Abstract

This paper describes an algebraic reconstruction algorithm that uses total variation (TV) regularization for differential phase contrast computed tomography (DPC-CT) using a limited number of views. In order to overcome over-flattening inherent in TV regularization, a two-step reconstruction process is used: we first reconstruct tomographic images of gradient refractive index from differential projections with TV regularization; these images are then used to compute tomographic images of refractive index by solving the Poisson equation. We incorporate TV regularization in the reconstruction process because the distribution of gradient refractive index is much more flattened than the refractive index. Simulations of the proposed method demonstrate that it can achieve satisfactory image quality from a much smaller number of projections than is required by the Nyquist sampling theorem. We experimentally prove the feasibility of the proposed method using dark field imaging optics at PF-14C beamline at the Photon Factory, KEK. The differential phase contrast projection data was experimentally acquired from a biological sample and DPC-CT images were reconstructed. We show that far fewer projections are needed when the proposed algorithm is used.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]

2014 (2)

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal analyser-based X-ray phase contrast imaging in the dark field: implementation and evaluation using excised tissue specimens,” Eur. Radiol. 24(2), 423–433 (2014).
[Crossref] [PubMed]

S. Gasilov, A. Mittone, E. Brun, A. Bravin, S. Grandl, A. Mirone, and P. Coan, “Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach,” Opt. Express 22(5), 5216–5227 (2014).
[Crossref] [PubMed]

2013 (1)

P. Suortti, J. Keyrilainen, and W. Thomlinson, “Analyser-based x-ray imaging for biomedical research,” J. Phys. D Appl. Phys. 46(49), 494002 (2013).
[Crossref]

2012 (1)

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “X-ray refraction-contrast computed tomography images using dark field imaging optics,” Appl. Phys. Lett. 97(15), 153701 (2010).
[Crossref]

2009 (1)

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

2008 (4)

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[Crossref] [PubMed]

P. Coan, J. Mollenhauer, A. Wagner, C. Muehleman, and A. Bravin, “Analyzer-based imaging technique in tomography of cartilage and metal implants: a study at the ESRF,” Eur. J. Radiol. 68(3Suppl), S41–S48 (2008).
[Crossref] [PubMed]

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

2006 (2)

2005 (1)

A. Maksimenko, M. Ando, H. Sugiyama, and T. Yuasa, “Computed tomographic reconstruction based on x-ray refraction contrast,” Appl. Phys. Lett. 86(12), 124105 (2005).
[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 (2)

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray talbot interferometry,” Jpn. J. Appl. Phys. 42(2), L866–L868 (2003).
[Crossref]

2002 (1)

M. Ando, A. Maksimenko, H. Sugiyama, W. Pattanasiriwissawa, K. Hyodo, and C. Uyama, “Simple X-ray dark- and bright-field imaging using achromatic Laue optics,” Jpn. J. Appl. Phys. 41(2), 1016 (2002).
[Crossref]

2000 (1)

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45(4), 933–946 (2000).
[Crossref] [PubMed]

1997 (1)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

1996 (1)

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[Crossref] [PubMed]

1995 (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[Crossref]

1992 (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[Crossref]

1988 (1)

Akatsuka, T.

Anastasio, M. A.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Ando, M.

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal analyser-based X-ray phase contrast imaging in the dark field: implementation and evaluation using excised tissue specimens,” Eur. Radiol. 24(2), 423–433 (2014).
[Crossref] [PubMed]

N. Sunaguchi, T. Yuasa, Q. Huo, and M. Ando, “Convolution reconstruction algorithm for refraction-contrast computed tomography using a Laue-case analyzer for dark-field imaging,” Opt. Lett. 36(3), 391–393 (2011).
[Crossref] [PubMed]

N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “X-ray refraction-contrast computed tomography images using dark field imaging optics,” Appl. Phys. Lett. 97(15), 153701 (2010).
[Crossref]

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

T. Yuasa, A. Maksimenko, E. Hashimoto, H. Sugiyama, K. Hyodo, T. Akatsuka, and M. Ando, “Hard-x-ray region tomographic reconstruction of the refractive-index gradient vector field: Imaging principles and comparisons with diffraction-enhanced-imaging-based computed tomography,” Opt. Lett. 31(12), 1818–1820 (2006).
[Crossref] [PubMed]

A. Maksimenko, M. Ando, H. Sugiyama, and T. Yuasa, “Computed tomographic reconstruction based on x-ray refraction contrast,” Appl. Phys. Lett. 86(12), 124105 (2005).
[Crossref]

M. Ando, A. Maksimenko, H. Sugiyama, W. Pattanasiriwissawa, K. Hyodo, and C. Uyama, “Simple X-ray dark- and bright-field imaging using achromatic Laue optics,” Jpn. J. Appl. Phys. 41(2), 1016 (2002).
[Crossref]

Arai, Y.

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

Arfelli, F.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Beck, A.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[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]

Brankov, J. G.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Bravin, A.

S. Gasilov, A. Mittone, E. Brun, A. Bravin, S. Grandl, A. Mirone, and P. Coan, “Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach,” Opt. Express 22(5), 5216–5227 (2014).
[Crossref] [PubMed]

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

P. Coan, J. Mollenhauer, A. Wagner, C. Muehleman, and A. Bravin, “Analyzer-based imaging technique in tomography of cartilage and metal implants: a study at the ESRF,” Eur. J. Radiol. 68(3Suppl), S41–S48 (2008).
[Crossref] [PubMed]

Brun, E.

S. Gasilov, A. Mittone, E. Brun, A. Bravin, S. Grandl, A. Mirone, and P. Coan, “Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach,” Opt. Express 22(5), 5216–5227 (2014).
[Crossref] [PubMed]

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

Byer, R. L.

Candes, E. J.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Chapman, D.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Chapman, L. D.

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45(4), 933–946 (2000).
[Crossref] [PubMed]

Chen, G. H.

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Coan, P.

S. Gasilov, A. Mittone, E. Brun, A. Bravin, S. Grandl, A. Mirone, and P. Coan, “Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach,” Opt. Express 22(5), 5216–5227 (2014).
[Crossref] [PubMed]

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

P. Coan, J. Mollenhauer, A. Wagner, C. Muehleman, and A. Bravin, “Analyzer-based imaging technique in tomography of cartilage and metal implants: a study at the ESRF,” Eur. J. Radiol. 68(3Suppl), S41–S48 (2008).
[Crossref] [PubMed]

Diemoz, P. C.

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

Dilmanian, F. A.

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45(4), 933–946 (2000).
[Crossref] [PubMed]

Do, S.

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal analyser-based X-ray phase contrast imaging in the dark field: implementation and evaluation using excised tissue specimens,” Eur. Radiol. 24(2), 423–433 (2014).
[Crossref] [PubMed]

Endo, T.

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

Faris, G. W.

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[Crossref]

Galatsanos, N. P.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Gasilov, S.

S. Gasilov, A. Mittone, E. Brun, A. Bravin, S. Grandl, A. Mirone, and P. Coan, “Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach,” Opt. Express 22(5), 5216–5227 (2014).
[Crossref] [PubMed]

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

Gmür, N.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Grandl, S.

Gupta, R.

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal analyser-based X-ray phase contrast imaging in the dark field: implementation and evaluation using excised tissue specimens,” Eur. Radiol. 24(2), 423–433 (2014).
[Crossref] [PubMed]

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray talbot interferometry,” Jpn. J. Appl. Phys. 42(2), L866–L868 (2003).
[Crossref]

Hashimoto, E.

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

T. Yuasa, A. Maksimenko, E. Hashimoto, H. Sugiyama, K. Hyodo, T. Akatsuka, and M. Ando, “Hard-x-ray region tomographic reconstruction of the refractive-index gradient vector field: Imaging principles and comparisons with diffraction-enhanced-imaging-based computed tomography,” Opt. Lett. 31(12), 1818–1820 (2006).
[Crossref] [PubMed]

Hirano, K.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[Crossref] [PubMed]

Hooper, S. B.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[Crossref] [PubMed]

Huang, Z.

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

Huo, Q.

N. Sunaguchi, T. Yuasa, Q. Huo, and M. Ando, “Convolution reconstruction algorithm for refraction-contrast computed tomography using a Laue-case analyzer for dark-field imaging,” Opt. Lett. 36(3), 391–393 (2011).
[Crossref] [PubMed]

N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “X-ray refraction-contrast computed tomography images using dark field imaging optics,” Appl. Phys. Lett. 97(15), 153701 (2010).
[Crossref]

Hyodo, K.

Ichihara, S.

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal analyser-based X-ray phase contrast imaging in the dark field: implementation and evaluation using excised tissue specimens,” Eur. Radiol. 24(2), 423–433 (2014).
[Crossref] [PubMed]

N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “X-ray refraction-contrast computed tomography images using dark field imaging optics,” Appl. Phys. Lett. 97(15), 153701 (2010).
[Crossref]

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

Itai, Y.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[Crossref] [PubMed]

Johnston, R. E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray talbot interferometry,” Jpn. J. Appl. Phys. 42(2), L866–L868 (2003).
[Crossref]

Keyrilainen, J.

P. Suortti, J. Keyrilainen, and W. Thomlinson, “Analyser-based x-ray imaging for biomedical research,” J. Phys. D Appl. Phys. 46(49), 494002 (2013).
[Crossref]

Kitchen, M. J.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[Crossref] [PubMed]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[Crossref]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray talbot interferometry,” Jpn. J. Appl. Phys. 42(2), L866–L868 (2003).
[Crossref]

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[Crossref]

Leng, S.

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Lewis, R. A.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[Crossref] [PubMed]

Liebhardt, S.

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

Louissaint, A.

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal analyser-based X-ray phase contrast imaging in the dark field: implementation and evaluation using excised tissue specimens,” Eur. Radiol. 24(2), 423–433 (2014).
[Crossref] [PubMed]

Maksimenko, A.

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

T. Yuasa, A. Maksimenko, E. Hashimoto, H. Sugiyama, K. Hyodo, T. Akatsuka, and M. Ando, “Hard-x-ray region tomographic reconstruction of the refractive-index gradient vector field: Imaging principles and comparisons with diffraction-enhanced-imaging-based computed tomography,” Opt. Lett. 31(12), 1818–1820 (2006).
[Crossref] [PubMed]

A. Maksimenko, M. Ando, H. Sugiyama, and T. Yuasa, “Computed tomographic reconstruction based on x-ray refraction contrast,” Appl. Phys. Lett. 86(12), 124105 (2005).
[Crossref]

M. Ando, A. Maksimenko, H. Sugiyama, W. Pattanasiriwissawa, K. Hyodo, and C. Uyama, “Simple X-ray dark- and bright-field imaging using achromatic Laue optics,” Jpn. J. Appl. Phys. 41(2), 1016 (2002).
[Crossref]

Menk, R.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Miao, J.

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

Mirone, A.

Mittone, A.

S. Gasilov, A. Mittone, E. Brun, A. Bravin, S. Grandl, A. Mirone, and P. Coan, “Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach,” Opt. Express 22(5), 5216–5227 (2014).
[Crossref] [PubMed]

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

Mollenhauer, J.

P. Coan, J. Mollenhauer, A. Wagner, C. Muehleman, and A. Bravin, “Analyzer-based imaging technique in tomography of cartilage and metal implants: a study at the ESRF,” Eur. J. Radiol. 68(3Suppl), S41–S48 (2008).
[Crossref] [PubMed]

Momose, A.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray talbot interferometry,” Jpn. J. Appl. Phys. 42(2), L866–L868 (2003).
[Crossref]

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[Crossref] [PubMed]

Mori, K.

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

Muehleman, C.

P. Coan, J. Mollenhauer, A. Wagner, C. Muehleman, and A. Bravin, “Analyzer-based imaging technique in tomography of cartilage and metal implants: a study at the ESRF,” Eur. J. Radiol. 68(3Suppl), S41–S48 (2008).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Ohbayashi, C.

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

Oltulu, O.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Orion, I.

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45(4), 933–946 (2000).
[Crossref] [PubMed]

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[Crossref]

Pattanasiriwissawa, W.

M. Ando, A. Maksimenko, H. Sugiyama, W. Pattanasiriwissawa, K. Hyodo, and C. Uyama, “Simple X-ray dark- and bright-field imaging using achromatic Laue optics,” Jpn. J. Appl. Phys. 41(2), 1016 (2002).
[Crossref]

Pavlov, K. M.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[Crossref] [PubMed]

Pisano, E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Ren, B.

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45(4), 933–946 (2000).
[Crossref] [PubMed]

Romberg, J.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1–4), 259–268 (1992).
[Crossref]

Sayers, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[Crossref]

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]

Siew, M. L. L.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[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]

Siu, K. K. W.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[Crossref] [PubMed]

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[Crossref]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486 (1995).
[Crossref]

Sugiyama, H.

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

T. Yuasa, A. Maksimenko, E. Hashimoto, H. Sugiyama, K. Hyodo, T. Akatsuka, and M. Ando, “Hard-x-ray region tomographic reconstruction of the refractive-index gradient vector field: Imaging principles and comparisons with diffraction-enhanced-imaging-based computed tomography,” Opt. Lett. 31(12), 1818–1820 (2006).
[Crossref] [PubMed]

A. Maksimenko, M. Ando, H. Sugiyama, and T. Yuasa, “Computed tomographic reconstruction based on x-ray refraction contrast,” Appl. Phys. Lett. 86(12), 124105 (2005).
[Crossref]

M. Ando, A. Maksimenko, H. Sugiyama, W. Pattanasiriwissawa, K. Hyodo, and C. Uyama, “Simple X-ray dark- and bright-field imaging using achromatic Laue optics,” Jpn. J. Appl. Phys. 41(2), 1016 (2002).
[Crossref]

Sunaguchi, N.

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal analyser-based X-ray phase contrast imaging in the dark field: implementation and evaluation using excised tissue specimens,” Eur. Radiol. 24(2), 423–433 (2014).
[Crossref] [PubMed]

N. Sunaguchi, T. Yuasa, Q. Huo, and M. Ando, “Convolution reconstruction algorithm for refraction-contrast computed tomography using a Laue-case analyzer for dark-field imaging,” Opt. Lett. 36(3), 391–393 (2011).
[Crossref] [PubMed]

N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “X-ray refraction-contrast computed tomography images using dark field imaging optics,” Appl. Phys. Lett. 97(15), 153701 (2010).
[Crossref]

Sung, Y.

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal analyser-based X-ray phase contrast imaging in the dark field: implementation and evaluation using excised tissue specimens,” Eur. Radiol. 24(2), 423–433 (2014).
[Crossref] [PubMed]

Suortti, P.

P. Suortti, J. Keyrilainen, and W. Thomlinson, “Analyser-based x-ray imaging for biomedical research,” J. Phys. D Appl. Phys. 46(49), 494002 (2013).
[Crossref]

Suzuki, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray talbot interferometry,” Jpn. J. Appl. Phys. 42(2), L866–L868 (2003).
[Crossref]

Sztrókay, A.

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

Takai, K.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray talbot interferometry,” Jpn. J. Appl. Phys. 42(2), L866–L868 (2003).
[Crossref]

Takeda, T.

A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med. 2(4), 473–475 (1996).
[Crossref] [PubMed]

Tang, J.

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Tao, T.

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
[Crossref]

Teboulle, M.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

Thomlinson, W.

P. Suortti, J. Keyrilainen, and W. Thomlinson, “Analyser-based x-ray imaging for biomedical research,” J. Phys. D Appl. Phys. 46(49), 494002 (2013).
[Crossref]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Thomlinson, W. C.

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45(4), 933–946 (2000).
[Crossref] [PubMed]

Uesugi, K.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[Crossref] [PubMed]

Uyama, C.

M. Ando, A. Maksimenko, H. Sugiyama, W. Pattanasiriwissawa, K. Hyodo, and C. Uyama, “Simple X-ray dark- and bright-field imaging using achromatic Laue optics,” Jpn. J. Appl. Phys. 41(2), 1016 (2002).
[Crossref]

Vine, D. J.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[Crossref] [PubMed]

Wagner, A.

P. Coan, J. Mollenhauer, A. Wagner, C. Muehleman, and A. Bravin, “Analyzer-based imaging technique in tomography of cartilage and metal implants: a study at the ESRF,” Eur. J. Radiol. 68(3Suppl), S41–S48 (2008).
[Crossref] [PubMed]

Wallace, M. J.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[Crossref] [PubMed]

Wang, Z.

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]

Washburn, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

Wernick, M. N.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Wirjadi, O.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Wu, X. Y.

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45(4), 933–946 (2000).
[Crossref] [PubMed]

Wu, Y.

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal analyser-based X-ray phase contrast imaging in the dark field: implementation and evaluation using excised tissue specimens,” Eur. Radiol. 24(2), 423–433 (2014).
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Yagi, N.

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
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Yamasaki, K.

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

Yang, Y.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

Yuasa, T.

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal analyser-based X-ray phase contrast imaging in the dark field: implementation and evaluation using excised tissue specimens,” Eur. Radiol. 24(2), 423–433 (2014).
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N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “X-ray refraction-contrast computed tomography images using dark field imaging optics,” Appl. Phys. Lett. 97(15), 153701 (2010).
[Crossref]

S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

T. Yuasa, A. Maksimenko, E. Hashimoto, H. Sugiyama, K. Hyodo, T. Akatsuka, and M. Ando, “Hard-x-ray region tomographic reconstruction of the refractive-index gradient vector field: Imaging principles and comparisons with diffraction-enhanced-imaging-based computed tomography,” Opt. Lett. 31(12), 1818–1820 (2006).
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A. Maksimenko, M. Ando, H. Sugiyama, and T. Yuasa, “Computed tomographic reconstruction based on x-ray refraction contrast,” Appl. Phys. Lett. 86(12), 124105 (2005).
[Crossref]

Zhao, Y.

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
[Crossref] [PubMed]

Zhong, Z.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45(4), 933–946 (2000).
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D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
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Appl. Opt. (1)

Appl. Phys. Lett. (2)

A. Maksimenko, M. Ando, H. Sugiyama, and T. Yuasa, “Computed tomographic reconstruction based on x-ray refraction contrast,” Appl. Phys. Lett. 86(12), 124105 (2005).
[Crossref]

N. Sunaguchi, T. Yuasa, Q. Huo, S. Ichihara, and M. Ando, “X-ray refraction-contrast computed tomography images using dark field imaging optics,” Appl. Phys. Lett. 97(15), 153701 (2010).
[Crossref]

Eur. J. Radiol. (2)

M. J. Kitchen, K. M. Pavlov, S. B. Hooper, D. J. Vine, K. K. W. Siu, M. J. Wallace, M. L. L. Siew, N. Yagi, K. Uesugi, and R. A. Lewis, “Simultaneous acquisition of dual analyser-based phase contrast X-ray images for small animal imaging,” Eur. J. Radiol. 68(3Suppl), S49–S53 (2008).
[Crossref] [PubMed]

P. Coan, J. Mollenhauer, A. Wagner, C. Muehleman, and A. Bravin, “Analyzer-based imaging technique in tomography of cartilage and metal implants: a study at the ESRF,” Eur. J. Radiol. 68(3Suppl), S41–S48 (2008).
[Crossref] [PubMed]

Eur. Radiol. (1)

M. Ando, N. Sunaguchi, Y. Wu, S. Do, Y. Sung, A. Louissaint, T. Yuasa, S. Ichihara, and R. Gupta, “Crystal analyser-based X-ray phase contrast imaging in the dark field: implementation and evaluation using excised tissue specimens,” Eur. Radiol. 24(2), 423–433 (2014).
[Crossref] [PubMed]

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).
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IEEE Trans. Inf. Theory (1)

E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006).
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J. Phys. D Appl. Phys. (1)

P. Suortti, J. Keyrilainen, and W. Thomlinson, “Analyser-based x-ray imaging for biomedical research,” J. Phys. D Appl. Phys. 46(49), 494002 (2013).
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A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray talbot interferometry,” Jpn. J. Appl. Phys. 42(2), L866–L868 (2003).
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M. Ando, A. Maksimenko, H. Sugiyama, W. Pattanasiriwissawa, K. Hyodo, and C. Uyama, “Simple X-ray dark- and bright-field imaging using achromatic Laue optics,” Jpn. J. Appl. Phys. 41(2), 1016 (2002).
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G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
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Opt. Express (1)

Opt. Lett. (2)

Phys. Med. Biol. (3)

F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, and W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45(4), 933–946 (2000).
[Crossref] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol. 48(23), 3875–3895 (2003).
[Crossref] [PubMed]

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42(11), 2015–2025 (1997).
[Crossref] [PubMed]

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[Crossref]

Proc. Natl. Acad. Sci. U.S.A. (1)

Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrókay, P. C. Diemoz, S. Liebhardt, A. Mittone, S. Gasilov, J. Miao, and A. Bravin, “High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers,” Proc. Natl. Acad. Sci. U.S.A. 109(45), 18290–18294 (2012).
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S. Ichihara, M. Ando, E. Hashimoto, A. Maksimenko, H. Sugiyama, C. Ohbayashi, T. Yuasa, K. Yamasaki, Y. Arai, K. Mori, and T. Endo, “3-D reconstruction of high-grade ductal carcinoma in situ of the breast with casting type calcifications using refraction-based X-ray CT,” Virchows Arch. 452(1), 41–47 (2008).
[Crossref] [PubMed]

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Figures (12)

Fig. 1
Fig. 1 Examples of DPC-CT images of human coronary artery obtained using dark field imaging optics: (a) the phase image showing a map of δ(r) (δ-map), (b) differential phase image showing δ(r) x (i.e., the gδ-map with respect to x), and (c) δ(r) y (i.e., the gδ-map with respect to y).
Fig. 2
Fig. 2 Flowchart of the proposed two-step reconstruction algorithm.
Fig. 3
Fig. 3 Numerical phantom.
Fig. 4
Fig. 4 Flowcharts of the one-step reconstruction with (a) FBP and (b) ART + TV.
Fig. 5
Fig. 5 Convergence of the proposed reconstruction method: RMSE as a function number of iterations for different number of differential projections.
Fig. 6
Fig. 6 Tomographic images reconstructed using FBP, δ-ART + TV, and gδ-ART + TV algorithms for different number of projections.
Fig. 7
Fig. 7 Zoomed regions that correspond to the regions indicated by a square in Fig. 6.
Fig. 8
Fig. 8 Dependence of structural similarity on the number of projections.
Fig. 9
Fig. 9 Dependence of root mean square error on the number of projections.
Fig. 10
Fig. 10 Schematic of DPC-CT system with a dark field imaging optics.
Fig. 11
Fig. 11 Tomographic images reconstructed by FBP, δ-ART + TV, and the gδ-ART + TV for three different number of projections.
Fig. 12
Fig. 12 Zoomed regions which correspond to the regions indicated by a square in Fig. 11.

Equations (8)

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| δ( r l ) | exp[ iϕ( r l ) ]dq=iΔα( p )exp( iθ ) ,
{ | δ( r l ) | cosϕ( r l )dq=Δα( p )sinθ | δ( r l ) | sinϕ( r l )dq=Δα( p )cosθ   .
{ j=1 N w ij ξ j = h i i=1,2,,M j=1 N w ij η j = v i i=1,2,,M   ,
{ min ξ Wξh 2 +λTV( ξ ) min η Wηv 2 +λTV( η )     ,
{ δ x =ξ δ y =η     .
( 2 x 2 + 2 y 2 )δ= ξ x + η y  .
d ds [ δ( r )t( r ) ]=δ( r ) ,
{ dδ ds =δt dα ds =δv ,

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