamp, I. Khairoun, J.M. Bouler, D. Chappard, O. Gauthier, and G. Daculsi, “Synchrotron x-ray microtomography (on a micron scale) provides three dimensional imaging representation of bone ingrowth in calcium phosphate biomaterials,” Biomat.24, 4591 (2003). [CrossRef]
- 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]
- J. Xu, A. W. Stevenson, D. Gao, M. Tykocinski, D. Lawrence, S. W. Wilkins, G. M. Clark, E. Saunders, and R. S. Cowan, “The role of radiographic phase-contrast imaging in the development of intracochlear electrode arrays,” Otology and Neur.22, 862–868 (2001). [CrossRef]
- X. Wu and A. Yan, “Phase retrieval from one single phase contrast x-ray image,” Opt. Express17, 11187 (2009). [CrossRef] [PubMed]
- X. Wu and H. Liu, “A general theoretical formalism for x-ray phase contrast imaging,” J. of X-ray Sci. and Techn.11, 33–42 (2003).
- J. Xu, A. W. Stevenson, D. Gao, M. Tykocinski, D. Lawrence, S. W. Wilkins, G. M. Clark, E. Saunders, and R. S. Cowan, “The role of radiographic phase-contrast imaging in the development of intracochlear electrode arrays,” Otology and Neur.22, 862–868 (2001). [CrossRef]
- Q. Tao, D. li, L. Zhang, and S. Luo, “Using x-ray in-line phase-contrast imaging for the investigation of nude mouse hepatic tumors,” PLoS ONE7, e39936, (2012). [CrossRef] [PubMed]
- R. Barrett, R. Baker, P. Cloetens, Y. Dabin, C. Morawe, H. Suhonen, R. Tucoulou, A. Vivo, and L. Zhang. “Dynamically-figured mirror system for high-energy nanofocusing at the ESRF, Proc. SPIE12, 813904 (2011). [CrossRef]
- A. A. Appel, J. C. Larson, S. Somo, Z. Zhong, P. P. Spicer, F. K. Kasper, A. B. Garson, A. M. Zysk, A. G. Mikos, M. A. Anastasio, and E. M. Brey, “Imaging of poly(α-hydroxy-ester) scaffolds with x-ray phase-contrast microcomputed tomography,” Tissue Eng. Part C18, (2012).
- A. A. Appel, J. C. Larson, S. Somo, Z. Zhong, P. P. Spicer, F. K. Kasper, A. B. Garson, A. M. Zysk, A. G. Mikos, M. A. Anastasio, and E. M. Brey, “Imaging of poly(α-hydroxy-ester) scaffolds with x-ray phase-contrast microcomputed tomography,” Tissue Eng. Part C18, (2012).
Acta Mater.
- M. Herbig, A. King, P. Reischig, H. Proudhon, E. M. Lauridsen, J. Marrow, J. -Y. Buffire, and W. Ludwig, “3-D growth of a short fatigue crack within a polycrystalline microstructure studied using combined diffraction and phase-contrast x-ray tomography,” Acta Mater.59, 590–601 (2011). [CrossRef]
Adv. Eng. Mat.
- O. Coindreau, C. Mulat, C. Germain, J. Lachaud, and G. L. Vignoles, “Benefits of x-ray CMT for the modeling of C/C composites,” Adv. Eng. Mat.13, 178–185 (2011). [CrossRef]
Appl. Opt.
- T.E. Gureyev, T.J. Davis, A. Pogany, S.C. Mayo, and S.W. Wilkins, “Optical phase retrieval by use of first Born- and Rytov-type approximations,” Appl. Opt.43, 2418–2430 (2004). [CrossRef] [PubMed]
Appl. Phys. Lett.
- 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.75, 2912–2914 (1999). [CrossRef]
- R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffire, “Nanoscale zoom tomography with hard x-rays using Kirkpatrick-Baez optics, Appl. Phys. Lett.90, 144104 (2007). [CrossRef]
Appl. Rad. and Isot.
- E. C. Ismaila, W. Kaabara, D. Garritya, O. Gundogdua, O. Bunkb, F. Pfeifferb, M. J. Farquharsond, and D. A. Bradleya, “X-ray phase contrast imaging of the bone-cartilage interface,” Appl. Rad. and Isot.68, 767–771 (2010). [CrossRef]
Biomat.
- P. Weiss, L. Obadia, D. Magne, X. Bourges, C. Rau, T. Weitkamp, I. Khairoun, J.M. Bouler, D. Chappard, O. Gauthier, and G. Daculsi, “Synchrotron x-ray microtomography (on a micron scale) provides three dimensional imaging representation of bone ingrowth in calcium phosphate biomaterials,” Biomat.24, 4591 (2003). [CrossRef]
Compos. Sci. Technol.
- F. Cosmi, A. Bernasconi, and N. Sodini, “Phase contrast micro-tomography and morphological analysis of a short carbon fibre reinforced polyamide,” Compos. Sci. Technol.71, 23–30 (2011). [CrossRef]
IEEE Trans. Im. Proc.
- A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” IEEE Trans. Im. Proc.18, 2419–2434 (2009). [CrossRef]
- A. W. M. van Eekeren, K. Schutte, and L. J. van Vliet, “Multiframe super-resolution reconstruction of small moving objects,” IEEE Trans. Im. Proc.19, 2901–2912 (2010). [CrossRef]
IEEE Trans. Inform. Theory
- E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory52, 489–509 (2006). [CrossRef]
Inverse Probl. and Imag.
- X. Bresson and T. F. Chan, “Fast dual minimization of the vectorial total variation norm and applications to color image processing,” Inverse Probl. and Imag.2, 455–484 (2008). [CrossRef]
J. Math. Imaging Vision
- A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision20, 89–97 (2004). [CrossRef]
J. Microsc.
- 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]
J. of X-ray Sci. and Techn.
- X. Wu and H. Liu, “A general theoretical formalism for x-ray phase contrast imaging,” J. of X-ray Sci. and Techn.11, 33–42 (2003).
J. Opt. Soc. Am. A
- M. Langer, P. Cloetens, and F. Peyrin, “Fourier-wavelet regularization of phase retrieval in x-ray in-line phase tomography,” J. Opt. Soc. Am. A26, 1876–1881 (2009). [CrossRef]
J. Phys.: Conf.
- T. Q. Pham, L. J. van Vliet, and K. Schutte, “Robust super-resolution by minimizing a gaussian-weighted l2 error norm,” J. Phys.: Conf.124, 012037 (2008). [CrossRef]
Med. Phys.
- M. Langer, F. Peyrin, P. Cloetens, and J. -P. Guigay, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.35, 4556 (2008). [CrossRef] [PubMed]
Nucl. Instr. and Meth. Phys. Res. A
- P. Coan, F. Gruener, C. Glaser, T. Schneider, A. Bravin, M. Reiser, and D. Habs, “Phase contrast medical imaging with compact x-ray sources at the Munich-centre for advance photonics,” Nucl. Instr. and Meth. Phys. Res. A608, S44–S46 (2009). [CrossRef]
Num. Alg.
- J. Dahl, P. C. Hansen, S. H. Jensen, and T. L. Jensen, “Algorithms and software for total variation image reconstruction via first-order methods,” Num. Alg.53, 67–92 (2010). [CrossRef]
Opt. Express
- E. Y. Sidky, M. A. Anastasio, and X. Pan, “Image reconstruction exploiting object sparsity in boundary-enhanced x-ray phase-contrast tomography,” Opt. Express18, 10404 (2010). [CrossRef] [PubMed]
- L. Turner, B. Dhal, J. Hayes, A. Mancuso, K. Nugent, D. Paterson, R. Scholten, C. Tran, and A. Peele, “X-ray phase imaging: demonstration of extended conditions with homogeneous objects,” Opt. Express12, 2960–2965 (2004). [CrossRef] [PubMed]
- X. Wu and A. Yan, “Phase retrieval from one single phase contrast x-ray image,” Opt. Express17, 11187 (2009). [CrossRef] [PubMed]
- R. Hofmann, J. Moosmann, and T. Baumbach, “Criticality in single-distance phase retrieval,” Opt. Express19, 25881–25890 (2011). [CrossRef]
Opt. Lett.
- J. -P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “A mixed contrast transfer and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett.32, 1617–1619 (2007). [CrossRef] [PubMed]
Otology and Neur.
- J. Xu, A. W. Stevenson, D. Gao, M. Tykocinski, D. Lawrence, S. W. Wilkins, G. M. Clark, E. Saunders, and R. S. Cowan, “The role of radiographic phase-contrast imaging in the development of intracochlear electrode arrays,” Otology and Neur.22, 862–868 (2001). [CrossRef]
Phys. Status Solid. A Appl. Mat.
- T. Argunova, M. Gutkin, J. H. Je, E. Mokhov, S. Nagalyuk, S. Sergey, and Y. Hwu, “SR phase-contrast imaging to address the evolution of defects during SiC growth,” Phys. Status Solid. A Appl. Mat.208, 819–824 (2011). [CrossRef]
Physica D.
- L.I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D.60, 259–268 (1992). [CrossRef]
PLoS ONE
- Q. Tao, D. li, L. Zhang, and S. Luo, “Using x-ray in-line phase-contrast imaging for the investigation of nude mouse hepatic tumors,” PLoS ONE7, e39936, (2012). [CrossRef] [PubMed]
Proc. SPIE
- R. Barrett, R. Baker, P. Cloetens, Y. Dabin, C. Morawe, H. Suhonen, R. Tucoulou, A. Vivo, and L. Zhang. “Dynamically-figured mirror system for high-energy nanofocusing at the ESRF, Proc. SPIE12, 813904 (2011). [CrossRef]
Scr. Mater.
- A. Kostenko, H. Sharma, E. G. Dere, A. King, W. Ludwig, W. van Oel, S. Stallinga, L. J. van Vliet, and S. E. Offerman, “Three-dimensional morphology of cementite in steel studied by x-ray phase-contrast tomography,” Scr. Mater.67, 261–264 (2012). [CrossRef]
SIAM J. Im. Sci.
- A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Im. Sci.2, 183–202 (2009). [CrossRef]
Tissue Eng. Part C
- A. A. Appel, J. C. Larson, S. Somo, Z. Zhong, P. P. Spicer, F. K. Kasper, A. B. Garson, A. M. Zysk, A. G. Mikos, M. A. Anastasio, and E. M. Brey, “Imaging of poly(α-hydroxy-ester) scaffolds with x-ray phase-contrast microcomputed tomography,” Tissue Eng. Part C18, (2012).
2012, Kostenko, Scr. Mater.
- A. Kostenko, H. Sharma, E. G. Dere, A. King, W. Ludwig, W. van Oel, S. Stallinga, L. J. van Vliet, and S. E. Offerman, “Three-dimensional morphology of cementite in steel studied by x-ray phase-contrast tomography,” Scr. Mater.67, 261–264 (2012). [CrossRef]
- Q. Tao, D. li, L. Zhang, and S. Luo, “Using x-ray in-line phase-contrast imaging for the investigation of nude mouse hepatic tumors,” PLoS ONE7, e39936, (2012). [CrossRef] [PubMed]
- A. A. Appel, J. C. Larson, S. Somo, Z. Zhong, P. P. Spicer, F. K. Kasper, A. B. Garson, A. M. Zysk, A. G. Mikos, M. A. Anastasio, and E. M. Brey, “Imaging of poly(α-hydroxy-ester) scaffolds with x-ray phase-contrast microcomputed tomography,” Tissue Eng. Part C18, (2012).
- T. Argunova, M. Gutkin, J. H. Je, E. Mokhov, S. Nagalyuk, S. Sergey, and Y. Hwu, “SR phase-contrast imaging to address the evolution of defects during SiC growth,” Phys. Status Solid. A Appl. Mat.208, 819–824 (2011). [CrossRef]
- O. Coindreau, C. Mulat, C. Germain, J. Lachaud, and G. L. Vignoles, “Benefits of x-ray CMT for the modeling of C/C composites,” Adv. Eng. Mat.13, 178–185 (2011). [CrossRef]
- F. Cosmi, A. Bernasconi, and N. Sodini, “Phase contrast micro-tomography and morphological analysis of a short carbon fibre reinforced polyamide,” Compos. Sci. Technol.71, 23–30 (2011). [CrossRef]
- M. Herbig, A. King, P. Reischig, H. Proudhon, E. M. Lauridsen, J. Marrow, J. -Y. Buffire, and W. Ludwig, “3-D growth of a short fatigue crack within a polycrystalline microstructure studied using combined diffraction and phase-contrast x-ray tomography,” Acta Mater.59, 590–601 (2011). [CrossRef]
- R. Barrett, R. Baker, P. Cloetens, Y. Dabin, C. Morawe, H. Suhonen, R. Tucoulou, A. Vivo, and L. Zhang. “Dynamically-figured mirror system for high-energy nanofocusing at the ESRF, Proc. SPIE12, 813904 (2011). [CrossRef]
- J. Dahl, P. C. Hansen, S. H. Jensen, and T. L. Jensen, “Algorithms and software for total variation image reconstruction via first-order methods,” Num. Alg.53, 67–92 (2010). [CrossRef]
- A. W. M. van Eekeren, K. Schutte, and L. J. van Vliet, “Multiframe super-resolution reconstruction of small moving objects,” IEEE Trans. Im. Proc.19, 2901–2912 (2010). [CrossRef]
- E. C. Ismaila, W. Kaabara, D. Garritya, O. Gundogdua, O. Bunkb, F. Pfeifferb, M. J. Farquharsond, and D. A. Bradleya, “X-ray phase contrast imaging of the bone-cartilage interface,” Appl. Rad. and Isot.68, 767–771 (2010). [CrossRef]
- P. Coan, F. Gruener, C. Glaser, T. Schneider, A. Bravin, M. Reiser, and D. Habs, “Phase contrast medical imaging with compact x-ray sources at the Munich-centre for advance photonics,” Nucl. Instr. and Meth. Phys. Res. A608, S44–S46 (2009). [CrossRef]
- A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Im. Sci.2, 183–202 (2009). [CrossRef]
- A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” IEEE Trans. Im. Proc.18, 2419–2434 (2009). [CrossRef]
- T. Q. Pham, L. J. van Vliet, and K. Schutte, “Robust super-resolution by minimizing a gaussian-weighted l2 error norm,” J. Phys.: Conf.124, 012037 (2008). [CrossRef]
- X. Bresson and T. F. Chan, “Fast dual minimization of the vectorial total variation norm and applications to color image processing,” Inverse Probl. and Imag.2, 455–484 (2008). [CrossRef]
- M. Langer, F. Peyrin, P. Cloetens, and J. -P. Guigay, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.35, 4556 (2008). [CrossRef] [PubMed]
- R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. Buffire, “Nanoscale zoom tomography with hard x-rays using Kirkpatrick-Baez optics, Appl. Phys. Lett.90, 144104 (2007). [CrossRef]
- E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inform. Theory52, 489–509 (2006). [CrossRef]
- A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision20, 89–97 (2004). [CrossRef]
- X. Wu and H. Liu, “A general theoretical formalism for x-ray phase contrast imaging,” J. of X-ray Sci. and Techn.11, 33–42 (2003).
- P. Weiss, L. Obadia, D. Magne, X. Bourges, C. Rau, T. Weitkamp, I. Khairoun, J.M. Bouler, D. Chappard, O. Gauthier, and G. Daculsi, “Synchrotron x-ray microtomography (on a micron scale) provides three dimensional imaging representation of bone ingrowth in calcium phosphate biomaterials,” Biomat.24, 4591 (2003). [CrossRef]
- 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]
- J. Xu, A. W. Stevenson, D. Gao, M. Tykocinski, D. Lawrence, S. W. Wilkins, G. M. Clark, E. Saunders, and R. S. Cowan, “The role of radiographic phase-contrast imaging in the development of intracochlear electrode arrays,” Otology and Neur.22, 862–868 (2001). [CrossRef]
- 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.75, 2912–2914 (1999). [CrossRef]
- L.I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D.60, 259–268 (1992). [CrossRef]
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