Abstract

Differential phase contrast imaging using grating interferometer is a promising alternative to conventional X-ray radiographic methods. It provides the absorption, differential phase and scattering information of the underlying sample simultaneously. Phase retrieval from the differential phase signal is an essential problem for quantitative analysis in medical imaging. In this paper, we formalize the phase retrieval as a regularized inverse problem, and propose a novel discretization scheme for the derivative operator based on B-spline calculus. The inverse problem is then solved by a constrained regularized weighted-norm algorithm (CRWN) which adopts the properties of B-spline and ensures a fast implementation. The method is evaluated with a tomographic dataset and differential phase contrast mammography data. We demonstrate that the proposed method is able to produce phase image with enhanced and higher soft tissue contrast compared to conventional absorption-based approach, which can potentially provide useful information to mammographic investigations.

© 2015 Optical Society of America

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  1. C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
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    [Crossref]
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    [Crossref]
  4. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,”, Nature Mater. 7134–137 (2008).
    [Crossref]
  5. M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
    [Crossref] [PubMed]
  6. T. Thüring, R. Guggenberger, H. Alkadhi, M. Vich, Z. Wang, C. David, and M. Stampanoni, “Human hand radiography using X-ray differential phase contrast combined with dark-field imaging,” Skeletal radiol. 42, 827–835 (2013).
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    [Crossref]
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    [Crossref] [PubMed]
  20. M. Nilchian, C. Vonesch, S. Lefkimmiatis, P. Modregger, M. Stampanoni, and M. Unser, “Constrained regularized reconstruction of X-ray DPCI tomograms with weighted-norm,” Opt. Express 31, 32340–32348 (2013).
    [Crossref]
  21. S. A. McDonald, F. Marone, C. Hintermueller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
    [Crossref] [PubMed]
  22. N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
    [Crossref]
  23. V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaing,” Rev. Sci. Instrum. 81, 073709 (2010).
    [Crossref]

2014 (2)

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

J. I. Sperl, D. Bequé, G. P. Kudielka, K. Mahdi, P. M. Edic, and C. Cozzini, “A Fourier-domain algorithm for total-variation regularized phase retrieval in differential X-ray phase contrast imaging,” Opt. Express 22(1), 450–462 (2014).
[Crossref] [PubMed]

2013 (7)

A. Kostenko, K. J. Batenburg, H. Suhonen, S. E. Offerman, and L. J. van Vliet, “Phase retrieval in in-line x-ray phase contrast imaging based on total variation minimization,” Opt. Express 21(1) 710–723 (2013).
[Crossref] [PubMed]

M. Nilchian, C. Vonesch, P. Modregger, M. Stampanoni, and M. Unser, “Fast iterative reconstruction of differential phase contrast X-ray tomograms,” Opt. Express 21(26), 5511–5528 (2013).
[Crossref] [PubMed]

M. Nilchian, C. Vonesch, S. Lefkimmiatis, P. Modregger, M. Stampanoni, and M. Unser, “Constrained regularized reconstruction of X-ray DPCI tomograms with weighted-norm,” Opt. Express 31, 32340–32348 (2013).
[Crossref]

T. Thüring, R. Guggenberger, H. Alkadhi, M. Vich, Z. Wang, C. David, and M. Stampanoni, “Human hand radiography using X-ray differential phase contrast combined with dark-field imaging,” Skeletal radiol. 42, 827–835 (2013).
[Crossref] [PubMed]

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23222–227 (2013).
[Crossref]

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, P. Bruyndonckx, A. Sasov, and F. Pfeiffer, “In-vivo dark-field and phase-contrast X-ray imaging,” Sci. Rep. 3, 3209 (2013).
[Crossref] [PubMed]

2011 (2)

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[Crossref] [PubMed]

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), 25545–25558 (2011).
[Crossref]

2010 (1)

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaing,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref]

2009 (1)

S. A. McDonald, F. Marone, C. Hintermueller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[Crossref] [PubMed]

2008 (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,”, Nature Mater. 7134–137 (2008).
[Crossref]

2007 (1)

2006 (1)

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

2004 (1)

R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys Med Biol. 49, 3573–3583 (2004).
[Crossref] [PubMed]

2003 (1)

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

2002 (1)

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

1996 (2)

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

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

Alkadhi, H.

T. Thüring, R. Guggenberger, H. Alkadhi, M. Vich, Z. Wang, C. David, and M. Stampanoni, “Human hand radiography using X-ray differential phase contrast combined with dark-field imaging,” Skeletal radiol. 42, 827–835 (2013).
[Crossref] [PubMed]

Auweter, S.

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Bamberg, F.

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Batenburg, K. J.

Bech, M.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, P. Bruyndonckx, A. Sasov, and F. Pfeiffer, “In-vivo dark-field and phase-contrast X-ray imaging,” Sci. Rep. 3, 3209 (2013).
[Crossref] [PubMed]

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,”, Nature Mater. 7134–137 (2008).
[Crossref]

Bequé, D.

Bohla, A.

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Brönnimann, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,”, Nature Mater. 7134–137 (2008).
[Crossref]

Bruyndonckx, P.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, P. Bruyndonckx, A. Sasov, and F. Pfeiffer, “In-vivo dark-field and phase-contrast X-ray imaging,” Sci. Rep. 3, 3209 (2013).
[Crossref] [PubMed]

Bunk, O.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,”, Nature Mater. 7134–137 (2008).
[Crossref]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “Two-directional approach for grating based differential phase contrast imaging using hard X-rays,” Opt. Express 15, 1175–1181 (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,” Nature Phys. 2, 258–261 (2006).
[Crossref]

Cozzini, C.

David, C.

T. Thüring, R. Guggenberger, H. Alkadhi, M. Vich, Z. Wang, C. David, and M. Stampanoni, “Human hand radiography using X-ray differential phase contrast combined with dark-field imaging,” Skeletal radiol. 42, 827–835 (2013).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[Crossref] [PubMed]

S. A. McDonald, F. Marone, C. Hintermueller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[Crossref] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,”, Nature Mater. 7134–137 (2008).
[Crossref]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “Two-directional approach for grating based differential phase contrast imaging using hard X-rays,” Opt. Express 15, 1175–1181 (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,” Nature Phys. 2, 258–261 (2006).
[Crossref]

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

Edic, P. M.

Eickelberg, O.

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,”, Nature Mater. 7134–137 (2008).
[Crossref]

Gao, D.

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

Grünzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,”, Nature Mater. 7134–137 (2008).
[Crossref]

Guggenberger, R.

T. Thüring, R. Guggenberger, H. Alkadhi, M. Vich, Z. Wang, C. David, and M. Stampanoni, “Human hand radiography using X-ray differential phase contrast combined with dark-field imaging,” Skeletal radiol. 42, 827–835 (2013).
[Crossref] [PubMed]

Gureyev, T.

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

Hamaishi, Y.

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

Hauser, N.

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[Crossref] [PubMed]

Hintermueller, C.

S. A. McDonald, F. Marone, C. Hintermueller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[Crossref] [PubMed]

Hirono, K.

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

Hohl, M. K.

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[Crossref] [PubMed]

Hoshino, Y.

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23222–227 (2013).
[Crossref]

Hostens, J.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, P. Bruyndonckx, A. Sasov, and F. Pfeiffer, “In-vivo dark-field and phase-contrast X-ray imaging,” Sci. Rep. 3, 3209 (2013).
[Crossref] [PubMed]

Itai, Y.

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

Kaufmann, R.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaing,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref]

Kawamoto, S.

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

Kido, K.

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23222–227 (2013).
[Crossref]

Kiyohara, J.

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23222–227 (2013).
[Crossref]

Koehler, T.

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

Kostenko, A.

Kottler, C.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaing,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “Two-directional approach for grating based differential phase contrast imaging using hard X-rays,” Opt. Express 15, 1175–1181 (2007).
[Crossref] [PubMed]

Koyama, I.

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

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,”, Nature Mater. 7134–137 (2008).
[Crossref]

Kubik-Huch, R. A.

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[Crossref] [PubMed]

Kudielka, G. P.

Lefkimmiatis, S.

M. Nilchian, C. Vonesch, S. Lefkimmiatis, P. Modregger, M. Stampanoni, and M. Unser, “Constrained regularized reconstruction of X-ray DPCI tomograms with weighted-norm,” Opt. Express 31, 32340–32348 (2013).
[Crossref]

Lewis, R. A.

R. A. Lewis, “Medical phase contrast x-ray imaging: current status and future prospects,” Phys Med Biol. 49, 3573–3583 (2004).
[Crossref] [PubMed]

Mahdi, K.

Makifuchi, C.

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23222–227 (2013).
[Crossref]

Marone, F.

S. A. McDonald, F. Marone, C. Hintermueller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[Crossref] [PubMed]

McDonald, S. A.

S. A. McDonald, F. Marone, C. Hintermueller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[Crossref] [PubMed]

Meinel, F. G.

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Mikuljan, G.

S. A. McDonald, F. Marone, C. Hintermueller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[Crossref] [PubMed]

Modregger, P.

Momose, A.

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23222–227 (2013).
[Crossref]

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

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

Nagashima, M.

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23222–227 (2013).
[Crossref]

Nagatsuka, S.

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23222–227 (2013).
[Crossref]

Niemann, B.

D. Rudolph, G. Schmal, and B. Niemann, “Amplitude and phase contrast in X-ray microscopy,” in Modern Microscopies, Techniques and Applications, A. G. Michette and P. Duke, eds. (Plenum Press, 1990).
[Crossref]

Nikolaou, K.

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Nilchian, M.

M. Nilchian, C. Vonesch, S. Lefkimmiatis, P. Modregger, M. Stampanoni, and M. Unser, “Constrained regularized reconstruction of X-ray DPCI tomograms with weighted-norm,” Opt. Express 31, 32340–32348 (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(26), 5511–5528 (2013).
[Crossref] [PubMed]

M. Nilchian and M. Unser, “Differential phase-contrast X-ray computed tomography: From model discretization to image reconstruction,” In Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium on, 90–93 (2012).

Nishino, S.

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23222–227 (2013).
[Crossref]

Nöhammer, B.

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

Offerman, S. E.

Pauwels, B.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, P. Bruyndonckx, A. Sasov, and F. Pfeiffer, “In-vivo dark-field and phase-contrast X-ray imaging,” Sci. Rep. 3, 3209 (2013).
[Crossref] [PubMed]

Pfeiffer, F.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, P. Bruyndonckx, A. Sasov, and F. Pfeiffer, “In-vivo dark-field and phase-contrast X-ray imaging,” Sci. Rep. 3, 3209 (2013).
[Crossref] [PubMed]

S. A. McDonald, F. Marone, C. Hintermueller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[Crossref] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,”, Nature Mater. 7134–137 (2008).
[Crossref]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “Two-directional approach for grating based differential phase contrast imaging using hard X-rays,” Opt. Express 15, 1175–1181 (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,” Nature Phys. 2, 258–261 (2006).
[Crossref]

Pfeiffer., F.

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Pinzer, B. R.

Pogany, A.

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

Reiser, M. F.

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Revol, V.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaing,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref]

Roessl, E.

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[Crossref] [PubMed]

Rudolph, D.

D. Rudolph, G. Schmal, and B. Niemann, “Amplitude and phase contrast in X-ray microscopy,” in Modern Microscopies, Techniques and Applications, A. G. Michette and P. Duke, eds. (Plenum Press, 1990).
[Crossref]

Sasov, A.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, P. Bruyndonckx, A. Sasov, and F. Pfeiffer, “In-vivo dark-field and phase-contrast X-ray imaging,” Sci. Rep. 3, 3209 (2013).
[Crossref] [PubMed]

Schleede, S.

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Schmal, G.

D. Rudolph, G. Schmal, and B. Niemann, “Amplitude and phase contrast in X-ray microscopy,” in Modern Microscopies, Techniques and Applications, A. G. Michette and P. Duke, eds. (Plenum Press, 1990).
[Crossref]

Singer, G.

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[Crossref] [PubMed]

Solak, H.

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

Sperl, J. I.

Stampanoni, M.

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

M. Nilchian, C. Vonesch, S. Lefkimmiatis, P. Modregger, M. Stampanoni, and M. Unser, “Constrained regularized reconstruction of X-ray DPCI tomograms with weighted-norm,” Opt. Express 31, 32340–32348 (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(26), 5511–5528 (2013).
[Crossref] [PubMed]

T. Thüring, R. Guggenberger, H. Alkadhi, M. Vich, Z. Wang, C. David, and M. Stampanoni, “Human hand radiography using X-ray differential phase contrast combined with dark-field imaging,” Skeletal radiol. 42, 827–835 (2013).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[Crossref] [PubMed]

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), 25545–25558 (2011).
[Crossref]

S. A. McDonald, F. Marone, C. Hintermueller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
[Crossref] [PubMed]

Stevenson, A.

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

Straumann, U.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaing,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref]

Suhonen, H.

Suzuki, Y.

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

Takai, K.

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

Takeda, T.

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

Tanaka, J.

J. Tanaka, M. Nagashima, K. Kido, Y. Hoshino, J. Kiyohara, C. Makifuchi, S. Nishino, S. Nagatsuka, and A. Momose, “Cadaveric and in vivo human joint imaging based on differential phase contrast by X-ray Talbot-Lau interferometry,” Z. Med. Phys. 23222–227 (2013).
[Crossref]

Tapfer, A.

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, P. Bruyndonckx, A. Sasov, and F. Pfeiffer, “In-vivo dark-field and phase-contrast X-ray imaging,” Sci. Rep. 3, 3209 (2013).
[Crossref] [PubMed]

Thüring, T.

T. Thüring, R. Guggenberger, H. Alkadhi, M. Vich, Z. Wang, C. David, and M. Stampanoni, “Human hand radiography using X-ray differential phase contrast combined with dark-field imaging,” Skeletal radiol. 42, 827–835 (2013).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[Crossref] [PubMed]

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), 25545–25558 (2011).
[Crossref]

Trippel, M.

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[Crossref] [PubMed]

Unser, M.

M. Nilchian, C. Vonesch, S. Lefkimmiatis, P. Modregger, M. Stampanoni, and M. Unser, “Constrained regularized reconstruction of X-ray DPCI tomograms with weighted-norm,” Opt. Express 31, 32340–32348 (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(26), 5511–5528 (2013).
[Crossref] [PubMed]

M. Nilchian and M. Unser, “Differential phase-contrast X-ray computed tomography: From model discretization to image reconstruction,” In Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium on, 90–93 (2012).

Urban, C.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaing,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref]

van Stevendaal, U.

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

van Vliet, L. J.

Velroyen, A.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, P. Bruyndonckx, A. Sasov, and F. Pfeiffer, “In-vivo dark-field and phase-contrast X-ray imaging,” Sci. Rep. 3, 3209 (2013).
[Crossref] [PubMed]

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Vich, M.

T. Thüring, R. Guggenberger, H. Alkadhi, M. Vich, Z. Wang, C. David, and M. Stampanoni, “Human hand radiography using X-ray differential phase contrast combined with dark-field imaging,” Skeletal radiol. 42, 827–835 (2013).
[Crossref] [PubMed]

Vonesch, C.

M. Nilchian, C. Vonesch, P. Modregger, M. Stampanoni, and M. Unser, “Fast iterative reconstruction of differential phase contrast X-ray tomograms,” Opt. Express 21(26), 5511–5528 (2013).
[Crossref] [PubMed]

M. Nilchian, C. Vonesch, S. Lefkimmiatis, P. Modregger, M. Stampanoni, and M. Unser, “Constrained regularized reconstruction of X-ray DPCI tomograms with weighted-norm,” Opt. Express 31, 32340–32348 (2013).
[Crossref]

Wang, Z.

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

T. Thüring, R. Guggenberger, H. Alkadhi, M. Vich, Z. Wang, C. David, and M. Stampanoni, “Human hand radiography using X-ray differential phase contrast combined with dark-field imaging,” Skeletal radiol. 42, 827–835 (2013).
[Crossref] [PubMed]

M. Stampanoni, Z. Wang, T. Thüring, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[Crossref] [PubMed]

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), 25545–25558 (2011).
[Crossref]

Weitkamp, T.

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

Wieberneit, N.

N. Hauser, Z. Wang, R. A. Kubik-Huch, M. Trippel, G. Singer, M. K. Hohl, E. Roessl, T. Koehler, U. van Stevendaal, N. Wieberneit, and M. Stampanoni, “A study on mastectomy samples to evaluate breast imaging quality and potential clinical relevance of differential phase contrast mammography,” Invest. Radiol. 49, 131–137 (2014).
[Crossref]

Wilkins, S.

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

Yaroshenko, A.

M. Bech, A. Tapfer, A. Velroyen, A. Yaroshenko, B. Pauwels, J. Hostens, P. Bruyndonckx, A. Sasov, and F. Pfeiffer, “In-vivo dark-field and phase-contrast X-ray imaging,” Sci. Rep. 3, 3209 (2013).
[Crossref] [PubMed]

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Yildirim, A. Ö.

A. Yaroshenko, F. G. Meinel, M. Bech, A. Tapfer, A. Velroyen, S. Schleede, S. Auweter, A. Bohla, A. Ö. Yildirim, K. Nikolaou, F. Bamberg, O. Eickelberg, M. F. Reiser, and F. Pfeiffer., “Pulmonary Emphysema diagnosis with a preclinical small-animal X-ray dark-field scatter-contrast scanner,” Radiology 269(2), 427–433 (2013).
[Crossref] [PubMed]

Ziegler, E.

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C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
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Figures (4)

Fig. 1
Fig. 1 Quantitative comparison on phase tomographic data. (a) The phase projection obtained by forward-projection on a phase tomographic dataset. The projection image was used as the ground-truth in this experiment. (b) The differential phase contrast image obtained by taking the one-dimension derivative from the ground-truth. (c) The retrieved phase using the proposed method. (d) The profile (red line in (a)) comparison between the retrieved phase and the ground-truth.
Fig. 2
Fig. 2 The phase retrieval results of the biopsy sample (High SNR case). (a) The absorption image; (b) the differential phase contrast image; (c) the phase image obtained by direct integration; (d) the iterative-retrieved phase image; (e) (f) are the profile comparisons of the horizontal (L1) and vertical (L2) lines in (a), respectively. The orange shadow represents the selected ROI as the signal while the light blue shadow is the selected ROI as the backgroud.
Fig. 3
Fig. 3 The phase retrieval results of the mastectomy breast sample (Low SNR case). (a) The absorption image; (b) the differential phase contrast image; (c) the phase image obtained by direct integration; (d) the phase image obtained by the proposed method. The images are showed in the best display window selected manually to reveal as many structures as possible.
Fig. 4
Fig. 4 The results of a selected ROI from the whole breast phase retrieval. (a) The absorption image; (b) the phase image obtained by the proposed method, (c) the phase image obtained by our former method proposed in. [15]. (d)–(e), the line profile comparisons of the lines indicated in (a).

Equations (16)

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φ ( x , y ) = 2 π d p 2 α ( x , y ) ,
α ( x , y ) = λ 2 π ϕ ( x , y ) x ,
φ ( x , y ) = g φ ( x , y ) x ,
φ ( x , y ) = g 0 x φ ( x , y ) d x .
φ ˜ ( x , y ) = φ ( x , y ) + n ( x , y ) = g ϕ ( x , y ) x + n ( x , y ) ,
J ( ϕ ) = D x ϕ φ l 2 2 + Ψ ( ϕ ) ,
Ψ ( ϕ ) = λ D y ϕ l 1
D x ϕ ( i , j ) = { ϕ ( i + 1 , j ) ϕ ( i , j ) if 1 i < N i , 0 if i = N i .
ϕ ( x ) = k c k β n ( x k ) ,
β n ( x ) = β n ( x 1 , x 2 ) = β n ( x 1 ) β n ( x 2 ) .
φ ( x ) = g x 1 φ ( x ) = g k c k x 1 β n ( x 1 k 1 ) β n ( x 2 k 2 ) .
φ = H c ,
[ H ] l , k = g x 1 β n ( l k ) .
c = argmin c 𝒞 { J ( c ) 1 2 H c g W 2 + λ 1 i { L c } i 1 + λ 2 c 2 } ,
f x 1 [ k 1 , k 2 ] = ( ( h 1 [ . , k 2 ] * c [ . , k 2 ] ) [ k 1 , . ] * b 2 [ k 1 , . ] ) [ k 1 , k 2 ] f x 2 [ k 1 , k 2 ] = ( ( h 2 [ k 1 , ] * c [ k 1 , ] ) [ , k 2 ] * b 1 [ , k 2 ] ) [ k 1 , k 2 ]
C = I ¯ s I ¯ b σ b ,

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