Abstract

Propagation-based X-ray phase-contrast tomography (PCT) seeks to reconstruct information regarding the complex-valued refractive index distribution of an object. In many applications, a boundary-enhanced image is sought that reveals the locations of discontinuities in the real-valued component of the refractive index distribution. We investigate two iterative algorithms for few-view image reconstruction in boundary-enhanced PCT that exploit the fact that a boundary-enhanced PCT image, or its gradient, is often sparse. In order to exploit object sparseness, the reconstruction algorithms seek to minimize the l 1-norm or TV-norm of the image, subject to data consistency constraints. We demonstrate that the algorithms can reconstruct accurate boundary-enhanced images from highly incomplete few-view projection data.

© 2010 Optical Society of America

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  1. A. Barty, K. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175(4), 329–336 (2000).
    [CrossRef]
  2. T. Weitkamp, C. Rau, A. Snigirev, B. Brenner, T. Gunzler, M. Kuhlmann, and C. Schroer, ““In-line phase contrast in synchrotron-radiation microradiography and tomography,” in Developments in X-ray Tomography III,” Proc. SPIE 4503, 92–102 (2002).
  3. P. Cloetens, R. Barrett, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
    [CrossRef]
  4. A. V. Bronnikov, “Theory of quantitative phase-contrast computed tomography,” J. Opt. Soc. Am. A 19(3), 472–480 (2002).
    [CrossRef]
  5. T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(034), 102 (2006).
    [CrossRef]
  6. M. A. Anastasio, D. Shi, Y. Huang, and G. Gbur, “Image Reconstruction in Spherical Wave Intensity Diffraction Tomography,” J. Opt. Soc. Am. A 22, 2651–2661 (2005).
    [CrossRef]
  7. P. Cloetens, M. Pateyron-Salome, J. Y. Buffiere, G. Peix, J. Baruchel, F. Peyrin, and M. Schlenker, “Observation of microstructure and damage in materials by phase sensitive radiography and tomography,” J. Appl. Phys. 81, 5878–5886 (1997).
    [CrossRef]
  8. P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44(3), 741–749 (1999).
    [CrossRef] [PubMed]
  9. E. F. Donnelly, R. R. Price, K. G. Lewis, and D. R. Pickens, “Polychromatic phase-contrast computed tomography,” Med. Phys. 34(8), 3165–3168 (2007).
    [CrossRef] [PubMed]
  10. G. R. Myers, D. M. Paganin, T. Gureyev, and S. C. Mayo, “Phase-contrast tomography of single-material objects from few projections,” Opt. Express 16, 908–919 (2008).
    [CrossRef] [PubMed]
  11. G. R. Myers, T. E. Gureyev, D. M. Paganin, and S. C. Mayo, “The binary dissector: phase contrast tomography of two- and three-material objects from few projections,” Opt. Express 16, 10736–10749 (2008).
    [CrossRef] [PubMed]
  12. M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
    [CrossRef] [PubMed]
  13. D. Shi, M. Anastasio, and X. Pan, “Reconstruction of refractive index discontinuities from truncated phase contrast tomography projections,” Appl. Phys. Lett. 86, 034102 (2005).
    [CrossRef]
  14. Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
    [CrossRef]
  15. E. Candes, J. Romberg, and T. Tao, “Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 3526–3530 (2006).
    [CrossRef]
  16. A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
    [CrossRef]
  17. T. E. Gureyev, and S. W. Wilkins, “On x-ray phase imaging with a point source,” J. Opt. Soc. Am. A 15(3), 579–585 (1998).
    [CrossRef]
  18. F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986).
  19. M. Liebling, T. Blu, and M. Unser, “Fresnelets: New Multiresolution Wavelet Bases for Digital Holography,” IEEE Trans. Image Process. 12(1), 29–43 (2003).
    [CrossRef]
  20. H. Barrett, and K. Myers, Foundations of Image Science (Wiley Series in Pure and Applied Optics, 2004).
  21. A. Kak, and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988).
  22. J. Tropp, “Just relax: Convex programming methods for identifying sparse signals,” IEEE Trans. Inf. Theory 51, 1030–1051 (2006).
    [CrossRef]
  23. E. Y. Sidky, R. Chartrand, and X. Pan, “Image reconstruction from few views by non-convex optimization,” IEEE Nucl. Sci. Conf. Rec. 5, 3526–3530 (2007).
  24. R. Baraniuk, “Compressive Sensing,” IEEE Signal Process. Mag. 24, 118–121 (2007).
    [CrossRef]
  25. M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Process. 1, 586–598 (2007).
    [CrossRef]
  26. M. Li, H. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: Application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599–2609 (2002).
    [CrossRef] [PubMed]
  27. S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998).
    [CrossRef]
  28. F. Santosa, and W. Symes, “Linear inversion of band-limited reflection histograms,” SIAM J. Sci. Stat. Comput. 7, 1307–1330 (1986).
    [CrossRef]
  29. W. Souidene, A. Aissa-El-Bey, K. Abed-Meraim, and A. Beghdadi, “Blind Image Separation using Sparse Representation,” in ICIP 2007. IEEE International Conference on Image Processing, vol. 3, pp. III –125–III –128 (2007).
  30. E. Y. Sidky, C.-M. Kao, and X. Pan, ““Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-ray,” Sci. Tech. (Paris) 14, 119–139 (2006).
  31. E. Y. Sidky, and X. C. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).
    [CrossRef] [PubMed]
  32. 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]
  33. R. Chartrand, “Exact reconstruction of sparse signals via nonconvex minimization,” IEEE Signal Process. Lett. 14, 707–710 (2007).
    [CrossRef]
  34. T. Blumensath, and M. Davies, “Iterative hard thresholding for compressed sensing,” Appl. Comput. Harmon. Anal. 27, 265–274 (2009).
    [CrossRef]
  35. E. J. Candès, and M. B. Wakin, “An Introduction To Compressive Sampling,” IEEE Sig. Proc. Mag. 25, 21–30 (2008).
    [CrossRef]
  36. R. Garg, and K. Khandekar, “Gradient Descent with Sparsification: An iterative algorithm for sparse recovery with restricted isometry property,” Proceedings of the 26th Annual International Conference on Machine Learning 382, 337–344 (2009).
  37. C. Hamaker, and D. C. Solmon, “Angles between null spaces of x-rays,” J. Math. Anal. Appl. 62, 1–23 (1978).
    [CrossRef]
  38. G. T. Herman, and L. B. Meyer, “Algebraic reconstruction techniques can be made computationally efficient,” IEEE Trans. Med. Imaging 12, 600–609 (1993).
    [CrossRef]
  39. H. Q. Guan, and R. Gordon, “A projection access order for speedy convergence of ART (algebraic reconstruction technique) - a multilevel scheme for computed-tomography,” Phys. Med. Biol. 39, 2005–2022 (1994).
    [CrossRef] [PubMed]
  40. X. Pan, E. Y. Sidky, and M. Vannier, “Why do commercial CT scanners still employ traditional, filtered back projection for image reconstruction?” Inv. Prob. 25, 123009 (2009).
    [CrossRef]

2009 (2)

T. Blumensath, and M. Davies, “Iterative hard thresholding for compressed sensing,” Appl. Comput. Harmon. Anal. 27, 265–274 (2009).
[CrossRef]

X. Pan, E. Y. Sidky, and M. Vannier, “Why do commercial CT scanners still employ traditional, filtered back projection for image reconstruction?” Inv. Prob. 25, 123009 (2009).
[CrossRef]

2008 (5)

E. J. Candès, and M. B. Wakin, “An Introduction To Compressive Sampling,” IEEE Sig. Proc. Mag. 25, 21–30 (2008).
[CrossRef]

E. Y. Sidky, and X. C. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).
[CrossRef] [PubMed]

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]

G. R. Myers, D. M. Paganin, T. Gureyev, and S. C. Mayo, “Phase-contrast tomography of single-material objects from few projections,” Opt. Express 16, 908–919 (2008).
[CrossRef] [PubMed]

G. R. Myers, T. E. Gureyev, D. M. Paganin, and S. C. Mayo, “The binary dissector: phase contrast tomography of two- and three-material objects from few projections,” Opt. Express 16, 10736–10749 (2008).
[CrossRef] [PubMed]

2007 (5)

E. F. Donnelly, R. R. Price, K. G. Lewis, and D. R. Pickens, “Polychromatic phase-contrast computed tomography,” Med. Phys. 34(8), 3165–3168 (2007).
[CrossRef] [PubMed]

R. Chartrand, “Exact reconstruction of sparse signals via nonconvex minimization,” IEEE Signal Process. Lett. 14, 707–710 (2007).
[CrossRef]

E. Y. Sidky, R. Chartrand, and X. Pan, “Image reconstruction from few views by non-convex optimization,” IEEE Nucl. Sci. Conf. Rec. 5, 3526–3530 (2007).

R. Baraniuk, “Compressive Sensing,” IEEE Signal Process. Mag. 24, 118–121 (2007).
[CrossRef]

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Process. 1, 586–598 (2007).
[CrossRef]

2006 (4)

J. Tropp, “Just relax: Convex programming methods for identifying sparse signals,” IEEE Trans. Inf. Theory 51, 1030–1051 (2006).
[CrossRef]

E. Y. Sidky, C.-M. Kao, and X. Pan, ““Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-ray,” Sci. Tech. (Paris) 14, 119–139 (2006).

E. Candes, J. Romberg, and T. Tao, “Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 3526–3530 (2006).
[CrossRef]

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(034), 102 (2006).
[CrossRef]

2005 (2)

M. A. Anastasio, D. Shi, Y. Huang, and G. Gbur, “Image Reconstruction in Spherical Wave Intensity Diffraction Tomography,” J. Opt. Soc. Am. A 22, 2651–2661 (2005).
[CrossRef]

D. Shi, M. Anastasio, and X. Pan, “Reconstruction of refractive index discontinuities from truncated phase contrast tomography projections,” Appl. Phys. Lett. 86, 034102 (2005).
[CrossRef]

2004 (1)

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
[CrossRef] [PubMed]

2003 (1)

M. Liebling, T. Blu, and M. Unser, “Fresnelets: New Multiresolution Wavelet Bases for Digital Holography,” IEEE Trans. Image Process. 12(1), 29–43 (2003).
[CrossRef]

2002 (3)

M. Li, H. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: Application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599–2609 (2002).
[CrossRef] [PubMed]

T. Weitkamp, C. Rau, A. Snigirev, B. Brenner, T. Gunzler, M. Kuhlmann, and C. Schroer, ““In-line phase contrast in synchrotron-radiation microradiography and tomography,” in Developments in X-ray Tomography III,” Proc. SPIE 4503, 92–102 (2002).

A. V. Bronnikov, “Theory of quantitative phase-contrast computed tomography,” J. Opt. Soc. Am. A 19(3), 472–480 (2002).
[CrossRef]

2001 (1)

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

2000 (1)

A. Barty, K. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175(4), 329–336 (2000).
[CrossRef]

1999 (1)

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44(3), 741–749 (1999).
[CrossRef] [PubMed]

1998 (2)

T. E. Gureyev, and S. W. Wilkins, “On x-ray phase imaging with a point source,” J. Opt. Soc. Am. A 15(3), 579–585 (1998).
[CrossRef]

S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998).
[CrossRef]

1997 (2)

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
[CrossRef]

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

1996 (1)

P. Cloetens, R. Barrett, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
[CrossRef]

1994 (1)

H. Q. Guan, and R. Gordon, “A projection access order for speedy convergence of ART (algebraic reconstruction technique) - a multilevel scheme for computed-tomography,” Phys. Med. Biol. 39, 2005–2022 (1994).
[CrossRef] [PubMed]

1993 (1)

G. T. Herman, and L. B. Meyer, “Algebraic reconstruction techniques can be made computationally efficient,” IEEE Trans. Med. Imaging 12, 600–609 (1993).
[CrossRef]

1986 (1)

F. Santosa, and W. Symes, “Linear inversion of band-limited reflection histograms,” SIAM J. Sci. Stat. Comput. 7, 1307–1330 (1986).
[CrossRef]

1978 (1)

C. Hamaker, and D. C. Solmon, “Angles between null spaces of x-rays,” J. Math. Anal. Appl. 62, 1–23 (1978).
[CrossRef]

Anastasio, M.

D. Shi, M. Anastasio, and X. Pan, “Reconstruction of refractive index discontinuities from truncated phase contrast tomography projections,” Appl. Phys. Lett. 86, 034102 (2005).
[CrossRef]

Anastasio, M. A.

M. A. Anastasio, D. Shi, Y. Huang, and G. Gbur, “Image Reconstruction in Spherical Wave Intensity Diffraction Tomography,” J. Opt. Soc. Am. A 22, 2651–2661 (2005).
[CrossRef]

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
[CrossRef] [PubMed]

Baraniuk, R.

R. Baraniuk, “Compressive Sensing,” IEEE Signal Process. Mag. 24, 118–121 (2007).
[CrossRef]

Barrett, R.

P. Cloetens, R. Barrett, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
[CrossRef]

Barty, A.

A. Barty, K. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175(4), 329–336 (2000).
[CrossRef]

Baruchel, J.

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

Blu, T.

M. Liebling, T. Blu, and M. Unser, “Fresnelets: New Multiresolution Wavelet Bases for Digital Holography,” IEEE Trans. Image Process. 12(1), 29–43 (2003).
[CrossRef]

Blumensath, T.

T. Blumensath, and M. Davies, “Iterative hard thresholding for compressed sensing,” Appl. Comput. Harmon. Anal. 27, 265–274 (2009).
[CrossRef]

Brenner, B.

T. Weitkamp, C. Rau, A. Snigirev, B. Brenner, T. Gunzler, M. Kuhlmann, and C. Schroer, ““In-line phase contrast in synchrotron-radiation microradiography and tomography,” in Developments in X-ray Tomography III,” Proc. SPIE 4503, 92–102 (2002).

Bresnahan, J.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Bronnikov, A. V.

Buffiere, J. Y.

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

Candes, E.

E. Candes, J. Romberg, and T. Tao, “Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 3526–3530 (2006).
[CrossRef]

Candès, E. J.

E. J. Candès, and M. B. Wakin, “An Introduction To Compressive Sampling,” IEEE Sig. Proc. Mag. 25, 21–30 (2008).
[CrossRef]

Carlo, F. D.

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
[CrossRef] [PubMed]

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Chartrand, R.

E. Y. Sidky, R. Chartrand, and X. Pan, “Image reconstruction from few views by non-convex optimization,” IEEE Nucl. Sci. Conf. Rec. 5, 3526–3530 (2007).

R. Chartrand, “Exact reconstruction of sparse signals via nonconvex minimization,” IEEE Signal Process. Lett. 14, 707–710 (2007).
[CrossRef]

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]

Chen, S.

S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998).
[CrossRef]

Cloetens, P.

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

P. Cloetens, R. Barrett, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
[CrossRef]

Davies, M.

T. Blumensath, and M. Davies, “Iterative hard thresholding for compressed sensing,” Appl. Comput. Harmon. Anal. 27, 265–274 (2009).
[CrossRef]

Donnelly, E. F.

E. F. Donnelly, R. R. Price, K. G. Lewis, and D. R. Pickens, “Polychromatic phase-contrast computed tomography,” Med. Phys. 34(8), 3165–3168 (2007).
[CrossRef] [PubMed]

Donoho, D.

S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998).
[CrossRef]

Figueiredo, M. A.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Process. 1, 586–598 (2007).
[CrossRef]

Foster, I.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Gao, D.

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
[CrossRef]

Gbur, G.

Gordon, R.

H. Q. Guan, and R. Gordon, “A projection access order for speedy convergence of ART (algebraic reconstruction technique) - a multilevel scheme for computed-tomography,” Phys. Med. Biol. 39, 2005–2022 (1994).
[CrossRef] [PubMed]

Guan, H. Q.

H. Q. Guan, and R. Gordon, “A projection access order for speedy convergence of ART (algebraic reconstruction technique) - a multilevel scheme for computed-tomography,” Phys. Med. Biol. 39, 2005–2022 (1994).
[CrossRef] [PubMed]

Guigay, J.-P.

P. Cloetens, R. Barrett, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
[CrossRef]

Gunzler, T.

T. Weitkamp, C. Rau, A. Snigirev, B. Brenner, T. Gunzler, M. Kuhlmann, and C. Schroer, ““In-line phase contrast in synchrotron-radiation microradiography and tomography,” in Developments in X-ray Tomography III,” Proc. SPIE 4503, 92–102 (2002).

Gureyev, T.

Gureyev, T. E.

Hamaker, C.

C. Hamaker, and D. C. Solmon, “Angles between null spaces of x-rays,” J. Math. Anal. Appl. 62, 1–23 (1978).
[CrossRef]

Herman, G. T.

G. T. Herman, and L. B. Meyer, “Algebraic reconstruction techniques can be made computationally efficient,” IEEE Trans. Med. Imaging 12, 600–609 (1993).
[CrossRef]

Huang, Y.

Insley, J.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Kao, C.-M.

E. Y. Sidky, C.-M. Kao, and X. Pan, ““Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-ray,” Sci. Tech. (Paris) 14, 119–139 (2006).

Kesselman, C.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Kudo, H.

M. Li, H. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: Application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599–2609 (2002).
[CrossRef] [PubMed]

Kuhlmann, M.

T. Weitkamp, C. Rau, A. Snigirev, B. Brenner, T. Gunzler, M. Kuhlmann, and C. Schroer, ““In-line phase contrast in synchrotron-radiation microradiography and tomography,” in Developments in X-ray Tomography III,” Proc. SPIE 4503, 92–102 (2002).

Lane, P.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[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, K. G.

E. F. Donnelly, R. R. Price, K. G. Lewis, and D. R. Pickens, “Polychromatic phase-contrast computed tomography,” Med. Phys. 34(8), 3165–3168 (2007).
[CrossRef] [PubMed]

Li, M.

M. Li, H. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: Application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599–2609 (2002).
[CrossRef] [PubMed]

Liebling, M.

M. Liebling, T. Blu, and M. Unser, “Fresnelets: New Multiresolution Wavelet Bases for Digital Holography,” IEEE Trans. Image Process. 12(1), 29–43 (2003).
[CrossRef]

Mancini, D.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Mayo, S. C.

McNulty, I.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Meyer, L. B.

G. T. Herman, and L. B. Meyer, “Algebraic reconstruction techniques can be made computationally efficient,” IEEE Trans. Med. Imaging 12, 600–609 (1993).
[CrossRef]

Myers, G. R.

Nesterest, Y. I.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(034), 102 (2006).
[CrossRef]

Nowak, R. D.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Process. 1, 586–598 (2007).
[CrossRef]

Nugent, K.

A. Barty, K. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175(4), 329–336 (2000).
[CrossRef]

Paganin, D.

A. Barty, K. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175(4), 329–336 (2000).
[CrossRef]

Paganin, D. M.

Pan, X.

X. Pan, E. Y. Sidky, and M. Vannier, “Why do commercial CT scanners still employ traditional, filtered back projection for image reconstruction?” Inv. Prob. 25, 123009 (2009).
[CrossRef]

E. Y. Sidky, R. Chartrand, and X. Pan, “Image reconstruction from few views by non-convex optimization,” IEEE Nucl. Sci. Conf. Rec. 5, 3526–3530 (2007).

E. Y. Sidky, C.-M. Kao, and X. Pan, ““Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-ray,” Sci. Tech. (Paris) 14, 119–139 (2006).

D. Shi, M. Anastasio, and X. Pan, “Reconstruction of refractive index discontinuities from truncated phase contrast tomography projections,” Appl. Phys. Lett. 86, 034102 (2005).
[CrossRef]

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
[CrossRef] [PubMed]

Pan, X. C.

E. Y. Sidky, and X. C. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).
[CrossRef] [PubMed]

Pateyron-Salome, M.

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

Peix, G.

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

Peyrin, F.

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

Pickens, D. R.

E. F. Donnelly, R. R. Price, K. G. Lewis, and D. R. Pickens, “Polychromatic phase-contrast computed tomography,” Med. Phys. 34(8), 3165–3168 (2007).
[CrossRef] [PubMed]

Pogany, A.

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
[CrossRef]

Price, R. R.

E. F. Donnelly, R. R. Price, K. G. Lewis, and D. R. Pickens, “Polychromatic phase-contrast computed tomography,” Med. Phys. 34(8), 3165–3168 (2007).
[CrossRef] [PubMed]

Rau, C.

T. Weitkamp, C. Rau, A. Snigirev, B. Brenner, T. Gunzler, M. Kuhlmann, and C. Schroer, ““In-line phase contrast in synchrotron-radiation microradiography and tomography,” in Developments in X-ray Tomography III,” Proc. SPIE 4503, 92–102 (2002).

Raven, C.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44(3), 741–749 (1999).
[CrossRef] [PubMed]

Roberts, A.

A. Barty, K. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175(4), 329–336 (2000).
[CrossRef]

Romberg, J.

E. Candes, J. Romberg, and T. Tao, “Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 3526–3530 (2006).
[CrossRef]

Santosa, F.

F. Santosa, and W. Symes, “Linear inversion of band-limited reflection histograms,” SIAM J. Sci. Stat. Comput. 7, 1307–1330 (1986).
[CrossRef]

Saunders, M.

S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998).
[CrossRef]

Schlenker, M.

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

P. Cloetens, R. Barrett, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
[CrossRef]

Schroer, C.

T. Weitkamp, C. Rau, A. Snigirev, B. Brenner, T. Gunzler, M. Kuhlmann, and C. Schroer, ““In-line phase contrast in synchrotron-radiation microradiography and tomography,” in Developments in X-ray Tomography III,” Proc. SPIE 4503, 92–102 (2002).

Shi, D.

M. A. Anastasio, D. Shi, Y. Huang, and G. Gbur, “Image Reconstruction in Spherical Wave Intensity Diffraction Tomography,” J. Opt. Soc. Am. A 22, 2651–2661 (2005).
[CrossRef]

D. Shi, M. Anastasio, and X. Pan, “Reconstruction of refractive index discontinuities from truncated phase contrast tomography projections,” Appl. Phys. Lett. 86, 034102 (2005).
[CrossRef]

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
[CrossRef] [PubMed]

Sidky, E. Y.

X. Pan, E. Y. Sidky, and M. Vannier, “Why do commercial CT scanners still employ traditional, filtered back projection for image reconstruction?” Inv. Prob. 25, 123009 (2009).
[CrossRef]

E. Y. Sidky, and X. C. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).
[CrossRef] [PubMed]

E. Y. Sidky, R. Chartrand, and X. Pan, “Image reconstruction from few views by non-convex optimization,” IEEE Nucl. Sci. Conf. Rec. 5, 3526–3530 (2007).

E. Y. Sidky, C.-M. Kao, and X. Pan, ““Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-ray,” Sci. Tech. (Paris) 14, 119–139 (2006).

Snigirev, A.

T. Weitkamp, C. Rau, A. Snigirev, B. Brenner, T. Gunzler, M. Kuhlmann, and C. Schroer, ““In-line phase contrast in synchrotron-radiation microradiography and tomography,” in Developments in X-ray Tomography III,” Proc. SPIE 4503, 92–102 (2002).

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44(3), 741–749 (1999).
[CrossRef] [PubMed]

Snigireva, I.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44(3), 741–749 (1999).
[CrossRef] [PubMed]

Solmon, D. C.

C. Hamaker, and D. C. Solmon, “Angles between null spaces of x-rays,” J. Math. Anal. Appl. 62, 1–23 (1978).
[CrossRef]

Spanne, P.

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44(3), 741–749 (1999).
[CrossRef] [PubMed]

Su, M.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Symes, W.

F. Santosa, and W. Symes, “Linear inversion of band-limited reflection histograms,” SIAM J. Sci. Stat. Comput. 7, 1307–1330 (1986).
[CrossRef]

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. Candes, J. Romberg, and T. Tao, “Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 3526–3530 (2006).
[CrossRef]

Thiebaux, M.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Tieman, B.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Tropp, J.

J. Tropp, “Just relax: Convex programming methods for identifying sparse signals,” IEEE Trans. Inf. Theory 51, 1030–1051 (2006).
[CrossRef]

Unser, M.

M. Liebling, T. Blu, and M. Unser, “Fresnelets: New Multiresolution Wavelet Bases for Digital Holography,” IEEE Trans. Image Process. 12(1), 29–43 (2003).
[CrossRef]

Vannier, M.

X. Pan, E. Y. Sidky, and M. Vannier, “Why do commercial CT scanners still employ traditional, filtered back projection for image reconstruction?” Inv. Prob. 25, 123009 (2009).
[CrossRef]

von Laszewski, G.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Wakin, M. B.

E. J. Candès, and M. B. Wakin, “An Introduction To Compressive Sampling,” IEEE Sig. Proc. Mag. 25, 21–30 (2008).
[CrossRef]

Wang, Y.

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Weitkamp, T.

T. Weitkamp, C. Rau, A. Snigirev, B. Brenner, T. Gunzler, M. Kuhlmann, and C. Schroer, ““In-line phase contrast in synchrotron-radiation microradiography and tomography,” in Developments in X-ray Tomography III,” Proc. SPIE 4503, 92–102 (2002).

Wilkins, S. W.

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(034), 102 (2006).
[CrossRef]

T. E. Gureyev, and S. W. Wilkins, “On x-ray phase imaging with a point source,” J. Opt. Soc. Am. A 15(3), 579–585 (1998).
[CrossRef]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
[CrossRef]

Wright, S. J.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Process. 1, 586–598 (2007).
[CrossRef]

Yang, H.

M. Li, H. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: Application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599–2609 (2002).
[CrossRef] [PubMed]

Appl. Comput. Harmon. Anal. (1)

T. Blumensath, and M. Davies, “Iterative hard thresholding for compressed sensing,” Appl. Comput. Harmon. Anal. 27, 265–274 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterest, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(034), 102 (2006).
[CrossRef]

D. Shi, M. Anastasio, and X. Pan, “Reconstruction of refractive index discontinuities from truncated phase contrast tomography projections,” Appl. Phys. Lett. 86, 034102 (2005).
[CrossRef]

IEEE J. Sel. Top. Sig. Process. (1)

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Sig. Process. 1, 586–598 (2007).
[CrossRef]

IEEE Nucl. Sci. Conf. Rec. (1)

E. Y. Sidky, R. Chartrand, and X. Pan, “Image reconstruction from few views by non-convex optimization,” IEEE Nucl. Sci. Conf. Rec. 5, 3526–3530 (2007).

IEEE Sig. Proc. Mag. (1)

E. J. Candès, and M. B. Wakin, “An Introduction To Compressive Sampling,” IEEE Sig. Proc. Mag. 25, 21–30 (2008).
[CrossRef]

IEEE Signal Process. Lett. (1)

R. Chartrand, “Exact reconstruction of sparse signals via nonconvex minimization,” IEEE Signal Process. Lett. 14, 707–710 (2007).
[CrossRef]

IEEE Signal Process. Mag. (1)

R. Baraniuk, “Compressive Sensing,” IEEE Signal Process. Mag. 24, 118–121 (2007).
[CrossRef]

IEEE Trans. Image Process. (1)

M. Liebling, T. Blu, and M. Unser, “Fresnelets: New Multiresolution Wavelet Bases for Digital Holography,” IEEE Trans. Image Process. 12(1), 29–43 (2003).
[CrossRef]

IEEE Trans. Inf. Theory (2)

J. Tropp, “Just relax: Convex programming methods for identifying sparse signals,” IEEE Trans. Inf. Theory 51, 1030–1051 (2006).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, “Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 3526–3530 (2006).
[CrossRef]

IEEE Trans. Med. Imaging (1)

G. T. Herman, and L. B. Meyer, “Algebraic reconstruction techniques can be made computationally efficient,” IEEE Trans. Med. Imaging 12, 600–609 (1993).
[CrossRef]

Inv. Prob. (1)

X. Pan, E. Y. Sidky, and M. Vannier, “Why do commercial CT scanners still employ traditional, filtered back projection for image reconstruction?” Inv. Prob. 25, 123009 (2009).
[CrossRef]

J. Appl. Phys. (1)

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

J. Math. Anal. Appl. (1)

C. Hamaker, and D. C. Solmon, “Angles between null spaces of x-rays,” J. Math. Anal. Appl. 62, 1–23 (1978).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Phys. D Appl. Phys. (1)

P. Cloetens, R. Barrett, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D Appl. Phys. 29, 133–146 (1996).
[CrossRef]

Med. Phys. (2)

E. F. Donnelly, R. R. Price, K. G. Lewis, and D. R. Pickens, “Polychromatic phase-contrast computed tomography,” Med. Phys. 34(8), 3165–3168 (2007).
[CrossRef] [PubMed]

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]

Opt. Commun. (1)

A. Barty, K. Nugent, A. Roberts, and D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175(4), 329–336 (2000).
[CrossRef]

Opt. Express (2)

Phys. Med. Biol. (5)

M. A. Anastasio, D. Shi, F. D. Carlo, and X. Pan, “Analytic image reconstruction in local phase-contrast tomography,” Phys. Med. Biol. 49, 121–144 (2004).
[CrossRef] [PubMed]

P. Spanne, C. Raven, I. Snigireva, and A. Snigirev, “In-line holography and phase-contrast microtomography with high energy x-rays,” Phys. Med. Biol. 44(3), 741–749 (1999).
[CrossRef] [PubMed]

E. Y. Sidky, and X. C. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53, 4777–4807 (2008).
[CrossRef] [PubMed]

M. Li, H. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: Application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599–2609 (2002).
[CrossRef] [PubMed]

H. Q. Guan, and R. Gordon, “A projection access order for speedy convergence of ART (algebraic reconstruction technique) - a multilevel scheme for computed-tomography,” Phys. Med. Biol. 39, 2005–2022 (1994).
[CrossRef] [PubMed]

Proc. SPIE (1)

T. Weitkamp, C. Rau, A. Snigirev, B. Brenner, T. Gunzler, M. Kuhlmann, and C. Schroer, ““In-line phase contrast in synchrotron-radiation microradiography and tomography,” in Developments in X-ray Tomography III,” Proc. SPIE 4503, 92–102 (2002).

Rev. Sci. Instrum. (2)

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997).
[CrossRef]

Y. Wang, F. D. Carlo, D. Mancini, I. McNulty, B. Tieman, J. Bresnahan, I. Foster, J. Insley, P. Lane, G. von Laszewski, C. Kesselman, M. Su, and M. Thiebaux, “A high-throughput x-ray microtomography system at the Advanced Photon Source,” Rev. Sci. Instrum. 72, 2062–2068 (2001).
[CrossRef]

Sci. Tech. (Paris) (1)

E. Y. Sidky, C.-M. Kao, and X. Pan, ““Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-ray,” Sci. Tech. (Paris) 14, 119–139 (2006).

SIAM J. Sci. Comput. (1)

S. Chen, D. Donoho, and M. Saunders, “Atomic decomposition by basis pursuit,” SIAM J. Sci. Comput. 20, 33–61 (1998).
[CrossRef]

SIAM J. Sci. Stat. Comput. (1)

F. Santosa, and W. Symes, “Linear inversion of band-limited reflection histograms,” SIAM J. Sci. Stat. Comput. 7, 1307–1330 (1986).
[CrossRef]

Other (5)

W. Souidene, A. Aissa-El-Bey, K. Abed-Meraim, and A. Beghdadi, “Blind Image Separation using Sparse Representation,” in ICIP 2007. IEEE International Conference on Image Processing, vol. 3, pp. III –125–III –128 (2007).

F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986).

H. Barrett, and K. Myers, Foundations of Image Science (Wiley Series in Pure and Applied Optics, 2004).

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

R. Garg, and K. Khandekar, “Gradient Descent with Sparsification: An iterative algorithm for sparse recovery with restricted isometry property,” Proceedings of the 26th Annual International Conference on Machine Learning 382, 337–344 (2009).

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Figures (14)

Fig. 1.
Fig. 1.

The imaging geometry of in-line phase-contrast tomography.

Fig. 2.
Fig. 2.

Phantom composed of ellipses of high eccentricity that roughly resembles, in terms of sparsity, the object in the experimental results.

Fig. 3.
Fig. 3.

Estimated values of the isometry constants δs for the Radon transform with 90, equally-spaced views and 2048 detector bins per projection using 512×512 pixels to represent the scanned object. As only a restricted search is performed these values are interpreted as a lower bound on the true isometry constants.

Fig. 4.
Fig. 4.

Ellipse phantom made more challenging by adding f (min) 100 (bottom, left) and f (max) 100 (top, left). These images are added with a similar total energy as that of the original ellipse phantom.

Fig. 5.
Fig. 5.

Reconstructions of the ellipse phantom by IHT-POCS (left) and IHT (middle) algorithms and semi-log plots of the data and image error of both algorithms.

Fig. 6.
Fig. 6.

Reconstructions of the ellipse phantom, with f (min) 100 and f (max) 100 added, by IHT-POCS (left) and IHT (right) algorithms.

Fig. 7.
Fig. 7.

Image reconstructions of the ellipse phantom by IHT-POCS (left) and IHT (right) algorithms. For these results the data are generated from the continuous Radon transform of the ellipse phantom.

Fig. 8.
Fig. 8.

A plot of data residual vs. image sparsity for reconstruction of the ellipse phantom on a 2048×2048 grid using the IHT-POCS algorithm.

Fig. 9.
Fig. 9.

A plot of data residual vs. threshold parameter employed in the IHT-POCS and IHT-POCS-TV algorithms.

Fig. 10.
Fig. 10.

Boundary enhanced images corresponding to a slice of constant z. The image reconstructed from 1440 tomographic views by use of the FBP algorithm is contained in subfigure (a). Images reconstructed from 90 tomographic views by use of the POCS, IHT-POCS, and IHT-POCS-TV algorithms are displayed in subfigures (b)–(d), respectively.

Fig. 11.
Fig. 11.

550×900 pixel region-of-interest positioned near the center of the images in Fig. 1–(a)–(d) are displayed in subfigures (a)–(d).

Fig. 12.
Fig. 12.

500×900 pixel region-of-interest in reconstructed images corresponding to a slice of constant z. The image reconstructed from 1440 tomographic views by use of the FBP algorithm is contained in subfigure (a). Images reconstructed from 90 tomographic views by use of the IHT-POCS, and IHT-POCS-TV algorithms are displayed in subfigures (b) and (c).

Fig. 13.
Fig. 13.

600×350 pixel region-of-interest in reconstructed images corresponding to a slice of constant z. The image reconstructed from 1440 tomographic views by use of the FBP algorithm is contained in subfigure (a). Images reconstructed from 90 tomographic views by use of the IHT-POCS, and IHT-POCS-TV algorithms are displayed in subfigures (b) and (c).

Equations (16)

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g(xr,z,ϕ)1d[I(xr,z,ϕ)I0(xr,z,ϕ)1],
g(xr,z,ϕ)=xr,z2(r2;z) = xr,z2 d yr δ (r2;z),
g(xr,z,ϕ)=R2 δ (r2;z) ,
g[r,s,t]g(xr,z,ϕ)x=rΔd,z=sΔd,ϕ=tΔθ,
2δ(r2;z=snΔd)l=1M2 m=1M2 bz [l,m] Ψl.m (r2) ,
g=R̂ b ,
b0=argminb0 such that R̂bgε,
bs=argminR̂bg2 such that b0s,
bTV=argmin bTV such that R̂bgεandb0s*,
fs22(1δs)R̂fs22fs22 (1+δs),
f1(min)=argminf1 R̂f1,
f1(max)=argmaxf1 R̂f1.
σ1(min)=R̂f1(min)2 ,
σ1(max)=R̂f1(max)2 .
δ1=σ1(max)σ1(min)σ1(max)+σ1(min) .
fs(min)=argminα,pR̂cosαfs1(min)+R̂sinαp,

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