Abstract

Phase-contrast x-ray computed tomography has a high potential to become clinically implemented because of its complementarity to conventional absorption-contrast.

In this study, we investigate noise-reducing but resolution-preserving analytical reconstruction methods to improve differential phase-contrast imaging. We apply the non-linear Perona-Malik filter on phase-contrast data prior or post filtered backprojected reconstruction. Secondly, the Hilbert kernel is replaced by regularized iterative integration followed by ramp filtered backprojection as used for absorption-contrast imaging. Combining the Perona-Malik filter with this integration algorithm allows to successfully reveal relevant sample features, quantitatively confirmed by significantly increased structural similarity indices and contrast-to-noise ratios. With this concept, phase-contrast imaging can be performed at considerably lower dose.

© 2014 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
  27. D. Hahn, P. Thibault, M. Bech, M. Stockmar, S. Schleede, I. Zanette, and A. Rack, ”Numerical comparison of X-ray differential phase contrast and attenuation contrast,” Biomed. Opt. Express 3(6), 1141–1148 (2012).
    [Crossref] [PubMed]
  28. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, ”Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2014 (1)

J. Herzen, M. S. Willner, A. A. Fingerle, P. B. Noël, T. Koehler, E. Drecoll, E. J. Rummeny, and F. Pfeiffer, ”Imaging liver lesions using grating-based phase-contrast computed tomography with bi-lateral filter post-processing,” PLOS ONE 9(1), e83369 (2014).
[Crossref] [PubMed]

2013 (5)

Z. Liao, ”Low-dosed x-ray computed tomography imaging by regularized fully spatial fractional-order Perona-Malik diffusion,” Adv. Math. Phys. 2013, 371868 (2013).
[Crossref]

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, and F. Pfeiffer, ”In-vivo dark-field and phase-contrast x-ray imaging,” Sci. Rep. 3(3209), 1–3 (2013).
[Crossref]

A. Bravin, P. Coan, and P. Suortti, ”X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref]

M. Nilchian, C. Vonesch, P. Modregger, M. Stampanoni, and M. Unser, ”Fast iterative reconstruction of differential phase contrast x-ray tomograms,” Opt. Express 21(5), 5511–5528 (2013).
[Crossref] [PubMed]

T. Gaass, G. Potdevin, M. Bech, P. B. Noël, M. Willner, A. Tapfer, F. Pfeiffer, and A. Haase, ”Iterative reconstruction for few-view grating-based phase-contrast CT – an in vitro mouse model,” Europhys. Lett. 102(4), 48001 (2013).
[Crossref]

2012 (2)

K. Li, N. Bevins, J. Zambelli, and G.-H. Chen, ”A new image reconstruction method to improve noise properties in x-ray differential phase contrast computed tomography,” Proc. SPIE 8313, 83131V (2012).
[Crossref]

D. Hahn, P. Thibault, M. Bech, M. Stockmar, S. Schleede, I. Zanette, and A. Rack, ”Numerical comparison of X-ray differential phase contrast and attenuation contrast,” Biomed. Opt. Express 3(6), 1141–1148 (2012).
[Crossref] [PubMed]

2011 (6)

T. Thüring, P. Modregger, B. R. Pinzer, Z. Wang, and M. Stampanoni, ”Non-linear regularized phase retrieval for unidirectional x-ray differential phase contrast radiography,” Opt. Express 19(25), 25545–25548 (2011).
[Crossref]

E. Michel-González, M. H. Cho, and S.Y. Lee, ”Geometric nonlinear diffusion filter and its application to x-ray imaging,” Biomed. Eng. Online 10(47), 1–16 (2011).
[Crossref]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, and N. Hauser, ”The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Rad. 46(12), 801–806 (2011).
[Crossref]

T. Koehler, B. Brendel, and E. Roessl, ”Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. Phys. 38(8), 4542–4545 (2011).
[Crossref]

T. Koehler, K. J. Engel, and E. Roessl, ”Noise properties of grating-based x-ray phase contrast computed tomography,” Med. Phys. 38(7), S106–S116 (2011).
[Crossref]

R. Raupach and T. G. Flohr, ”Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56(7), 2219–2244 (2011).
[Crossref] [PubMed]

2009 (1)

2008 (2)

A. Faridani, R. Hass, and D. C. Solmon, ”Numerical and theoretical explorations in helical and fan-beam tomography,” J. Phys. Conf. Ser. 124(1), 012024 (2008).
[Crossref]

J. Q. Xia, J. Y. Lo, K. Yang, C. E. Floyd, and J. M. Boone, ”Dedicated breast computed tomography: volume image denoising via a partial-diffusion equation based technique,” Med. Phys. 35(5), 1950 (2008).
[Crossref] [PubMed]

2007 (1)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, ”Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[Crossref] [PubMed]

2006 (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, ”Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

2004 (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, ”Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

2003 (1)

F. Noo, J. Pack, and D. Heuscher, ”Exact helical reconstruction using native cone-beam geometries,” Phys. Med. Biol. 48(23), 3787–3818 (2003).
[Crossref]

1990 (1)

P. Perona and J. Malik, ”Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[Crossref]

Bech, M.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, and F. Pfeiffer, ”In-vivo dark-field and phase-contrast x-ray imaging,” Sci. Rep. 3(3209), 1–3 (2013).
[Crossref]

T. Gaass, G. Potdevin, M. Bech, P. B. Noël, M. Willner, A. Tapfer, F. Pfeiffer, and A. Haase, ”Iterative reconstruction for few-view grating-based phase-contrast CT – an in vitro mouse model,” Europhys. Lett. 102(4), 48001 (2013).
[Crossref]

D. Hahn, P. Thibault, M. Bech, M. Stockmar, S. Schleede, I. Zanette, and A. Rack, ”Numerical comparison of X-ray differential phase contrast and attenuation contrast,” Biomed. Opt. Express 3(6), 1141–1148 (2012).
[Crossref] [PubMed]

Beckmann, F.

Bevins, N.

K. Li, N. Bevins, J. Zambelli, and G.-H. Chen, ”A new image reconstruction method to improve noise properties in x-ray differential phase contrast computed tomography,” Proc. SPIE 8313, 83131V (2012).
[Crossref]

Boone, J. M.

J. Q. Xia, J. Y. Lo, K. Yang, C. E. Floyd, and J. M. Boone, ”Dedicated breast computed tomography: volume image denoising via a partial-diffusion equation based technique,” Med. Phys. 35(5), 1950 (2008).
[Crossref] [PubMed]

Bordeianu, C. C.

R. H. Landau, M. J. Páez Mejía, and C. C. Bordeianu, Computational Physics: Problem Solving with Computers (Wiley-VCH, 2007).
[Crossref]

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, ”Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Bravin, A.

A. Bravin, P. Coan, and P. Suortti, ”X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref]

Brendel, B.

T. Koehler, B. Brendel, and E. Roessl, ”Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. Phys. 38(8), 4542–4545 (2011).
[Crossref]

Bunk, O.

J. Herzen, T. Donath, F. Pfeiffer, O. Bunk, C. Padeste, F. Beckmann, A. Schreyer, and C. David, ”Quantitative phase-contrast tomography of a liquid phantom using a conventional x-ray tube source,” Opt. Express 17(12), 10010–10018 (2009).
[Crossref] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, ”Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[Crossref] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, ”Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

Chen, G.-H.

K. Li, N. Bevins, J. Zambelli, and G.-H. Chen, ”A new image reconstruction method to improve noise properties in x-ray differential phase contrast computed tomography,” Proc. SPIE 8313, 83131V (2012).
[Crossref]

Cho, M. H.

E. Michel-González, M. H. Cho, and S.Y. Lee, ”Geometric nonlinear diffusion filter and its application to x-ray imaging,” Biomed. Eng. Online 10(47), 1–16 (2011).
[Crossref]

Coan, P.

A. Bravin, P. Coan, and P. Suortti, ”X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref]

David, C.

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, and N. Hauser, ”The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Rad. 46(12), 801–806 (2011).
[Crossref]

J. Herzen, T. Donath, F. Pfeiffer, O. Bunk, C. Padeste, F. Beckmann, A. Schreyer, and C. David, ”Quantitative phase-contrast tomography of a liquid phantom using a conventional x-ray tube source,” Opt. Express 17(12), 10010–10018 (2009).
[Crossref] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, ”Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[Crossref] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, ”Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

Donath, T.

Drecoll, E.

J. Herzen, M. S. Willner, A. A. Fingerle, P. B. Noël, T. Koehler, E. Drecoll, E. J. Rummeny, and F. Pfeiffer, ”Imaging liver lesions using grating-based phase-contrast computed tomography with bi-lateral filter post-processing,” PLOS ONE 9(1), e83369 (2014).
[Crossref] [PubMed]

Engel, K. J.

T. Koehler, K. J. Engel, and E. Roessl, ”Noise properties of grating-based x-ray phase contrast computed tomography,” Med. Phys. 38(7), S106–S116 (2011).
[Crossref]

Euler, L.

L. Euler, Institutionum Calculi Integralis (Academiae Imperialis Scientiarum, 1768).

Faridani, A.

A. Faridani, R. Hass, and D. C. Solmon, ”Numerical and theoretical explorations in helical and fan-beam tomography,” J. Phys. Conf. Ser. 124(1), 012024 (2008).
[Crossref]

Fingerle, A. A.

J. Herzen, M. S. Willner, A. A. Fingerle, P. B. Noël, T. Koehler, E. Drecoll, E. J. Rummeny, and F. Pfeiffer, ”Imaging liver lesions using grating-based phase-contrast computed tomography with bi-lateral filter post-processing,” PLOS ONE 9(1), e83369 (2014).
[Crossref] [PubMed]

Flohr, T. G.

R. Raupach and T. G. Flohr, ”Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56(7), 2219–2244 (2011).
[Crossref] [PubMed]

Floyd, C. E.

J. Q. Xia, J. Y. Lo, K. Yang, C. E. Floyd, and J. M. Boone, ”Dedicated breast computed tomography: volume image denoising via a partial-diffusion equation based technique,” Med. Phys. 35(5), 1950 (2008).
[Crossref] [PubMed]

Gaass, T.

T. Gaass, G. Potdevin, M. Bech, P. B. Noël, M. Willner, A. Tapfer, F. Pfeiffer, and A. Haase, ”Iterative reconstruction for few-view grating-based phase-contrast CT – an in vitro mouse model,” Europhys. Lett. 102(4), 48001 (2013).
[Crossref]

Haase, A.

T. Gaass, G. Potdevin, M. Bech, P. B. Noël, M. Willner, A. Tapfer, F. Pfeiffer, and A. Haase, ”Iterative reconstruction for few-view grating-based phase-contrast CT – an in vitro mouse model,” Europhys. Lett. 102(4), 48001 (2013).
[Crossref]

Hahn, D.

Hass, R.

A. Faridani, R. Hass, and D. C. Solmon, ”Numerical and theoretical explorations in helical and fan-beam tomography,” J. Phys. Conf. Ser. 124(1), 012024 (2008).
[Crossref]

Hauser, N.

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, and N. Hauser, ”The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Rad. 46(12), 801–806 (2011).
[Crossref]

Herzen, J.

J. Herzen, M. S. Willner, A. A. Fingerle, P. B. Noël, T. Koehler, E. Drecoll, E. J. Rummeny, and F. Pfeiffer, ”Imaging liver lesions using grating-based phase-contrast computed tomography with bi-lateral filter post-processing,” PLOS ONE 9(1), e83369 (2014).
[Crossref] [PubMed]

J. Herzen, T. Donath, F. Pfeiffer, O. Bunk, C. Padeste, F. Beckmann, A. Schreyer, and C. David, ”Quantitative phase-contrast tomography of a liquid phantom using a conventional x-ray tube source,” Opt. Express 17(12), 10010–10018 (2009).
[Crossref] [PubMed]

Heuscher, D.

F. Noo, J. Pack, and D. Heuscher, ”Exact helical reconstruction using native cone-beam geometries,” Phys. Med. Biol. 48(23), 3787–3818 (2003).
[Crossref]

Hostens, J.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, and F. Pfeiffer, ”In-vivo dark-field and phase-contrast x-ray imaging,” Sci. Rep. 3(3209), 1–3 (2013).
[Crossref]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Kido, K.

J. Kiyohara, C. Makifuchi, K. Kido, S. Nagatsuka, J. Tanaka, M. Nagashima, and A. Momose, ”Development of the Talbot-Lau interferometry system available for clinical use,” in International Workshop on XNPIG (AIP Publishing, 2012), vol. 1466, pp. 97–102.

Kiyohara, J.

J. Kiyohara, C. Makifuchi, K. Kido, S. Nagatsuka, J. Tanaka, M. Nagashima, and A. Momose, ”Development of the Talbot-Lau interferometry system available for clinical use,” in International Workshop on XNPIG (AIP Publishing, 2012), vol. 1466, pp. 97–102.

Koehler, T.

J. Herzen, M. S. Willner, A. A. Fingerle, P. B. Noël, T. Koehler, E. Drecoll, E. J. Rummeny, and F. Pfeiffer, ”Imaging liver lesions using grating-based phase-contrast computed tomography with bi-lateral filter post-processing,” PLOS ONE 9(1), e83369 (2014).
[Crossref] [PubMed]

T. Koehler, K. J. Engel, and E. Roessl, ”Noise properties of grating-based x-ray phase contrast computed tomography,” Med. Phys. 38(7), S106–S116 (2011).
[Crossref]

T. Koehler, B. Brendel, and E. Roessl, ”Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. Phys. 38(8), 4542–4545 (2011).
[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(10), 108105 (2007).
[Crossref] [PubMed]

Landau, R. H.

R. H. Landau, M. J. Páez Mejía, and C. C. Bordeianu, Computational Physics: Problem Solving with Computers (Wiley-VCH, 2007).
[Crossref]

Lee, S.Y.

E. Michel-González, M. H. Cho, and S.Y. Lee, ”Geometric nonlinear diffusion filter and its application to x-ray imaging,” Biomed. Eng. Online 10(47), 1–16 (2011).
[Crossref]

Li, K.

K. Li, N. Bevins, J. Zambelli, and G.-H. Chen, ”A new image reconstruction method to improve noise properties in x-ray differential phase contrast computed tomography,” Proc. SPIE 8313, 83131V (2012).
[Crossref]

Liao, Z.

Z. Liao, ”Low-dosed x-ray computed tomography imaging by regularized fully spatial fractional-order Perona-Malik diffusion,” Adv. Math. Phys. 2013, 371868 (2013).
[Crossref]

Lo, J. Y.

J. Q. Xia, J. Y. Lo, K. Yang, C. E. Floyd, and J. M. Boone, ”Dedicated breast computed tomography: volume image denoising via a partial-diffusion equation based technique,” Med. Phys. 35(5), 1950 (2008).
[Crossref] [PubMed]

Makifuchi, C.

J. Kiyohara, C. Makifuchi, K. Kido, S. Nagatsuka, J. Tanaka, M. Nagashima, and A. Momose, ”Development of the Talbot-Lau interferometry system available for clinical use,” in International Workshop on XNPIG (AIP Publishing, 2012), vol. 1466, pp. 97–102.

Malik, J.

P. Perona and J. Malik, ”Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[Crossref]

Michel-González, E.

E. Michel-González, M. H. Cho, and S.Y. Lee, ”Geometric nonlinear diffusion filter and its application to x-ray imaging,” Biomed. Eng. Online 10(47), 1–16 (2011).
[Crossref]

Modregger, P.

Momose, A.

J. Kiyohara, C. Makifuchi, K. Kido, S. Nagatsuka, J. Tanaka, M. Nagashima, and A. Momose, ”Development of the Talbot-Lau interferometry system available for clinical use,” in International Workshop on XNPIG (AIP Publishing, 2012), vol. 1466, pp. 97–102.

Nagashima, M.

J. Kiyohara, C. Makifuchi, K. Kido, S. Nagatsuka, J. Tanaka, M. Nagashima, and A. Momose, ”Development of the Talbot-Lau interferometry system available for clinical use,” in International Workshop on XNPIG (AIP Publishing, 2012), vol. 1466, pp. 97–102.

Nagatsuka, S.

J. Kiyohara, C. Makifuchi, K. Kido, S. Nagatsuka, J. Tanaka, M. Nagashima, and A. Momose, ”Development of the Talbot-Lau interferometry system available for clinical use,” in International Workshop on XNPIG (AIP Publishing, 2012), vol. 1466, pp. 97–102.

Nilchian, M.

Noël, P. B.

J. Herzen, M. S. Willner, A. A. Fingerle, P. B. Noël, T. Koehler, E. Drecoll, E. J. Rummeny, and F. Pfeiffer, ”Imaging liver lesions using grating-based phase-contrast computed tomography with bi-lateral filter post-processing,” PLOS ONE 9(1), e83369 (2014).
[Crossref] [PubMed]

T. Gaass, G. Potdevin, M. Bech, P. B. Noël, M. Willner, A. Tapfer, F. Pfeiffer, and A. Haase, ”Iterative reconstruction for few-view grating-based phase-contrast CT – an in vitro mouse model,” Europhys. Lett. 102(4), 48001 (2013).
[Crossref]

Noo, F.

F. Noo, J. Pack, and D. Heuscher, ”Exact helical reconstruction using native cone-beam geometries,” Phys. Med. Biol. 48(23), 3787–3818 (2003).
[Crossref]

Pack, J.

F. Noo, J. Pack, and D. Heuscher, ”Exact helical reconstruction using native cone-beam geometries,” Phys. Med. Biol. 48(23), 3787–3818 (2003).
[Crossref]

Padeste, C.

Páez Mejía, M. J.

R. H. Landau, M. J. Páez Mejía, and C. C. Bordeianu, Computational Physics: Problem Solving with Computers (Wiley-VCH, 2007).
[Crossref]

Pauwels, B.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, and F. Pfeiffer, ”In-vivo dark-field and phase-contrast x-ray imaging,” Sci. Rep. 3(3209), 1–3 (2013).
[Crossref]

Perona, P.

P. Perona and J. Malik, ”Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[Crossref]

Pfeiffer, F.

J. Herzen, M. S. Willner, A. A. Fingerle, P. B. Noël, T. Koehler, E. Drecoll, E. J. Rummeny, and F. Pfeiffer, ”Imaging liver lesions using grating-based phase-contrast computed tomography with bi-lateral filter post-processing,” PLOS ONE 9(1), e83369 (2014).
[Crossref] [PubMed]

T. Gaass, G. Potdevin, M. Bech, P. B. Noël, M. Willner, A. Tapfer, F. Pfeiffer, and A. Haase, ”Iterative reconstruction for few-view grating-based phase-contrast CT – an in vitro mouse model,” Europhys. Lett. 102(4), 48001 (2013).
[Crossref]

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, and F. Pfeiffer, ”In-vivo dark-field and phase-contrast x-ray imaging,” Sci. Rep. 3(3209), 1–3 (2013).
[Crossref]

J. Herzen, T. Donath, F. Pfeiffer, O. Bunk, C. Padeste, F. Beckmann, A. Schreyer, and C. David, ”Quantitative phase-contrast tomography of a liquid phantom using a conventional x-ray tube source,” Opt. Express 17(12), 10010–10018 (2009).
[Crossref] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, ”Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[Crossref] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, ”Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

F. Pfeiffer, ”Milestones and basic principles of grating-based x-ray and neutron phase-contrast imaging,” in Proceedings of the AIP Conference1466(1) (American Institute of Physics, 2012), pp. 2–11.

Pinzer, B. R.

Potdevin, G.

T. Gaass, G. Potdevin, M. Bech, P. B. Noël, M. Willner, A. Tapfer, F. Pfeiffer, and A. Haase, ”Iterative reconstruction for few-view grating-based phase-contrast CT – an in vitro mouse model,” Europhys. Lett. 102(4), 48001 (2013).
[Crossref]

Rack, A.

Raupach, R.

R. Raupach and T. G. Flohr, ”Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56(7), 2219–2244 (2011).
[Crossref] [PubMed]

Roberts, L. G.

L. G. Roberts, Machine Perception of Three-Dimensional Solids, Lincoln Laboratory Technical Report #315 (Massachusetts Institute of Technology, 1963).

Roessl, E.

T. Koehler, K. J. Engel, and E. Roessl, ”Noise properties of grating-based x-ray phase contrast computed tomography,” Med. Phys. 38(7), S106–S116 (2011).
[Crossref]

T. Koehler, B. Brendel, and E. Roessl, ”Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. Phys. 38(8), 4542–4545 (2011).
[Crossref]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, and N. Hauser, ”The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Rad. 46(12), 801–806 (2011).
[Crossref]

Rummeny, E. J.

J. Herzen, M. S. Willner, A. A. Fingerle, P. B. Noël, T. Koehler, E. Drecoll, E. J. Rummeny, and F. Pfeiffer, ”Imaging liver lesions using grating-based phase-contrast computed tomography with bi-lateral filter post-processing,” PLOS ONE 9(1), e83369 (2014).
[Crossref] [PubMed]

Sauer, T.

T. Sauer, Numerical Analysis, II. ed. (Addison Wesley, 2012).

Schleede, S.

Schreyer, A.

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, ”Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, ”Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Solmon, D. C.

A. Faridani, R. Hass, and D. C. Solmon, ”Numerical and theoretical explorations in helical and fan-beam tomography,” J. Phys. Conf. Ser. 124(1), 012024 (2008).
[Crossref]

Stampanoni, M.

Stockmar, M.

Suortti, P.

A. Bravin, P. Coan, and P. Suortti, ”X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref]

Tanaka, J.

J. Kiyohara, C. Makifuchi, K. Kido, S. Nagatsuka, J. Tanaka, M. Nagashima, and A. Momose, ”Development of the Talbot-Lau interferometry system available for clinical use,” in International Workshop on XNPIG (AIP Publishing, 2012), vol. 1466, pp. 97–102.

Tapfer, A.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, and F. Pfeiffer, ”In-vivo dark-field and phase-contrast x-ray imaging,” Sci. Rep. 3(3209), 1–3 (2013).
[Crossref]

T. Gaass, G. Potdevin, M. Bech, P. B. Noël, M. Willner, A. Tapfer, F. Pfeiffer, and A. Haase, ”Iterative reconstruction for few-view grating-based phase-contrast CT – an in vitro mouse model,” Europhys. Lett. 102(4), 48001 (2013).
[Crossref]

Thibault, P.

Thüring, T.

T. Thüring, P. Modregger, B. R. Pinzer, Z. Wang, and M. Stampanoni, ”Non-linear regularized phase retrieval for unidirectional x-ray differential phase contrast radiography,” Opt. Express 19(25), 25545–25548 (2011).
[Crossref]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, and N. Hauser, ”The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Rad. 46(12), 801–806 (2011).
[Crossref]

Trippel, M.

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, and N. Hauser, ”The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Rad. 46(12), 801–806 (2011).
[Crossref]

Unser, M.

Velroyen, A.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, and F. Pfeiffer, ”In-vivo dark-field and phase-contrast x-ray imaging,” Sci. Rep. 3(3209), 1–3 (2013).
[Crossref]

Vonesch, C.

Wang, Z.

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, and N. Hauser, ”The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Rad. 46(12), 801–806 (2011).
[Crossref]

T. Thüring, P. Modregger, B. R. Pinzer, Z. Wang, and M. Stampanoni, ”Non-linear regularized phase retrieval for unidirectional x-ray differential phase contrast radiography,” Opt. Express 19(25), 25545–25548 (2011).
[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, ”Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

Weitkamp, T.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, ”Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

Willner, M.

T. Gaass, G. Potdevin, M. Bech, P. B. Noël, M. Willner, A. Tapfer, F. Pfeiffer, and A. Haase, ”Iterative reconstruction for few-view grating-based phase-contrast CT – an in vitro mouse model,” Europhys. Lett. 102(4), 48001 (2013).
[Crossref]

Willner, M. S.

J. Herzen, M. S. Willner, A. A. Fingerle, P. B. Noël, T. Koehler, E. Drecoll, E. J. Rummeny, and F. Pfeiffer, ”Imaging liver lesions using grating-based phase-contrast computed tomography with bi-lateral filter post-processing,” PLOS ONE 9(1), e83369 (2014).
[Crossref] [PubMed]

Xia, J. Q.

J. Q. Xia, J. Y. Lo, K. Yang, C. E. Floyd, and J. M. Boone, ”Dedicated breast computed tomography: volume image denoising via a partial-diffusion equation based technique,” Med. Phys. 35(5), 1950 (2008).
[Crossref] [PubMed]

Yang, K.

J. Q. Xia, J. Y. Lo, K. Yang, C. E. Floyd, and J. M. Boone, ”Dedicated breast computed tomography: volume image denoising via a partial-diffusion equation based technique,” Med. Phys. 35(5), 1950 (2008).
[Crossref] [PubMed]

Yaroshenko, A.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, and F. Pfeiffer, ”In-vivo dark-field and phase-contrast x-ray imaging,” Sci. Rep. 3(3209), 1–3 (2013).
[Crossref]

Zambelli, J.

K. Li, N. Bevins, J. Zambelli, and G.-H. Chen, ”A new image reconstruction method to improve noise properties in x-ray differential phase contrast computed tomography,” Proc. SPIE 8313, 83131V (2012).
[Crossref]

Zanette, I.

Adv. Math. Phys. (1)

Z. Liao, ”Low-dosed x-ray computed tomography imaging by regularized fully spatial fractional-order Perona-Malik diffusion,” Adv. Math. Phys. 2013, 371868 (2013).
[Crossref]

Biomed. Eng. Online (1)

E. Michel-González, M. H. Cho, and S.Y. Lee, ”Geometric nonlinear diffusion filter and its application to x-ray imaging,” Biomed. Eng. Online 10(47), 1–16 (2011).
[Crossref]

Biomed. Opt. Express (1)

Europhys. Lett. (1)

T. Gaass, G. Potdevin, M. Bech, P. B. Noël, M. Willner, A. Tapfer, F. Pfeiffer, and A. Haase, ”Iterative reconstruction for few-view grating-based phase-contrast CT – an in vitro mouse model,” Europhys. Lett. 102(4), 48001 (2013).
[Crossref]

IEEE Trans. Image Process. (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, ”Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process. 13(4), 600–612 (2004).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

P. Perona and J. Malik, ”Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[Crossref]

Invest. Rad. (1)

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, and N. Hauser, ”The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Rad. 46(12), 801–806 (2011).
[Crossref]

J. Phys. Conf. Ser. (1)

A. Faridani, R. Hass, and D. C. Solmon, ”Numerical and theoretical explorations in helical and fan-beam tomography,” J. Phys. Conf. Ser. 124(1), 012024 (2008).
[Crossref]

Med. Phys. (3)

J. Q. Xia, J. Y. Lo, K. Yang, C. E. Floyd, and J. M. Boone, ”Dedicated breast computed tomography: volume image denoising via a partial-diffusion equation based technique,” Med. Phys. 35(5), 1950 (2008).
[Crossref] [PubMed]

T. Koehler, K. J. Engel, and E. Roessl, ”Noise properties of grating-based x-ray phase contrast computed tomography,” Med. Phys. 38(7), S106–S116 (2011).
[Crossref]

T. Koehler, B. Brendel, and E. Roessl, ”Iterative reconstruction for differential phase contrast imaging using spherically symmetric basis functions,” Med. Phys. 38(8), 4542–4545 (2011).
[Crossref]

Nat. Phys. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, ”Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys. 2(4), 258–261 (2006).
[Crossref]

Opt. Express (3)

Phys. Med. Biol. (3)

A. Bravin, P. Coan, and P. Suortti, ”X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol. 58(1), R1–R35 (2013).
[Crossref]

R. Raupach and T. G. Flohr, ”Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56(7), 2219–2244 (2011).
[Crossref] [PubMed]

F. Noo, J. Pack, and D. Heuscher, ”Exact helical reconstruction using native cone-beam geometries,” Phys. Med. Biol. 48(23), 3787–3818 (2003).
[Crossref]

Phys. Rev. Lett. (1)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, ”Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[Crossref] [PubMed]

PLOS ONE (1)

J. Herzen, M. S. Willner, A. A. Fingerle, P. B. Noël, T. Koehler, E. Drecoll, E. J. Rummeny, and F. Pfeiffer, ”Imaging liver lesions using grating-based phase-contrast computed tomography with bi-lateral filter post-processing,” PLOS ONE 9(1), e83369 (2014).
[Crossref] [PubMed]

Proc. SPIE (1)

K. Li, N. Bevins, J. Zambelli, and G.-H. Chen, ”A new image reconstruction method to improve noise properties in x-ray differential phase contrast computed tomography,” Proc. SPIE 8313, 83131V (2012).
[Crossref]

Sci. Rep. (1)

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, and F. Pfeiffer, ”In-vivo dark-field and phase-contrast x-ray imaging,” Sci. Rep. 3(3209), 1–3 (2013).
[Crossref]

Other (7)

J. Kiyohara, C. Makifuchi, K. Kido, S. Nagatsuka, J. Tanaka, M. Nagashima, and A. Momose, ”Development of the Talbot-Lau interferometry system available for clinical use,” in International Workshop on XNPIG (AIP Publishing, 2012), vol. 1466, pp. 97–102.

L. Euler, Institutionum Calculi Integralis (Academiae Imperialis Scientiarum, 1768).

T. Sauer, Numerical Analysis, II. ed. (Addison Wesley, 2012).

R. H. Landau, M. J. Páez Mejía, and C. C. Bordeianu, Computational Physics: Problem Solving with Computers (Wiley-VCH, 2007).
[Crossref]

L. G. Roberts, Machine Perception of Three-Dimensional Solids, Lincoln Laboratory Technical Report #315 (Massachusetts Institute of Technology, 1963).

F. Pfeiffer, ”Milestones and basic principles of grating-based x-ray and neutron phase-contrast imaging,” in Proceedings of the AIP Conference1466(1) (American Institute of Physics, 2012), pp. 2–11.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Supplementary Material (1)

» Media 1: JPG (4 KB)     

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Figures (7)

Fig. 1
Fig. 1

Grating-based x-ray interferometer including a phase-grating and an analyzer absorption grating. The source grating can be omitted for brilliant (synchrotron) sources.

Fig. 2
Fig. 2

Two-dimensional noise power spectra from axial slices of (a) a Ram-Lak filtered backprojected (FBP) reconstruction of a sinogram containing Poisson-distributed noise and (b) a Hilbert FBP reconstruction of a sinogram with normal-distributed noise.

Fig. 3
Fig. 3

Description of the human heart specimen (axial slice, texp = 3.6 s per phase-step).

Fig. 4
Fig. 4

Reconstructed images from differential phase-contrast projections acquired with texp = 0.225, 0.1, 0.025 s (from left to right). Standard represents the standard Hilbert filtered backprojection (FBP); using PM2D, the 2D Perona-Malik (PM) filter is applied on projections; RII denotes the regularized iterative integration (RII) followed by Ram-Lak FBP; PM2D + RII shows the combination of 2D PM filter followed by RII; for RII + PM3D, first RII is performed - post reconstruction, the 3D PM filter reduces remaining noise.

Fig. 5
Fig. 5

Axial, sagittal and coronal view through the reconstructed volume for three data sets with an exposure time of 0.025, 0.1, 0.225 s. Reconstructed with regularized iterative reconstruction and 3D Perona-Malik filter, i.e. RII + PM3D. A Hilbert filtered backprojected, reconstructed image (exposure time: 0.025 s) is depicted for comparison.

Fig. 6
Fig. 6

Contrast-to-noise ratios from an axial and a coronal slice of the reconstructed volume depicted in the left and right histogram, respectively. The same reconstruction methods as in fig. 4 are analyzed for texp = [0.025, 0.1, 0.225 s]. The order of the bars from left to right follows the legend entries from top to bottom.

Fig. 7
Fig. 7

Structural similarity index (SSIM) for different reconstruction methods tested with an axial slice (left; images shown in fig. 4) and a coronal slice (right; images partially depicted in fig. 5) compared to a reference image (see fig. 3).

Tables (1)

Tables Icon

Table 1: Parameter setting according to each reconstruction concept.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

Δ Φ = δ k r
t f ( x , y , t ) = ( γ ( f ( x , y , t ) ) f ( x , y , t ) ) ,
f ( t + Δ t ) = f ( t ) + Δ t { [ γ ( f ( t ) ) f ( t ) ] } ,
γ ( f ( x , y , t ) ) = 1 [ 1 | f ( x , y , t ) | 2 / ξ 2 ] 1 / 2 ,
L = i , j 1 σ i , j 2 ( Φ ˜ i + 1 , j Φ ˜ i , j Δ Φ i , j ) 2
+ λ 1 i , j 1 ( σ i , j loc ) 2 ( Φ ˜ i , j + 1 Φ ˜ i , j ) 2
+ λ 2 i , j m i , j 2 Φ ˜ i , j 2 .
CNR = | C 1 ¯ C 2 ¯ | × ( σ C 1 2 + σ C 2 2 ) 1 / 2 .

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