Abstract

In this paper, a novel method was developed to improve the radiation dose efficiency, viz., contrast to noise ratio normalized by dose (CNRD), of the grating-based X-ray differential phase contrast (DPC) imaging system that is integrated with an energy-resolving photon counting detector. The method exploits the low-dimensionality of the spatial-spectral DPC image matrix acquired from different energy windows. A low rank approximation of the spatial-spectral image matrix was developed to reduce image noise while retaining the DPC signal accuracy for every energy window. Numerical simulations and experimental phantom studies have been performed to validate the proposed method by showing noise reduction and CNRD improvement for each energy window.

© 2016 Optical Society of America

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  1. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. Part 2 42(7B), 866–868 (2003).
    [Crossref]
  2. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12(16), 6296–6304 (2005).
    [Crossref]
  3. 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]
  4. D. Stutman, T. Beck, J. Carrino, and C. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Bio. 56(17), 5697–5720 (2011).
    [Crossref]
  5. J. Herzen, M. Willner, A. Fingerle, P. Noël, T. Köhler, E. Drecoll, E. 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]
  6. K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41(1), 011903 (2014).
    [Crossref] [PubMed]
  7. N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
    [Crossref]
  8. Y. Ge, K. Li, J. Garrett, and G-H. Chen, “Grating based x-ray differential phase contrast imaging without mechanical phase stepping,” Opt. Express 22(12), 14246–14252 (2014).
    [Crossref] [PubMed]
  9. J. Garrett, Y. Ge, K. Li, and G-H. Chen, “Anatomical background noise power spectrum in differential phase contrast and dark field contrast mammograms,” Med. Phys. 41(12), 120701 (2014).
    [Crossref] [PubMed]
  10. T. Thuering, W. Barber, Y. Seo, F. Alhassen, J. Iwanczyk, and M. Stampanoni, “Energy resolved X-ray grating interferometry,” Appl. Phys. Lett. 102(19), 191113 (2013).
    [Crossref]
  11. Y. Ge, K. Li, and G-H. Chen, “Cramér-Rao lower bound in differential phase contrast imaging and its application in the optimization of data acquisition systems,” Proc. SPIE 9033, 90330F (2014).
    [Crossref]
  12. M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, Joachim Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
    [Crossref] [PubMed]
  13. T. Thuering and M. Stampanoni, “Performance and optimization of X-ray grating interferometry,” Phil. Trans. R. Soc. A 372(2010), 20130027 (2014).
    [Crossref] [PubMed]
  14. G. Pelzer, T. Weber, G. Anton, R. Ballabriga, F. Bayer, M. Campbell, T. Gabor, W. Haas, F. Horn, X. Llopart, and N. Michel, “Grating-based x-ray phase-contrast imaging with a multi energy-channel photon-counting pixel detector,” Opt. Express 21(22), 25677–25684 (2013).
    [Crossref] [PubMed]
  15. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, CH. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
    [Crossref] [PubMed]
  16. V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010).
    [Crossref] [PubMed]
  17. T. Köhler, K. Engel, and E. Roessl, “Noise properties of grating-based x-ray phase contrast computed tomography,” Med. Phys. 38, S106–S116 (2011).
    [Crossref] [PubMed]
  18. R. Raupach and T.G. Flohr, “Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Bio. 56, 2219–2244 (2011).
    [Crossref]
  19. G-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys. 38, 584–588 (2011).
    [Crossref] [PubMed]
  20. T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38(7), 4133–4140 (2011).
    [Crossref] [PubMed]
  21. K. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in X-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A 648, S202–S207 (2011).
    [Crossref]
  22. R. Raupach and T.G. Flohr, “Performance evaluation of x-ray differential phase contrast computed tomography (PCT) with respect to medical imaging,” Med. Phys. 39(8), 4761–4774 (2012).
    [Crossref] [PubMed]
  23. G-H. Chen and Y. Li, “Synchronized multiartifact reduction with tomographic reconstruction (SMART-RECON): A statistical model based iterative image reconstruction method to eliminate limited-view artifacts and to mitigate the temporal-average artifacts in time-resolved CT,” Med. Phys. 42(8), 4698–4707 (2015).
    [Crossref] [PubMed]
  24. G. Strang, Introduction to linear algebra, (Wellesley-Cambridge Press, 1993).
  25. R. Zhang, L. Zhang, Z. Chen, W. Peng, and R. Li, “Sensitivity of a non-interferometric grating-based x-ray imaging system,” Phys. Med. Bio. 59(7), 1573–1588 (2014).
    [Crossref]

2015 (1)

G-H. Chen and Y. Li, “Synchronized multiartifact reduction with tomographic reconstruction (SMART-RECON): A statistical model based iterative image reconstruction method to eliminate limited-view artifacts and to mitigate the temporal-average artifacts in time-resolved CT,” Med. Phys. 42(8), 4698–4707 (2015).
[Crossref] [PubMed]

2014 (8)

R. Zhang, L. Zhang, Z. Chen, W. Peng, and R. Li, “Sensitivity of a non-interferometric grating-based x-ray imaging system,” Phys. Med. Bio. 59(7), 1573–1588 (2014).
[Crossref]

J. Garrett, Y. Ge, K. Li, and G-H. Chen, “Anatomical background noise power spectrum in differential phase contrast and dark field contrast mammograms,” Med. Phys. 41(12), 120701 (2014).
[Crossref] [PubMed]

J. Herzen, M. Willner, A. Fingerle, P. Noël, T. Köhler, E. Drecoll, E. 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]

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41(1), 011903 (2014).
[Crossref] [PubMed]

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

Y. Ge, K. Li, and G-H. Chen, “Cramér-Rao lower bound in differential phase contrast imaging and its application in the optimization of data acquisition systems,” Proc. SPIE 9033, 90330F (2014).
[Crossref]

T. Thuering and M. Stampanoni, “Performance and optimization of X-ray grating interferometry,” Phil. Trans. R. Soc. A 372(2010), 20130027 (2014).
[Crossref] [PubMed]

Y. Ge, K. Li, J. Garrett, and G-H. Chen, “Grating based x-ray differential phase contrast imaging without mechanical phase stepping,” Opt. Express 22(12), 14246–14252 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (1)

R. Raupach and T.G. Flohr, “Performance evaluation of x-ray differential phase contrast computed tomography (PCT) with respect to medical imaging,” Med. Phys. 39(8), 4761–4774 (2012).
[Crossref] [PubMed]

2011 (6)

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

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

G-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys. 38, 584–588 (2011).
[Crossref] [PubMed]

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38(7), 4133–4140 (2011).
[Crossref] [PubMed]

K. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in X-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A 648, S202–S207 (2011).
[Crossref]

D. Stutman, T. Beck, J. Carrino, and C. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Bio. 56(17), 5697–5720 (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 imaging,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref] [PubMed]

2008 (2)

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, Joachim Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[Crossref] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, CH. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[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]

2005 (1)

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12(16), 6296–6304 (2005).
[Crossref]

2003 (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. Part 2 42(7B), 866–868 (2003).
[Crossref]

Alhassen, F.

T. Thuering, W. Barber, Y. Seo, F. Alhassen, J. Iwanczyk, and M. Stampanoni, “Energy resolved X-ray grating interferometry,” Appl. Phys. Lett. 102(19), 191113 (2013).
[Crossref]

Anton, G.

Ballabriga, R.

Barber, W.

T. Thuering, W. Barber, Y. Seo, F. Alhassen, J. Iwanczyk, and M. Stampanoni, “Energy resolved X-ray grating interferometry,” Appl. Phys. Lett. 102(19), 191113 (2013).
[Crossref]

Bartl, P.

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38(7), 4133–4140 (2011).
[Crossref] [PubMed]

Baumann, Joachim

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, Joachim Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[Crossref] [PubMed]

Bayer, F.

Bech, M.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, CH. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Beck, T.

D. Stutman, T. Beck, J. Carrino, and C. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Bio. 56(17), 5697–5720 (2011).
[Crossref]

Bevins, N.

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41(1), 011903 (2014).
[Crossref] [PubMed]

G-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys. 38, 584–588 (2011).
[Crossref] [PubMed]

Bingham, C.

D. Stutman, T. Beck, J. Carrino, and C. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Bio. 56(17), 5697–5720 (2011).
[Crossref]

Brönnimann, CH.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, CH. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Bunk, O.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, CH. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, Joachim Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[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]

Campbell, M.

Carrino, J.

D. Stutman, T. Beck, J. Carrino, and C. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Bio. 56(17), 5697–5720 (2011).
[Crossref]

Chen, G-H.

G-H. Chen and Y. Li, “Synchronized multiartifact reduction with tomographic reconstruction (SMART-RECON): A statistical model based iterative image reconstruction method to eliminate limited-view artifacts and to mitigate the temporal-average artifacts in time-resolved CT,” Med. Phys. 42(8), 4698–4707 (2015).
[Crossref] [PubMed]

J. Garrett, Y. Ge, K. Li, and G-H. Chen, “Anatomical background noise power spectrum in differential phase contrast and dark field contrast mammograms,” Med. Phys. 41(12), 120701 (2014).
[Crossref] [PubMed]

Y. Ge, K. Li, and G-H. Chen, “Cramér-Rao lower bound in differential phase contrast imaging and its application in the optimization of data acquisition systems,” Proc. SPIE 9033, 90330F (2014).
[Crossref]

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41(1), 011903 (2014).
[Crossref] [PubMed]

Y. Ge, K. Li, J. Garrett, and G-H. Chen, “Grating based x-ray differential phase contrast imaging without mechanical phase stepping,” Opt. Express 22(12), 14246–14252 (2014).
[Crossref] [PubMed]

G-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys. 38, 584–588 (2011).
[Crossref] [PubMed]

Chen, Z.

R. Zhang, L. Zhang, Z. Chen, W. Peng, and R. Li, “Sensitivity of a non-interferometric grating-based x-ray imaging system,” Phys. Med. Bio. 59(7), 1573–1588 (2014).
[Crossref]

Cloetens, P.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12(16), 6296–6304 (2005).
[Crossref]

David, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, Joachim Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[Crossref] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, CH. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[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]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12(16), 6296–6304 (2005).
[Crossref]

Diaz, A.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12(16), 6296–6304 (2005).
[Crossref]

Drecoll, E.

J. Herzen, M. Willner, A. Fingerle, P. Noël, T. Köhler, E. Drecoll, E. 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]

Durst, J.

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38(7), 4133–4140 (2011).
[Crossref] [PubMed]

Eikenberry, E.F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, CH. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Engel, K.

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

K. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in X-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A 648, S202–S207 (2011).
[Crossref]

Engelhardt, M.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, Joachim Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[Crossref] [PubMed]

Fingerle, A.

J. Herzen, M. Willner, A. Fingerle, P. Noël, T. Köhler, E. Drecoll, E. 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, “Performance evaluation of x-ray differential phase contrast computed tomography (PCT) with respect to medical imaging,” Med. Phys. 39(8), 4761–4774 (2012).
[Crossref] [PubMed]

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

Gabor, T.

Garrett, J.

Y. Ge, K. Li, J. Garrett, and G-H. Chen, “Grating based x-ray differential phase contrast imaging without mechanical phase stepping,” Opt. Express 22(12), 14246–14252 (2014).
[Crossref] [PubMed]

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41(1), 011903 (2014).
[Crossref] [PubMed]

J. Garrett, Y. Ge, K. Li, and G-H. Chen, “Anatomical background noise power spectrum in differential phase contrast and dark field contrast mammograms,” Med. Phys. 41(12), 120701 (2014).
[Crossref] [PubMed]

Ge, Y.

J. Garrett, Y. Ge, K. Li, and G-H. Chen, “Anatomical background noise power spectrum in differential phase contrast and dark field contrast mammograms,” Med. Phys. 41(12), 120701 (2014).
[Crossref] [PubMed]

Y. Ge, K. Li, and G-H. Chen, “Cramér-Rao lower bound in differential phase contrast imaging and its application in the optimization of data acquisition systems,” Proc. SPIE 9033, 90330F (2014).
[Crossref]

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41(1), 011903 (2014).
[Crossref] [PubMed]

Y. Ge, K. Li, J. Garrett, and G-H. Chen, “Grating based x-ray differential phase contrast imaging without mechanical phase stepping,” Opt. Express 22(12), 14246–14252 (2014).
[Crossref] [PubMed]

Geller, D.

K. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in X-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A 648, S202–S207 (2011).
[Crossref]

Grünzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, CH. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Haas, W.

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. Part 2 42(7B), 866–868 (2003).
[Crossref]

Hauser, N.

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

Herzen, J.

J. Herzen, M. Willner, A. Fingerle, P. Noël, T. Köhler, E. Drecoll, E. 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]

Hohl, M.

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

Horn, F.

Iwanczyk, J.

T. Thuering, W. Barber, Y. Seo, F. Alhassen, J. Iwanczyk, and M. Stampanoni, “Energy resolved X-ray grating interferometry,” Appl. Phys. Lett. 102(19), 191113 (2013).
[Crossref]

Kaufmann, R.

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

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. Part 2 42(7B), 866–868 (2003).
[Crossref]

Köhler, T.

J. Herzen, M. Willner, A. Fingerle, P. Noël, T. Köhler, E. Drecoll, E. 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]

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

K. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in X-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A 648, S202–S207 (2011).
[Crossref]

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

Kottler, C.

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

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, Joachim Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[Crossref] [PubMed]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. Part 2 42(7B), 866–868 (2003).
[Crossref]

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, CH. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

Kubik-Huch, R.

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

Li, K.

Y. Ge, K. Li, J. Garrett, and G-H. Chen, “Grating based x-ray differential phase contrast imaging without mechanical phase stepping,” Opt. Express 22(12), 14246–14252 (2014).
[Crossref] [PubMed]

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41(1), 011903 (2014).
[Crossref] [PubMed]

Y. Ge, K. Li, and G-H. Chen, “Cramér-Rao lower bound in differential phase contrast imaging and its application in the optimization of data acquisition systems,” Proc. SPIE 9033, 90330F (2014).
[Crossref]

J. Garrett, Y. Ge, K. Li, and G-H. Chen, “Anatomical background noise power spectrum in differential phase contrast and dark field contrast mammograms,” Med. Phys. 41(12), 120701 (2014).
[Crossref] [PubMed]

G-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys. 38, 584–588 (2011).
[Crossref] [PubMed]

Li, R.

R. Zhang, L. Zhang, Z. Chen, W. Peng, and R. Li, “Sensitivity of a non-interferometric grating-based x-ray imaging system,” Phys. Med. Bio. 59(7), 1573–1588 (2014).
[Crossref]

Li, Y.

G-H. Chen and Y. Li, “Synchronized multiartifact reduction with tomographic reconstruction (SMART-RECON): A statistical model based iterative image reconstruction method to eliminate limited-view artifacts and to mitigate the temporal-average artifacts in time-resolved CT,” Med. Phys. 42(8), 4698–4707 (2015).
[Crossref] [PubMed]

Llopart, X.

Martens, G.

K. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in X-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A 648, S202–S207 (2011).
[Crossref]

Michel, N.

Michel, T.

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38(7), 4133–4140 (2011).
[Crossref] [PubMed]

Momose, A.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. Part 2 42(7B), 866–868 (2003).
[Crossref]

Nataly,

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

Noël, P.

J. Herzen, M. Willner, A. Fingerle, P. Noël, T. Köhler, E. Drecoll, E. 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]

Pelzer, G.

Peng, W.

R. Zhang, L. Zhang, Z. Chen, W. Peng, and R. Li, “Sensitivity of a non-interferometric grating-based x-ray imaging system,” Phys. Med. Bio. 59(7), 1573–1588 (2014).
[Crossref]

Pfeiffer, F.

J. Herzen, M. Willner, A. Fingerle, P. Noël, T. Köhler, E. Drecoll, E. 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]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, Joachim Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[Crossref] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, CH. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[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]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12(16), 6296–6304 (2005).
[Crossref]

Qi, Z.

G-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys. 38, 584–588 (2011).
[Crossref] [PubMed]

Raupach, R.

R. Raupach and T.G. Flohr, “Performance evaluation of x-ray differential phase contrast computed tomography (PCT) with respect to medical imaging,” Med. Phys. 39(8), 4761–4774 (2012).
[Crossref] [PubMed]

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

Revol, V.

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

Ritter, A.

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38(7), 4133–4140 (2011).
[Crossref] [PubMed]

Roessl, E.

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

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

Rössl, E.

K. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in X-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A 648, S202–S207 (2011).
[Crossref]

Rummeny, E.

J. Herzen, M. Willner, A. Fingerle, P. Noël, T. Köhler, E. Drecoll, E. 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]

Schroer, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, Joachim Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[Crossref] [PubMed]

Schusser, S.

K. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in X-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A 648, S202–S207 (2011).
[Crossref]

Schuster, M.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, Joachim Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[Crossref] [PubMed]

Seo, Y.

T. Thuering, W. Barber, Y. Seo, F. Alhassen, J. Iwanczyk, and M. Stampanoni, “Energy resolved X-ray grating interferometry,” Appl. Phys. Lett. 102(19), 191113 (2013).
[Crossref]

Singer, G.

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

Stampanoni, M.

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

T. Thuering and M. Stampanoni, “Performance and optimization of X-ray grating interferometry,” Phil. Trans. R. Soc. A 372(2010), 20130027 (2014).
[Crossref] [PubMed]

T. Thuering, W. Barber, Y. Seo, F. Alhassen, J. Iwanczyk, and M. Stampanoni, “Energy resolved X-ray grating interferometry,” Appl. Phys. Lett. 102(19), 191113 (2013).
[Crossref]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12(16), 6296–6304 (2005).
[Crossref]

Strang, G.

G. Strang, Introduction to linear algebra, (Wellesley-Cambridge Press, 1993).

Straumann, U.

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

Stutman, D.

D. Stutman, T. Beck, J. Carrino, and C. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Bio. 56(17), 5697–5720 (2011).
[Crossref]

Suzuki, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. Part 2 42(7B), 866–868 (2003).
[Crossref]

Takai, H.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. Part 2 42(7B), 866–868 (2003).
[Crossref]

Thuering, T.

T. Thuering and M. Stampanoni, “Performance and optimization of X-ray grating interferometry,” Phil. Trans. R. Soc. A 372(2010), 20130027 (2014).
[Crossref] [PubMed]

T. Thuering, W. Barber, Y. Seo, F. Alhassen, J. Iwanczyk, and M. Stampanoni, “Energy resolved X-ray grating interferometry,” Appl. Phys. Lett. 102(19), 191113 (2013).
[Crossref]

Trippel, M.

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

Urban, C.

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

van Stevendaal, U.

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

Vogtmeier, G.

K. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in X-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A 648, S202–S207 (2011).
[Crossref]

Wang, Z.

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

Weber, T.

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]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12(16), 6296–6304 (2005).
[Crossref]

Wieberneit, N.

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

Willner, M.

J. Herzen, M. Willner, A. Fingerle, P. Noël, T. Köhler, E. Drecoll, E. 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]

Zambelli, J.

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41(1), 011903 (2014).
[Crossref] [PubMed]

G-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys. 38, 584–588 (2011).
[Crossref] [PubMed]

Zeigler, E.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, E. Zeigler, and P. Cloetens, “X-ray phase imaging with a grating interferometer,” Opt. Express 12(16), 6296–6304 (2005).
[Crossref]

Zhang, L.

R. Zhang, L. Zhang, Z. Chen, W. Peng, and R. Li, “Sensitivity of a non-interferometric grating-based x-ray imaging system,” Phys. Med. Bio. 59(7), 1573–1588 (2014).
[Crossref]

Zhang, R.

R. Zhang, L. Zhang, Z. Chen, W. Peng, and R. Li, “Sensitivity of a non-interferometric grating-based x-ray imaging system,” Phys. Med. Bio. 59(7), 1573–1588 (2014).
[Crossref]

Appl. Phys. Lett. (1)

T. Thuering, W. Barber, Y. Seo, F. Alhassen, J. Iwanczyk, and M. Stampanoni, “Energy resolved X-ray grating interferometry,” Appl. Phys. Lett. 102(19), 191113 (2013).
[Crossref]

Invest. Radiol. (1)

N. Hauser, Z. Wang, R. Kubik-Huch, M. Trippel, G. Singer, M. Hohl, E. Roessl, T. Köhler, U. van Stevendaal, N. Wieberneit, Nataly, 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(3), 131–137 (2014).
[Crossref]

J. Microsc. (1)

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, Joachim Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232(1), 145–157 (2008).
[Crossref] [PubMed]

Jpn. J. Appl. Phys. Part 2 (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, H. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys. Part 2 42(7B), 866–868 (2003).
[Crossref]

Med. Phys. (7)

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

K. Li, Y. Ge, J. Garrett, N. Bevins, J. Zambelli, and G-H. Chen, “Grating-based phase contrast tomosynthesis imaging: Proof-of-concept experimental studies,” Med. Phys. 41(1), 011903 (2014).
[Crossref] [PubMed]

G-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys. 38, 584–588 (2011).
[Crossref] [PubMed]

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38(7), 4133–4140 (2011).
[Crossref] [PubMed]

R. Raupach and T.G. Flohr, “Performance evaluation of x-ray differential phase contrast computed tomography (PCT) with respect to medical imaging,” Med. Phys. 39(8), 4761–4774 (2012).
[Crossref] [PubMed]

G-H. Chen and Y. Li, “Synchronized multiartifact reduction with tomographic reconstruction (SMART-RECON): A statistical model based iterative image reconstruction method to eliminate limited-view artifacts and to mitigate the temporal-average artifacts in time-resolved CT,” Med. Phys. 42(8), 4698–4707 (2015).
[Crossref] [PubMed]

J. Garrett, Y. Ge, K. Li, and G-H. Chen, “Anatomical background noise power spectrum in differential phase contrast and dark field contrast mammograms,” Med. Phys. 41(12), 120701 (2014).
[Crossref] [PubMed]

Nat. Mater. (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E.F. Eikenberry, CH. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
[Crossref] [PubMed]

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]

Nucl. Instrum. Meth. A (1)

K. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in X-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A 648, S202–S207 (2011).
[Crossref]

Opt. Express (3)

Phil. Trans. R. Soc. A (1)

T. Thuering and M. Stampanoni, “Performance and optimization of X-ray grating interferometry,” Phil. Trans. R. Soc. A 372(2010), 20130027 (2014).
[Crossref] [PubMed]

Phys. Med. Bio. (3)

D. Stutman, T. Beck, J. Carrino, and C. Bingham, “Talbot phase-contrast x-ray imaging for the small joints of the hand,” Phys. Med. Bio. 56(17), 5697–5720 (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. Bio. 56, 2219–2244 (2011).
[Crossref]

R. Zhang, L. Zhang, Z. Chen, W. Peng, and R. Li, “Sensitivity of a non-interferometric grating-based x-ray imaging system,” Phys. Med. Bio. 59(7), 1573–1588 (2014).
[Crossref]

PloS one (1)

J. Herzen, M. Willner, A. Fingerle, P. Noël, T. Köhler, E. Drecoll, E. 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)

Y. Ge, K. Li, and G-H. Chen, “Cramér-Rao lower bound in differential phase contrast imaging and its application in the optimization of data acquisition systems,” Proc. SPIE 9033, 90330F (2014).
[Crossref]

Rev. Sci. Instrum. (1)

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

Other (1)

G. Strang, Introduction to linear algebra, (Wellesley-Cambridge Press, 1993).

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Figures (11)

Fig. 1
Fig. 1 The full x-ray spectrum is equally divided into either two consecutive energy bins (a) or three consecutive energy bins (b). Energy threshold is denoted by E T H i.

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Fig. 2
Fig. 2 (a) PMMA tube phantom containing a vegetable bath and spheres of different materials and diameters. (b) PMMA wedge phantom with a slope of 10 degrees. Three regions correspond to different PMMA thicknesses were selected, A, B, and C, to evaluate the DPC image CNRs.

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Fig. 3
Fig. 3 The singular value distributions of the spatial-spectral DPC image matrix J with and without quantum noise for energy bin number Λ = 3,5,7,9.

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Fig. 4
Fig. 4 DPC images generated by numerical simulations. Denoising using rank-one approximation. All images are displayed with a range of [−0.9 0.9].

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Fig. 5
Fig. 5 (a) Number of detected x-ray photons at different energies. The peak corresponds to 27 keV. (b) Measured fringe visibility at different energies. The peak corresponds to 28 keV.

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Fig. 6
Fig. 6 (a) Magnitude of singular values σi of the spatial-spectral matrix JP. (b)–(d) correspond to the three columns ( u → 1, u → 2, and u → 3) of the decomposed spatial basis matrix U. Clearly, the object information is predominantly contained in the first basis u → 1.

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Fig. 7
Fig. 7 Experimental imaging results for both the tube and the wedge phantom. The first image row show the original images of different energy bins. Images processed by the proposed rank-one approximation method are listed in the second row. The difference between the first two rows are listed in the bottom row. Images of the wedge phantom, the upper dark part corresponds to air, and the lower bright part corresponds to the PMMA wedge. The three ROIs used for quantitative measurements are marked as: A, B, and C. All images are displayed with a range of [−0.5 1.5].

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Fig. 8
Fig. 8 Line profiles of the tube phantom (central image region) in each energy bin.

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Fig. 9
Fig. 9 CNR of the three energy bins measured at ROIs A-C that correspond to regions in the wedge phantom with different thicknesses.

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Fig. 10
Fig. 10 Comparisons of the measured CNRs from three different methods for different exposure levels. The linear relationship between the square of CNR and the exposure level is well maintained after the rank-one approximations.

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Fig. 11
Fig. 11 Comparisons of the measured CNRs from three different methods for different energy window numbers.

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Tables (1)

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Table 1 List of mean±standard deviation values of DPC images generated with conventional method and with the proposed rank-one approximation methods.

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Equations (9)

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ϕ ( x , y , E ) = C E 2 ∂ ∂ y ∫ L ρ e ( x , y , z ) d z ,
N ( k ) ( p , q , E ) = N 0 ( p , q , E ) + N 1 ( p , q , E ) cos [ 2 π k M + ϕ ( p , q , E ) ] ,
ϕ ( p , q , E ) = tan − 1 [ ∑ k N ( k ) ( p , q , E ) sin ( 2 π k M ) ∑ k N ( k ) ( p , q , E ) cos ( 2 π k M ) ] .
σ ϕ ( E ) 2 = 1 M N 0 ( E ) × 2 ε 2 ( E ) ,
ϕ → ( p , q , E i ) = [ ϕ ( 1 , 1 , E i ) ϕ ( 1 , 2 , E i ) ⋮ ϕ ( 2 , 1 , E i ) ϕ ( 2 , 2 , E i ) ⋮ ϕ ( P , Q , E i ) ] ,
J = [ ϕ → ( p , q , E 1 ) ⋯ ϕ → ( p , q , E Λ ) ] = [ ϕ ( 1 , 1 , E 1 ) ⋯ ϕ ( 1 , 1 , E Λ ) ϕ ( 1 , 2 , E 1 ) ⋯ ϕ ( 1 , 2 , E Λ ) ⋮ ⋮ ⋮ ϕ ( P , Q , E 1 ) ⋯ ϕ ( P , Q , E Λ ) ] .
J P = [ ϕ ( 1 , 1 , E 1 ) ⋯ ϕ ( 1 , 1 , E Λ ) ϕ ( 1 , 1 , E 1 p ) ⋯ ϕ ( 1 , 1 , E λ p ) ϕ ( 1 , 2 , E 1 ) ⋯ ϕ ( 1 , 2 , E Λ ) ϕ ( 1 , 2 , E 1 p ) ⋯ ϕ ( 1 , 2 , E λ p ) ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ϕ ( P , Q , E 1 ) ⋯ ϕ ( P , Q , E Λ ) ϕ ( P , Q , E 1 p ) ⋯ ϕ ( P , Q , E λ p ) ] .
J P = U ∑ V T = ∑ i = 1 Λ + λ σ i u → i ⊗ v → i T .
J P * ≈ σ 1 u → 1 ⊗ v → 1 T .

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