Abstract

With increased resolution in x-ray computed tomography, refraction adds increasingly to the attenuation signal. Though potentially beneficial, the artifacts caused by refraction often need to be removed from the image. In this paper, we propose a postprocessing method, based on deconvolution, that is able to remove these artifacts after conventional reconstruction. This method poses two advantages over existing projection-based (preprocessing) phase-retrieval or phase-removal algorithms. First, evaluation of the parameters can be done very quickly, improving the overall speed of the method. Second, postprocessing methods can be applied when projection data is not available, which occurs in several commercial systems with closed software or when projection data has been deleted. It is shown that the proposed method performs comparably to state-of-the-art methods in terms of image quality.

© 2013 Optical Society of America

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2012

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

M. N. Boone, W. Devulder, M. Dierick, L. Brabant, E. Pauwels, and L. V. Hoorebeke, “Comparison of two single-image phase-retrieval algorithms for in-line x-ray phase-contrast imaging,” J. Opt. Soc. Am. A 29, 2667–2672 (2012).

2011

2010

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[CrossRef]

B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
[CrossRef]

2009

J. Van den Bulcke, M. Boone, J. Van Acker, and L. Van Hoorebeke, “Three-dimensional x-ray imaging and analysis of fungi on and in wood,” Microsc. Microanal. 15, 395–402 (2009).
[CrossRef]

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105, 102005 (2009).
[CrossRef]

D. Prell, Y. Kyriakou, and W. A. Kalender, “Comparison of ring artifact correction methods for flat-detector CT,” Phys. Med. Biol. 54, 3881–3895 (2009).
[CrossRef]

Y. De Witte, M. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “The Bronnikov aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
[CrossRef]

M. Langer, P. Cloetens, and F. Peyrin, “Fourier-wavelet regularization of phase retrieval in x-ray in-line phase tomography,” J. Opt. Soc. Am. A 26, 1876–1881 (2009).
[CrossRef]

2008

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for constant, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16, 3223–3241 (2008).
[CrossRef]

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

2007

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007).
[CrossRef]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta Part B 62, 626–630 (2007).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res. A 580, 442–445 (2007).
[CrossRef]

2006

2005

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects on the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617–3727 (2005).
[CrossRef]

2002

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. 206, 33–40 (2002).
[CrossRef]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[CrossRef]

A. V. Bronnikov, “Theory of quantitative phase-contrast computed tomography,” J. Opt. Soc. Am. A 19, 472–480 (2002).
[CrossRef]

1999

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. 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]

1997

P. M. Joseph and C. Ruth, “A method for simultaneous correction of spectrum hardening artifacts in CT images containing both bone and iodine,” Med. Phys. 24, 1629–1634 (1997).
[CrossRef]

P. Cloetens, M. Pateyron-Salomé, J. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

1996

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

1995

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature 373, 595–598 (1995).
[CrossRef]

1985

M. R. Teague, “Image formation in terms of the transport equation,” J. Opt. Soc. Am. 2, 2019–2026 (1985).
[CrossRef]

1983

Abela, R.

Almeida, A.

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

Anastasio, M. A.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Arhatari, B. D.

B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
[CrossRef]

Axelsson, M.

M. Axelsson, S. Svensson, and G. Borgefors, “Reduction of ring artefacts in high resolution x-ray microtomography images,” in DAGM Symposium on Pattern Recognition (Springer, 2006), pp. 61–70.

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. 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. Cloetens, M. Pateyron-Salomé, J. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

Beltran, M. A.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[CrossRef]

Boone, M.

J. Van den Bulcke, M. Boone, J. Van Acker, and L. Van Hoorebeke, “Three-dimensional x-ray imaging and analysis of fungi on and in wood,” Microsc. Microanal. 15, 395–402 (2009).
[CrossRef]

Y. De Witte, M. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “The Bronnikov aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
[CrossRef]

Boone, M. N.

M. N. Boone, W. Devulder, M. Dierick, L. Brabant, E. Pauwels, and L. V. Hoorebeke, “Comparison of two single-image phase-retrieval algorithms for in-line x-ray phase-contrast imaging,” J. Opt. Soc. Am. A 29, 2667–2672 (2012).

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

Borgefors, G.

M. Axelsson, S. Svensson, and G. Borgefors, “Reduction of ring artefacts in high resolution x-ray microtomography images,” in DAGM Symposium on Pattern Recognition (Springer, 2006), pp. 61–70.

Brabant, L.

Bronnikov, A. V.

Bruder, J.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta Part B 62, 626–630 (2007).
[CrossRef]

Buffière, J.

P. Cloetens, M. Pateyron-Salomé, J. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

Bunk, O.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta Part B 62, 626–630 (2007).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007).
[CrossRef]

Burvall, A.

Cloetens, P.

M. Langer, P. Cloetens, and F. Peyrin, “Fourier-wavelet regularization of phase retrieval in x-ray in-line phase tomography,” J. Opt. Soc. Am. A 26, 1876–1881 (2009).
[CrossRef]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta Part B 62, 626–630 (2007).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. 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. Cloetens, M. Pateyron-Salomé, J. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

Cnudde, V.

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res. A 580, 442–445 (2007).
[CrossRef]

David, C.

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007).
[CrossRef]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta Part B 62, 626–630 (2007).
[CrossRef]

Davis, T. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature 373, 595–598 (1995).
[CrossRef]

De Witte, Y.

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

Y. De Witte, M. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “The Bronnikov aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
[CrossRef]

Y. De Witte, “Improved and practically feasible reconstruction methods for high resolution x-ray tomography,” Ph.D. thesis (Ghent University, 2010).

Derdak, Z.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Devulder, W.

Diaz, A.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta Part B 62, 626–630 (2007).
[CrossRef]

Diebold, G.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Dierick, M.

M. N. Boone, W. Devulder, M. Dierick, L. Brabant, E. Pauwels, and L. V. Hoorebeke, “Comparison of two single-image phase-retrieval algorithms for in-line x-ray phase-contrast imaging,” J. Opt. Soc. Am. A 29, 2667–2672 (2012).

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

Y. De Witte, M. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “The Bronnikov aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res. A 580, 442–445 (2007).
[CrossRef]

Dreossi, D.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects on the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617–3727 (2005).
[CrossRef]

Dyck, D. V.

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. 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]

Eastwood, S. A.

Estiaghi, N.

B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
[CrossRef]

Fouras, A.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

Fujita, H.

S. Matsuo, H. Fujita, J. Morishita, T. Katafuchi, C. Honda, and J. Sugiyama, “Preliminary evaluation of a phase contrast imaging with digital mammography,” in Digital Mammography/IWDM’08 (Springer, 2008), pp. 130–136.

Gao, D.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature 373, 595–598 (1995).
[CrossRef]

Gates, W. P.

B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
[CrossRef]

Groso, A.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta Part B 62, 626–630 (2007).
[CrossRef]

A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express 14, 8103–8110 (2006).
[CrossRef]

Guigay, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. 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]

Gureyev, T. E.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105, 102005 (2009).
[CrossRef]

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for constant, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16, 3223–3241 (2008).
[CrossRef]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[CrossRef]

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. 206, 33–40 (2002).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature 373, 595–598 (1995).
[CrossRef]

Hamilton, T. J.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Hertz, H. M.

Honda, C.

S. Matsuo, H. Fujita, J. Morishita, T. Katafuchi, C. Honda, and J. Sugiyama, “Preliminary evaluation of a phase contrast imaging with digital mammography,” in Digital Mammography/IWDM’08 (Springer, 2008), pp. 130–136.

Hooper, S. B.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

Hoorebeke, L. V.

Jacobs, P.

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res. A 580, 442–445 (2007).
[CrossRef]

Joseph, P. M.

P. M. Joseph and C. Ruth, “A method for simultaneous correction of spectrum hardening artifacts in CT images containing both bone and iodine,” Med. Phys. 24, 1629–1634 (1997).
[CrossRef]

Kalender, W. A.

D. Prell, Y. Kyriakou, and W. A. Kalender, “Comparison of ring artifact correction methods for flat-detector CT,” Phys. Med. Biol. 54, 3881–3895 (2009).
[CrossRef]

Katafuchi, T.

S. Matsuo, H. Fujita, J. Morishita, T. Katafuchi, C. Honda, and J. Sugiyama, “Preliminary evaluation of a phase contrast imaging with digital mammography,” in Digital Mammography/IWDM’08 (Springer, 2008), pp. 130–136.

Kitchen, M. J.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[CrossRef]

Kottler, C.

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007).
[CrossRef]

Kroon, D.-J.

D.-J. Kroon, C. H. Slump, and T. J. J. Maal, “Optimized anisotropic rotational invariant diffusion scheme on cone-beam CT,” in 13th International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI 2010) (2010), pp. 221–228.

Kyriakou, Y.

D. Prell, Y. Kyriakou, and W. A. Kalender, “Comparison of ring artifact correction methods for flat-detector CT,” Phys. Med. Biol. 54, 3881–3895 (2009).
[CrossRef]

Landuyt, J. V.

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. 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]

Langer, M.

Laperle, C. M.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Larsson, D. H.

Lindblad, J.

J. Lindblad, N. Sladoje, and T. Lukic, “De-noising of SR μ CT fiber images by total variation minimization,” in International Conference on Pattern Recognition (ICPR) 2010 (IEEE, 2010), pp. 4621–4624.

Liu, A. C. Y.

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. 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]

Lukic, T.

J. Lindblad, N. Sladoje, and T. Lukic, “De-noising of SR μ CT fiber images by total variation minimization,” in International Conference on Pattern Recognition (ICPR) 2010 (IEEE, 2010), pp. 4621–4624.

Lundström, U.

Maal, T. J. J.

D.-J. Kroon, C. H. Slump, and T. J. J. Maal, “Optimized anisotropic rotational invariant diffusion scheme on cone-beam CT,” in 13th International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI 2010) (2010), pp. 221–228.

Masschaele, B.

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res. A 580, 442–445 (2007).
[CrossRef]

Matsuo, S.

S. Matsuo, H. Fujita, J. Morishita, T. Katafuchi, C. Honda, and J. Sugiyama, “Preliminary evaluation of a phase contrast imaging with digital mammography,” in Digital Mammography/IWDM’08 (Springer, 2008), pp. 130–136.

Mayo, S. C.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105, 102005 (2009).
[CrossRef]

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. 206, 33–40 (2002).
[CrossRef]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[CrossRef]

Miller, P. R.

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for constant, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16, 3223–3241 (2008).
[CrossRef]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[CrossRef]

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. 206, 33–40 (2002).
[CrossRef]

Morishita, J.

S. Matsuo, H. Fujita, J. Morishita, T. Katafuchi, C. Honda, and J. Sugiyama, “Preliminary evaluation of a phase contrast imaging with digital mammography,” in Digital Mammography/IWDM’08 (Springer, 2008), pp. 130–136.

Myers, D. E.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105, 102005 (2009).
[CrossRef]

Nesterets, Y.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105, 102005 (2009).
[CrossRef]

Nesterets, Y. I.

Olivo, A.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects on the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617–3727 (2005).
[CrossRef]

Paganin, D.

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. 206, 33–40 (2002).
[CrossRef]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[CrossRef]

Paganin, D. M.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

S. A. Eastwood, D. M. Paganin, and A. C. Y. Liu, “Automated phase retrieval of a single-material object using a single out-of-focus image,” Opt. Lett. 36, 1878–1880 (2011).
[CrossRef]

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[CrossRef]

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105, 102005 (2009).
[CrossRef]

Pani, S.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects on the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617–3727 (2005).
[CrossRef]

Parry, D. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[CrossRef]

Pateyron-Salomé, M.

P. Cloetens, M. Pateyron-Salomé, J. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

Pauwels, E.

Peele, A. G.

B. D. Arhatari, W. P. Gates, N. Estiaghi, and A. G. Peele, “Phase retrieval tomography in the presence of noise,” J. Appl. Phys. 107, 034904 (2010).
[CrossRef]

Peix, G.

P. Cloetens, M. Pateyron-Salomé, J. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

Peterzol, A.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects on the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617–3727 (2005).
[CrossRef]

Peyrin, F.

M. Langer, P. Cloetens, and F. Peyrin, “Fourier-wavelet regularization of phase retrieval in x-ray in-line phase tomography,” J. Opt. Soc. Am. A 26, 1876–1881 (2009).
[CrossRef]

P. Cloetens, M. Pateyron-Salomé, J. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

Pfeiffer, F.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta Part B 62, 626–630 (2007).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007).
[CrossRef]

Pogany, A.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105, 102005 (2009).
[CrossRef]

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for constant, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16, 3223–3241 (2008).
[CrossRef]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

Prell, D.

D. Prell, Y. Kyriakou, and W. A. Kalender, “Comparison of ring artifact correction methods for flat-detector CT,” Phys. Med. Biol. 54, 3881–3895 (2009).
[CrossRef]

Reser, D. H.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

Rigon, L.

A. Peterzol, A. Olivo, L. Rigon, S. Pani, and D. Dreossi, “The effects on the imaging system on the validity limits of the ray-optical approach to phase contrast imaging,” Med. Phys. 32, 3617–3727 (2005).
[CrossRef]

Rohbeck, T.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta Part B 62, 626–630 (2007).
[CrossRef]

Rose-Petruck, C.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Ruth, C.

P. M. Joseph and C. Ruth, “A method for simultaneous correction of spectrum hardening artifacts in CT images containing both bone and iodine,” Med. Phys. 24, 1629–1634 (1997).
[CrossRef]

Schlenker, M.

P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. 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. Cloetens, M. Pateyron-Salomé, J. Buffière, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
[CrossRef]

Shi, D.

C. M. Laperle, T. J. Hamilton, P. Wintermeyer, E. J. Walker, D. Shi, M. A. Anastasio, Z. Derdak, J. R. Wands, G. Diebold, and C. Rose-Petruck, “Low density contrast agents for x-ray phase contrast imaging: the use of ambient air for x-ray angiography of excised murine liver tissue,” Phys. Med. Biol. 53, 6911–6923 (2008).
[CrossRef]

Siu, K. W.

M. A. Beltran, D. M. Paganin, K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[CrossRef]

Sladoje, N.

J. Lindblad, N. Sladoje, and T. Lukic, “De-noising of SR μ CT fiber images by total variation minimization,” in International Conference on Pattern Recognition (ICPR) 2010 (IEEE, 2010), pp. 4621–4624.

Slump, C. H.

D.-J. Kroon, C. H. Slump, and T. J. J. Maal, “Optimized anisotropic rotational invariant diffusion scheme on cone-beam CT,” in 13th International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI 2010) (2010), pp. 221–228.

Stampanoni, M.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard x-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta Part B 62, 626–630 (2007).
[CrossRef]

A. Groso, R. Abela, and M. Stampanoni, “Implementation of a fast method for high resolution phase contrast tomography,” Opt. Express 14, 8103–8110 (2006).
[CrossRef]

Stevenson, A. W.

T. E. Gureyev, S. C. Mayo, D. E. Myers, Y. Nesterets, D. M. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “Refracting Röntgen’s rays: propagation-based x-ray phase contrast for biomedical imaging,” J. Appl. Phys. 105, 102005 (2009).
[CrossRef]

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for constant, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express 16, 3223–3241 (2008).
[CrossRef]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative x-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[CrossRef]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard x-rays,” Nature 373, 595–598 (1995).
[CrossRef]

Sugiyama, J.

S. Matsuo, H. Fujita, J. Morishita, T. Katafuchi, C. Honda, and J. Sugiyama, “Preliminary evaluation of a phase contrast imaging with digital mammography,” in Digital Mammography/IWDM’08 (Springer, 2008), pp. 130–136.

Svensson, S.

M. Axelsson, S. Svensson, and G. Borgefors, “Reduction of ring artefacts in high resolution x-ray microtomography images,” in DAGM Symposium on Pattern Recognition (Springer, 2006), pp. 61–70.

Takman, P. A. C.

Teague, M. R.

M. R. Teague, “Image formation in terms of the transport equation,” J. Opt. Soc. Am. 2, 2019–2026 (1985).
[CrossRef]

M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983).
[CrossRef]

Uesugi, K.

Van Acker, J.

J. Van den Bulcke, M. Boone, J. Van Acker, and L. Van Hoorebeke, “Three-dimensional x-ray imaging and analysis of fungi on and in wood,” Microsc. Microanal. 15, 395–402 (2009).
[CrossRef]

Van den Bulcke, J.

J. Van den Bulcke, M. Boone, J. Van Acker, and L. Van Hoorebeke, “Three-dimensional x-ray imaging and analysis of fungi on and in wood,” Microsc. Microanal. 15, 395–402 (2009).
[CrossRef]

Van Hoorebeke, L.

M. N. Boone, Y. De Witte, M. Dierick, A. Almeida, and L. Van Hoorebeke, “Improved signal-to-noise ratio in laboratory-based phase contrast tomography,” Microsc. Microanal. 18, 399–405 (2012).
[CrossRef]

J. Van den Bulcke, M. Boone, J. Van Acker, and L. Van Hoorebeke, “Three-dimensional x-ray imaging and analysis of fungi on and in wood,” Microsc. Microanal. 15, 395–402 (2009).
[CrossRef]

Y. De Witte, M. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “The Bronnikov aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
[CrossRef]

J. Vlassenbroeck, M. Dierick, B. Masschaele, V. Cnudde, L. Van Hoorebeke, and P. Jacobs, “Software tools for quantification of x-ray microtomography at the UGCT,” Nucl. Instrum. Methods Phys. Res. A 580, 442–445 (2007).
[CrossRef]

Vlassenbroeck, J.

Y. De Witte, M. Boone, J. Vlassenbroeck, M. Dierick, and L. Van Hoorebeke, “The Bronnikov aided correction for x-ray computed tomography,” J. Opt. Soc. Am. A 26, 890–894 (2009).
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Figures (5)

Fig. 1.
Fig. 1.

Phase-artifact removal from a phantom using SPR. (a), (b) Slice number 256, of size 512×512pixels. (c) 1D line profiles through the samples; top, from (a); bottom, from (b). The reference image is not shown but looks very similar to the image in (b).

Fig. 2.
Fig. 2.

(a) Slice from a CT image of a sample with wood (the bright structure), nutrition medium (in the middle cell), and air (dark regions corresponds to air). (b)–(f) Filtered to remove phase artifacts. LP denotes a Gaussian low-pass filter with standard deviation s and SPR the method introduced in this paper. Corresponding histograms are shown in Fig. 5.

Fig. 3.
Fig. 3.

Examples of filtering on different data sets.

Fig. 4.
Fig. 4.

Slice from a volumetric image of a paper sheet captured with a MicroXCT-200 from Xradia.

Fig. 5.
Fig. 5.

Histograms of the volumes corresponding to the slices shown in Fig. 2. For the visualization, the histograms are scaled from the 0.5th to the 99.5th percentile on horizontal axes and from 0 to max count on vertical axes. Note that, in this situation, BAC also would benefit from additional low-pass filtering.

Tables (1)

Tables Icon

Table 1. Normalized Root-Mean-Square Error (NRMSE) of Reconstructions from a Phantom Image (see Fig. 1)a

Equations (11)

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IattenuatedIsource=exp(p(s)μds),
I(x,y,z)z=λ2π[I(x,y,z)ϕ0(x,y)],
I(x,y,D)I(x,y,0)[1λD2πS2ϕ+λD2πS(μ0xϕ0x+μ0yϕ0y)],
μreconstructed(x)=μ(x)+DΔn(x),
μreconstructed(x)=μ(x)+cΔσμ(x),
μreconstructed=(δ+cΔσ)*μ,
μ=F1{F{μreconstructed}/F{δ+cΔσ}}.
F{f}(ρ)=(2π)N2cρ2(2π)N2eρ2σ22.
ddρF{f}(ρ)(ρ3σ22ρ)eρ2σ22=0,
F{f}(ρm)=(2π)N22cσ2(2π)N2e1,
cσ2<e2.

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