Abstract

Conventional X-ray micro-computed tomography (μCT) is unable to meet the need for real-time, high-resolution, time-resolved imaging of multi-phase fluid flow. High signal-to-noise-ratio (SNR) data acquisition is too slow and results in motion artefacts in the images, while fast acquisition is too noisy and results in poor image contrast. We present a Bayesian framework for time-resolved tomography that uses priors to drastically reduce the required amount of experiment data. This enables high-quality time-resolved imaging through a data acquisition protocol that is both rapid and high SNR. Here we show that the framework: (i) encompasses our previous, algorithms for imaging two-phase flow as limiting cases; (ii) produces more accurate results from imperfect (i.e. real) data, where it can be compared to our previous work; and (iii) is generalisable to previously intractable systems, such as three-phase flow.

© 2015 Optical Society of America

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References

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  1. C. Caubit, G. Hamon, A. P. Sheppard, and P. E. Øren, “Evaluation of the reliability of prediction of petrophysical data through imagery and pore network modelling,” in “22nd International Symposium of the Society of Core Analysts,” (Society of Core Analysts, Abu Dhabi, UAE, 2008). SCA2008-33.
  2. J. E. Aravena, M. Berli, T. A. Ghezzehei, and S. W. Tyler, “Effects of root-induced compaction on rhizosphere hydraulic properties–X-ray microtomography imaging and numerical simulations,” Environ. Sci. Technol. 45, 425–431 (2011).
    [Crossref]
  3. H. Derluyn, J. Dewanckele, M. N. Boone, V. Cnudde, D. Derome, and J. Carmeliet, “Crystallization of hydrated and anhydrous salts in porous limestone resolved by synchrotron X-ray microtomography,” Nucl. Instrum. Meth. B 324, 102–112 (2014).
    [Crossref]
  4. G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic tomography with a priori information,” Appl. Opt. 50, 3685–3690 (2011).
    [Crossref] [PubMed]
  5. R. L. OHalloran, Z. Wen, J. H. Holmes, and S. B. Fain, “Iterative projection reconstruction of time-resolved images using highly-constrained back-projection (hypr),” Magn. Reson. Med. 59, 132–139 (2008).
    [Crossref]
  6. C. A. Mistretta, “Sub-nyquist acquisition and constrained reconstruction in time resolved angiography,” Med. Phys. 38, 2975–2985 (2011).
    [Crossref] [PubMed]
  7. Z. Tian, X. Jia, B. Dong, Y. Lou, and S. B. Jiang, “Low-dose 4DCT reconstruction via temporal nonlocal means,” Med. Phys. 38, 1359 (2011).
    [Crossref] [PubMed]
  8. Y. Shi and W. C. Karl, “Level set methods for dynamic tomography,” in IEEE International Symposium on Biomedical Imaging (2004), pp. 620–623.
  9. S. Dubsky, S. B. Hooper, K. K. W. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9, 2213–2224 (2012).
    [Crossref] [PubMed]
  10. G. 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. Lett. 35, 660–663 (2008).
  11. R. T. Armstrong, A. Georgiadis, H. Ott, D. Klemin, and S. Berg, “Critical capillary number: desaturation studied with fast x-ray computed microtomography,” Geophys. Res. Lett. 41, 55–60 (2014).
    [Crossref]
  12. F. Natterer, The Mathematics of Computerized Tomography (Society for Industrial and Applied Mathematics, 2001).
    [Crossref]
  13. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
    [Crossref]
  14. K. Lange and J. A. Fessler, “Globally convergent algorithms for maximum a posteriori transmission tomography,” IEEE Trans. Image Process. 4, 1430–1438 (1995).
    [Crossref] [PubMed]
  15. C. A. Bouman and K. Sauer, “A unified approach to statistical tomography using coordinate descent optimization,” IEEE Trans. Image Process. 5, 480–492 (1996).
    [Crossref] [PubMed]
  16. S. V. Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and-Play priors for model based reconstruction,” in “IEEE Global Conference on Signal and Information Processing (GlobalSIP)” (2013), pp. 945–948.
  17. G. Myers, M. Geleta, A. Kingston, B. Recur, and A. Sheppard, “Improving dynamic tomography, through maximum a posteriori estimation,” Proc. SPIE,  9212, 921211 (2014).
    [Crossref]
  18. G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic x-ray micro-tomography for real time imaging of drainage and imbibition processes at the pore scale,” in Procedings of the International Symposium of the Society of Core Analysts 20112011, SCA2011–27 (2011).
  19. G. Myers, T. Varslot, A. Kingston, A. Herring, and A. Sheppard, “Ground-truth verification of dynamic x-ray micro-tomography images of fluid displacement,” Proc. SPIE,  8506, 85060P (2012).
    [Crossref]
  20. A. Kingston, A. Sakellariou, T. Varslot, G. R. Myers, and A. Sheppard, “Reliable automatic alignment of tomographic projection data by passive auto-focus,” Med. Phys. 38, 4934 (2011).
    [Crossref] [PubMed]
  21. G. Myers, A. Kingston, T. Varslot, and A. Sheppard, “Extending reference scan drift correction to high-magnification high-cone-angle tomography,” Opt. Lett. 36, 4809–4811 (2011).
    [Crossref] [PubMed]
  22. A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
    [Crossref]
  23. K. J. Batenburg and J. Sijbers, “Adaptive thresholding of tomograms by projection distance minimization,” Pattern Recognition 42, 2297–2305 (2009).
    [Crossref]
  24. J.-B. Thibault, K. D. Sauer, C. A. Bouman, and J. Hsieh, “A three-dimensional statistical approach to improved image quality for multislice helical CT,” Med. Phys. 34, 4526 (2007).
    [Crossref] [PubMed]
  25. W. B. Haines, “Studies in the physical properties of soil. v. the hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith,” J. Agr. Sci. 20, 97–116 (1930).
    [Crossref]
  26. S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
    [Crossref] [PubMed]
  27. D. A. DiCarlo, J. I. G. Cidoncha, and C. Hickey, “Acoustic measurements of pore-scale displacements,” Geophys. Res. Lett. 30, 1901 (2003).
    [Crossref]
  28. R. G. Larson, H. T. Davis, and L. E. Scriven, “Displacement of residual nonwetting fluid from porous media,” Chem. Eng. Sci. 36, 75–85 (1981).
    [Crossref]
  29. K. K. Mohanty, H. T. Davis, and L. E. Scriven, “Physics of oil entrapment in water-wet rock,” SPE Reservoir Eng. 2, 113–128 (1987).
    [Crossref]

2014 (4)

R. T. Armstrong, A. Georgiadis, H. Ott, D. Klemin, and S. Berg, “Critical capillary number: desaturation studied with fast x-ray computed microtomography,” Geophys. Res. Lett. 41, 55–60 (2014).
[Crossref]

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

G. Myers, M. Geleta, A. Kingston, B. Recur, and A. Sheppard, “Improving dynamic tomography, through maximum a posteriori estimation,” Proc. SPIE,  9212, 921211 (2014).
[Crossref]

H. Derluyn, J. Dewanckele, M. N. Boone, V. Cnudde, D. Derome, and J. Carmeliet, “Crystallization of hydrated and anhydrous salts in porous limestone resolved by synchrotron X-ray microtomography,” Nucl. Instrum. Meth. B 324, 102–112 (2014).
[Crossref]

2013 (1)

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

2012 (2)

G. Myers, T. Varslot, A. Kingston, A. Herring, and A. Sheppard, “Ground-truth verification of dynamic x-ray micro-tomography images of fluid displacement,” Proc. SPIE,  8506, 85060P (2012).
[Crossref]

S. Dubsky, S. B. Hooper, K. K. W. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9, 2213–2224 (2012).
[Crossref] [PubMed]

2011 (6)

C. A. Mistretta, “Sub-nyquist acquisition and constrained reconstruction in time resolved angiography,” Med. Phys. 38, 2975–2985 (2011).
[Crossref] [PubMed]

Z. Tian, X. Jia, B. Dong, Y. Lou, and S. B. Jiang, “Low-dose 4DCT reconstruction via temporal nonlocal means,” Med. Phys. 38, 1359 (2011).
[Crossref] [PubMed]

A. Kingston, A. Sakellariou, T. Varslot, G. R. Myers, and A. Sheppard, “Reliable automatic alignment of tomographic projection data by passive auto-focus,” Med. Phys. 38, 4934 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic tomography with a priori information,” Appl. Opt. 50, 3685–3690 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, and A. Sheppard, “Extending reference scan drift correction to high-magnification high-cone-angle tomography,” Opt. Lett. 36, 4809–4811 (2011).
[Crossref] [PubMed]

J. E. Aravena, M. Berli, T. A. Ghezzehei, and S. W. Tyler, “Effects of root-induced compaction on rhizosphere hydraulic properties–X-ray microtomography imaging and numerical simulations,” Environ. Sci. Technol. 45, 425–431 (2011).
[Crossref]

2009 (1)

K. J. Batenburg and J. Sijbers, “Adaptive thresholding of tomograms by projection distance minimization,” Pattern Recognition 42, 2297–2305 (2009).
[Crossref]

2008 (2)

G. 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. Lett. 35, 660–663 (2008).

R. L. OHalloran, Z. Wen, J. H. Holmes, and S. B. Fain, “Iterative projection reconstruction of time-resolved images using highly-constrained back-projection (hypr),” Magn. Reson. Med. 59, 132–139 (2008).
[Crossref]

2007 (1)

J.-B. Thibault, K. D. Sauer, C. A. Bouman, and J. Hsieh, “A three-dimensional statistical approach to improved image quality for multislice helical CT,” Med. Phys. 34, 4526 (2007).
[Crossref] [PubMed]

2003 (1)

D. A. DiCarlo, J. I. G. Cidoncha, and C. Hickey, “Acoustic measurements of pore-scale displacements,” Geophys. Res. Lett. 30, 1901 (2003).
[Crossref]

1996 (1)

C. A. Bouman and K. Sauer, “A unified approach to statistical tomography using coordinate descent optimization,” IEEE Trans. Image Process. 5, 480–492 (1996).
[Crossref] [PubMed]

1995 (1)

K. Lange and J. A. Fessler, “Globally convergent algorithms for maximum a posteriori transmission tomography,” IEEE Trans. Image Process. 4, 1430–1438 (1995).
[Crossref] [PubMed]

1987 (1)

K. K. Mohanty, H. T. Davis, and L. E. Scriven, “Physics of oil entrapment in water-wet rock,” SPE Reservoir Eng. 2, 113–128 (1987).
[Crossref]

1981 (1)

R. G. Larson, H. T. Davis, and L. E. Scriven, “Displacement of residual nonwetting fluid from porous media,” Chem. Eng. Sci. 36, 75–85 (1981).
[Crossref]

1930 (1)

W. B. Haines, “Studies in the physical properties of soil. v. the hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith,” J. Agr. Sci. 20, 97–116 (1930).
[Crossref]

Aravena, J. E.

J. E. Aravena, M. Berli, T. A. Ghezzehei, and S. W. Tyler, “Effects of root-induced compaction on rhizosphere hydraulic properties–X-ray microtomography imaging and numerical simulations,” Environ. Sci. Technol. 45, 425–431 (2011).
[Crossref]

Armstrong, R. T.

R. T. Armstrong, A. Georgiadis, H. Ott, D. Klemin, and S. Berg, “Critical capillary number: desaturation studied with fast x-ray computed microtomography,” Geophys. Res. Lett. 41, 55–60 (2014).
[Crossref]

Arns, C.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

Batenburg, K. J.

K. J. Batenburg and J. Sijbers, “Adaptive thresholding of tomograms by projection distance minimization,” Pattern Recognition 42, 2297–2305 (2009).
[Crossref]

Berg, S.

R. T. Armstrong, A. Georgiadis, H. Ott, D. Klemin, and S. Berg, “Critical capillary number: desaturation studied with fast x-ray computed microtomography,” Geophys. Res. Lett. 41, 55–60 (2014).
[Crossref]

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Berli, M.

J. E. Aravena, M. Berli, T. A. Ghezzehei, and S. W. Tyler, “Effects of root-induced compaction on rhizosphere hydraulic properties–X-ray microtomography imaging and numerical simulations,” Environ. Sci. Technol. 45, 425–431 (2011).
[Crossref]

Boone, M. N.

H. Derluyn, J. Dewanckele, M. N. Boone, V. Cnudde, D. Derome, and J. Carmeliet, “Crystallization of hydrated and anhydrous salts in porous limestone resolved by synchrotron X-ray microtomography,” Nucl. Instrum. Meth. B 324, 102–112 (2014).
[Crossref]

Bouman, C. A.

J.-B. Thibault, K. D. Sauer, C. A. Bouman, and J. Hsieh, “A three-dimensional statistical approach to improved image quality for multislice helical CT,” Med. Phys. 34, 4526 (2007).
[Crossref] [PubMed]

C. A. Bouman and K. Sauer, “A unified approach to statistical tomography using coordinate descent optimization,” IEEE Trans. Image Process. 5, 480–492 (1996).
[Crossref] [PubMed]

S. V. Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and-Play priors for model based reconstruction,” in “IEEE Global Conference on Signal and Information Processing (GlobalSIP)” (2013), pp. 945–948.

Brussee, N.

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Carmeliet, J.

H. Derluyn, J. Dewanckele, M. N. Boone, V. Cnudde, D. Derome, and J. Carmeliet, “Crystallization of hydrated and anhydrous salts in porous limestone resolved by synchrotron X-ray microtomography,” Nucl. Instrum. Meth. B 324, 102–112 (2014).
[Crossref]

Caubit, C.

C. Caubit, G. Hamon, A. P. Sheppard, and P. E. Øren, “Evaluation of the reliability of prediction of petrophysical data through imagery and pore network modelling,” in “22nd International Symposium of the Society of Core Analysts,” (Society of Core Analysts, Abu Dhabi, UAE, 2008). SCA2008-33.

Chen, G.

G. 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. Lett. 35, 660–663 (2008).

Cidoncha, J. I. G.

D. A. DiCarlo, J. I. G. Cidoncha, and C. Hickey, “Acoustic measurements of pore-scale displacements,” Geophys. Res. Lett. 30, 1901 (2003).
[Crossref]

Cnudde, V.

H. Derluyn, J. Dewanckele, M. N. Boone, V. Cnudde, D. Derome, and J. Carmeliet, “Crystallization of hydrated and anhydrous salts in porous limestone resolved by synchrotron X-ray microtomography,” Nucl. Instrum. Meth. B 324, 102–112 (2014).
[Crossref]

Cruikshank, R.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

Davis, H. T.

K. K. Mohanty, H. T. Davis, and L. E. Scriven, “Physics of oil entrapment in water-wet rock,” SPE Reservoir Eng. 2, 113–128 (1987).
[Crossref]

R. G. Larson, H. T. Davis, and L. E. Scriven, “Displacement of residual nonwetting fluid from porous media,” Chem. Eng. Sci. 36, 75–85 (1981).
[Crossref]

Derluyn, H.

H. Derluyn, J. Dewanckele, M. N. Boone, V. Cnudde, D. Derome, and J. Carmeliet, “Crystallization of hydrated and anhydrous salts in porous limestone resolved by synchrotron X-ray microtomography,” Nucl. Instrum. Meth. B 324, 102–112 (2014).
[Crossref]

Derome, D.

H. Derluyn, J. Dewanckele, M. N. Boone, V. Cnudde, D. Derome, and J. Carmeliet, “Crystallization of hydrated and anhydrous salts in porous limestone resolved by synchrotron X-ray microtomography,” Nucl. Instrum. Meth. B 324, 102–112 (2014).
[Crossref]

Dewanckele, J.

H. Derluyn, J. Dewanckele, M. N. Boone, V. Cnudde, D. Derome, and J. Carmeliet, “Crystallization of hydrated and anhydrous salts in porous limestone resolved by synchrotron X-ray microtomography,” Nucl. Instrum. Meth. B 324, 102–112 (2014).
[Crossref]

DiCarlo, D. A.

D. A. DiCarlo, J. I. G. Cidoncha, and C. Hickey, “Acoustic measurements of pore-scale displacements,” Geophys. Res. Lett. 30, 1901 (2003).
[Crossref]

Dong, B.

Z. Tian, X. Jia, B. Dong, Y. Lou, and S. B. Jiang, “Low-dose 4DCT reconstruction via temporal nonlocal means,” Med. Phys. 38, 1359 (2011).
[Crossref] [PubMed]

Dubsky, S.

S. Dubsky, S. B. Hooper, K. K. W. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9, 2213–2224 (2012).
[Crossref] [PubMed]

Enzmann, F.

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Fain, S. B.

R. L. OHalloran, Z. Wen, J. H. Holmes, and S. B. Fain, “Iterative projection reconstruction of time-resolved images using highly-constrained back-projection (hypr),” Magn. Reson. Med. 59, 132–139 (2008).
[Crossref]

Fessler, J. A.

K. Lange and J. A. Fessler, “Globally convergent algorithms for maximum a posteriori transmission tomography,” IEEE Trans. Image Process. 4, 1430–1438 (1995).
[Crossref] [PubMed]

Fogden, A.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

Fouras, A.

S. Dubsky, S. B. Hooper, K. K. W. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9, 2213–2224 (2012).
[Crossref] [PubMed]

Francois, N.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

Geleta, M.

G. Myers, M. Geleta, A. Kingston, B. Recur, and A. Sheppard, “Improving dynamic tomography, through maximum a posteriori estimation,” Proc. SPIE,  9212, 921211 (2014).
[Crossref]

Georgiadis, A.

R. T. Armstrong, A. Georgiadis, H. Ott, D. Klemin, and S. Berg, “Critical capillary number: desaturation studied with fast x-ray computed microtomography,” Geophys. Res. Lett. 41, 55–60 (2014).
[Crossref]

Ghezzehei, T. A.

J. E. Aravena, M. Berli, T. A. Ghezzehei, and S. W. Tyler, “Effects of root-induced compaction on rhizosphere hydraulic properties–X-ray microtomography imaging and numerical simulations,” Environ. Sci. Technol. 45, 425–431 (2011).
[Crossref]

Haines, W. B.

W. B. Haines, “Studies in the physical properties of soil. v. the hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith,” J. Agr. Sci. 20, 97–116 (1930).
[Crossref]

Hamon, G.

C. Caubit, G. Hamon, A. P. Sheppard, and P. E. Øren, “Evaluation of the reliability of prediction of petrophysical data through imagery and pore network modelling,” in “22nd International Symposium of the Society of Core Analysts,” (Society of Core Analysts, Abu Dhabi, UAE, 2008). SCA2008-33.

Herring, A.

G. Myers, T. Varslot, A. Kingston, A. Herring, and A. Sheppard, “Ground-truth verification of dynamic x-ray micro-tomography images of fluid displacement,” Proc. SPIE,  8506, 85060P (2012).
[Crossref]

Hickey, C.

D. A. DiCarlo, J. I. G. Cidoncha, and C. Hickey, “Acoustic measurements of pore-scale displacements,” Geophys. Res. Lett. 30, 1901 (2003).
[Crossref]

Holmes, J. H.

R. L. OHalloran, Z. Wen, J. H. Holmes, and S. B. Fain, “Iterative projection reconstruction of time-resolved images using highly-constrained back-projection (hypr),” Magn. Reson. Med. 59, 132–139 (2008).
[Crossref]

Hooper, S. B.

S. Dubsky, S. B. Hooper, K. K. W. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9, 2213–2224 (2012).
[Crossref] [PubMed]

Hsieh, J.

J.-B. Thibault, K. D. Sauer, C. A. Bouman, and J. Hsieh, “A three-dimensional statistical approach to improved image quality for multislice helical CT,” Med. Phys. 34, 4526 (2007).
[Crossref] [PubMed]

Irvine, S.

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Jia, X.

Z. Tian, X. Jia, B. Dong, Y. Lou, and S. B. Jiang, “Low-dose 4DCT reconstruction via temporal nonlocal means,” Med. Phys. 38, 1359 (2011).
[Crossref] [PubMed]

Jiang, S. B.

Z. Tian, X. Jia, B. Dong, Y. Lou, and S. B. Jiang, “Low-dose 4DCT reconstruction via temporal nonlocal means,” Med. Phys. 38, 1359 (2011).
[Crossref] [PubMed]

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
[Crossref]

Karl, W. C.

Y. Shi and W. C. Karl, “Level set methods for dynamic tomography,” in IEEE International Symposium on Biomedical Imaging (2004), pp. 620–623.

Kersten, M.

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Kingston, A.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

G. Myers, M. Geleta, A. Kingston, B. Recur, and A. Sheppard, “Improving dynamic tomography, through maximum a posteriori estimation,” Proc. SPIE,  9212, 921211 (2014).
[Crossref]

G. Myers, T. Varslot, A. Kingston, A. Herring, and A. Sheppard, “Ground-truth verification of dynamic x-ray micro-tomography images of fluid displacement,” Proc. SPIE,  8506, 85060P (2012).
[Crossref]

A. Kingston, A. Sakellariou, T. Varslot, G. R. Myers, and A. Sheppard, “Reliable automatic alignment of tomographic projection data by passive auto-focus,” Med. Phys. 38, 4934 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic tomography with a priori information,” Appl. Opt. 50, 3685–3690 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, and A. Sheppard, “Extending reference scan drift correction to high-magnification high-cone-angle tomography,” Opt. Lett. 36, 4809–4811 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic x-ray micro-tomography for real time imaging of drainage and imbibition processes at the pore scale,” in Procedings of the International Symposium of the Society of Core Analysts 20112011, SCA2011–27 (2011).

Klapp, S. A.

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Klemin, D.

R. T. Armstrong, A. Georgiadis, H. Ott, D. Klemin, and S. Berg, “Critical capillary number: desaturation studied with fast x-ray computed microtomography,” Geophys. Res. Lett. 41, 55–60 (2014).
[Crossref]

Lange, K.

K. Lange and J. A. Fessler, “Globally convergent algorithms for maximum a posteriori transmission tomography,” IEEE Trans. Image Process. 4, 1430–1438 (1995).
[Crossref] [PubMed]

Larson, R. G.

R. G. Larson, H. T. Davis, and L. E. Scriven, “Displacement of residual nonwetting fluid from porous media,” Chem. Eng. Sci. 36, 75–85 (1981).
[Crossref]

Latham, S.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

Leng, S.

G. 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. Lett. 35, 660–663 (2008).

Leu, L.

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Lou, Y.

Z. Tian, X. Jia, B. Dong, Y. Lou, and S. B. Jiang, “Low-dose 4DCT reconstruction via temporal nonlocal means,” Med. Phys. 38, 1359 (2011).
[Crossref] [PubMed]

Makurat, A.

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Middleton, J.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

Mistretta, C. A.

C. A. Mistretta, “Sub-nyquist acquisition and constrained reconstruction in time resolved angiography,” Med. Phys. 38, 2975–2985 (2011).
[Crossref] [PubMed]

Mohanty, K. K.

K. K. Mohanty, H. T. Davis, and L. E. Scriven, “Physics of oil entrapment in water-wet rock,” SPE Reservoir Eng. 2, 113–128 (1987).
[Crossref]

Myers, G.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

G. Myers, M. Geleta, A. Kingston, B. Recur, and A. Sheppard, “Improving dynamic tomography, through maximum a posteriori estimation,” Proc. SPIE,  9212, 921211 (2014).
[Crossref]

G. Myers, T. Varslot, A. Kingston, A. Herring, and A. Sheppard, “Ground-truth verification of dynamic x-ray micro-tomography images of fluid displacement,” Proc. SPIE,  8506, 85060P (2012).
[Crossref]

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic tomography with a priori information,” Appl. Opt. 50, 3685–3690 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, and A. Sheppard, “Extending reference scan drift correction to high-magnification high-cone-angle tomography,” Opt. Lett. 36, 4809–4811 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic x-ray micro-tomography for real time imaging of drainage and imbibition processes at the pore scale,” in Procedings of the International Symposium of the Society of Core Analysts 20112011, SCA2011–27 (2011).

Myers, G. R.

A. Kingston, A. Sakellariou, T. Varslot, G. R. Myers, and A. Sheppard, “Reliable automatic alignment of tomographic projection data by passive auto-focus,” Med. Phys. 38, 4934 (2011).
[Crossref] [PubMed]

Natterer, F.

F. Natterer, The Mathematics of Computerized Tomography (Society for Industrial and Applied Mathematics, 2001).
[Crossref]

Neiteler, R.

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

OHalloran, R. L.

R. L. OHalloran, Z. Wen, J. H. Holmes, and S. B. Fain, “Iterative projection reconstruction of time-resolved images using highly-constrained back-projection (hypr),” Magn. Reson. Med. 59, 132–139 (2008).
[Crossref]

Øren, P. E.

C. Caubit, G. Hamon, A. P. Sheppard, and P. E. Øren, “Evaluation of the reliability of prediction of petrophysical data through imagery and pore network modelling,” in “22nd International Symposium of the Society of Core Analysts,” (Society of Core Analysts, Abu Dhabi, UAE, 2008). SCA2008-33.

Ott, H.

R. T. Armstrong, A. Georgiadis, H. Ott, D. Klemin, and S. Berg, “Critical capillary number: desaturation studied with fast x-ray computed microtomography,” Geophys. Res. Lett. 41, 55–60 (2014).
[Crossref]

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Recur, B.

G. Myers, M. Geleta, A. Kingston, B. Recur, and A. Sheppard, “Improving dynamic tomography, through maximum a posteriori estimation,” Proc. SPIE,  9212, 921211 (2014).
[Crossref]

Saadatfar, M.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

Sakellariou, A.

A. Kingston, A. Sakellariou, T. Varslot, G. R. Myers, and A. Sheppard, “Reliable automatic alignment of tomographic projection data by passive auto-focus,” Med. Phys. 38, 4934 (2011).
[Crossref] [PubMed]

Sauer, K.

C. A. Bouman and K. Sauer, “A unified approach to statistical tomography using coordinate descent optimization,” IEEE Trans. Image Process. 5, 480–492 (1996).
[Crossref] [PubMed]

Sauer, K. D.

J.-B. Thibault, K. D. Sauer, C. A. Bouman, and J. Hsieh, “A three-dimensional statistical approach to improved image quality for multislice helical CT,” Med. Phys. 34, 4526 (2007).
[Crossref] [PubMed]

Sawkins, T.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

Schwarz, J. O.

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Schwing, A.

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Scriven, L. E.

K. K. Mohanty, H. T. Davis, and L. E. Scriven, “Physics of oil entrapment in water-wet rock,” SPE Reservoir Eng. 2, 113–128 (1987).
[Crossref]

R. G. Larson, H. T. Davis, and L. E. Scriven, “Displacement of residual nonwetting fluid from porous media,” Chem. Eng. Sci. 36, 75–85 (1981).
[Crossref]

Senden, T.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

Sheppard, A.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

G. Myers, M. Geleta, A. Kingston, B. Recur, and A. Sheppard, “Improving dynamic tomography, through maximum a posteriori estimation,” Proc. SPIE,  9212, 921211 (2014).
[Crossref]

G. Myers, T. Varslot, A. Kingston, A. Herring, and A. Sheppard, “Ground-truth verification of dynamic x-ray micro-tomography images of fluid displacement,” Proc. SPIE,  8506, 85060P (2012).
[Crossref]

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic tomography with a priori information,” Appl. Opt. 50, 3685–3690 (2011).
[Crossref] [PubMed]

A. Kingston, A. Sakellariou, T. Varslot, G. R. Myers, and A. Sheppard, “Reliable automatic alignment of tomographic projection data by passive auto-focus,” Med. Phys. 38, 4934 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, and A. Sheppard, “Extending reference scan drift correction to high-magnification high-cone-angle tomography,” Opt. Lett. 36, 4809–4811 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic x-ray micro-tomography for real time imaging of drainage and imbibition processes at the pore scale,” in Procedings of the International Symposium of the Society of Core Analysts 20112011, SCA2011–27 (2011).

Sheppard, A. P.

C. Caubit, G. Hamon, A. P. Sheppard, and P. E. Øren, “Evaluation of the reliability of prediction of petrophysical data through imagery and pore network modelling,” in “22nd International Symposium of the Society of Core Analysts,” (Society of Core Analysts, Abu Dhabi, UAE, 2008). SCA2008-33.

Shi, Y.

Y. Shi and W. C. Karl, “Level set methods for dynamic tomography,” in IEEE International Symposium on Biomedical Imaging (2004), pp. 620–623.

Sijbers, J.

K. J. Batenburg and J. Sijbers, “Adaptive thresholding of tomograms by projection distance minimization,” Pattern Recognition 42, 2297–2305 (2009).
[Crossref]

Siu, K. K. W.

S. Dubsky, S. B. Hooper, K. K. W. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9, 2213–2224 (2012).
[Crossref] [PubMed]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
[Crossref]

Stampanoni, M.

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Tang, J.

G. 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. Lett. 35, 660–663 (2008).

Thibault, J.-B.

J.-B. Thibault, K. D. Sauer, C. A. Bouman, and J. Hsieh, “A three-dimensional statistical approach to improved image quality for multislice helical CT,” Med. Phys. 34, 4526 (2007).
[Crossref] [PubMed]

Tian, Z.

Z. Tian, X. Jia, B. Dong, Y. Lou, and S. B. Jiang, “Low-dose 4DCT reconstruction via temporal nonlocal means,” Med. Phys. 38, 1359 (2011).
[Crossref] [PubMed]

Turner, M.

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic tomography with a priori information,” Appl. Opt. 50, 3685–3690 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic x-ray micro-tomography for real time imaging of drainage and imbibition processes at the pore scale,” in Procedings of the International Symposium of the Society of Core Analysts 20112011, SCA2011–27 (2011).

Tyler, S. W.

J. E. Aravena, M. Berli, T. A. Ghezzehei, and S. W. Tyler, “Effects of root-induced compaction on rhizosphere hydraulic properties–X-ray microtomography imaging and numerical simulations,” Environ. Sci. Technol. 45, 425–431 (2011).
[Crossref]

Varslot, T.

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

G. Myers, T. Varslot, A. Kingston, A. Herring, and A. Sheppard, “Ground-truth verification of dynamic x-ray micro-tomography images of fluid displacement,” Proc. SPIE,  8506, 85060P (2012).
[Crossref]

A. Kingston, A. Sakellariou, T. Varslot, G. R. Myers, and A. Sheppard, “Reliable automatic alignment of tomographic projection data by passive auto-focus,” Med. Phys. 38, 4934 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic tomography with a priori information,” Appl. Opt. 50, 3685–3690 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, and A. Sheppard, “Extending reference scan drift correction to high-magnification high-cone-angle tomography,” Opt. Lett. 36, 4809–4811 (2011).
[Crossref] [PubMed]

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic x-ray micro-tomography for real time imaging of drainage and imbibition processes at the pore scale,” in Procedings of the International Symposium of the Society of Core Analysts 20112011, SCA2011–27 (2011).

Venkatakrishnan, S. V.

S. V. Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and-Play priors for model based reconstruction,” in “IEEE Global Conference on Signal and Information Processing (GlobalSIP)” (2013), pp. 945–948.

Wen, Z.

R. L. OHalloran, Z. Wen, J. H. Holmes, and S. B. Fain, “Iterative projection reconstruction of time-resolved images using highly-constrained back-projection (hypr),” Magn. Reson. Med. 59, 132–139 (2008).
[Crossref]

Wohlberg, B.

S. V. Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and-Play priors for model based reconstruction,” in “IEEE Global Conference on Signal and Information Processing (GlobalSIP)” (2013), pp. 945–948.

Appl. Opt. (1)

Chem. Eng. Sci. (1)

R. G. Larson, H. T. Davis, and L. E. Scriven, “Displacement of residual nonwetting fluid from porous media,” Chem. Eng. Sci. 36, 75–85 (1981).
[Crossref]

Environ. Sci. Technol. (1)

J. E. Aravena, M. Berli, T. A. Ghezzehei, and S. W. Tyler, “Effects of root-induced compaction on rhizosphere hydraulic properties–X-ray microtomography imaging and numerical simulations,” Environ. Sci. Technol. 45, 425–431 (2011).
[Crossref]

Geophys. Res. Lett. (2)

R. T. Armstrong, A. Georgiadis, H. Ott, D. Klemin, and S. Berg, “Critical capillary number: desaturation studied with fast x-ray computed microtomography,” Geophys. Res. Lett. 41, 55–60 (2014).
[Crossref]

D. A. DiCarlo, J. I. G. Cidoncha, and C. Hickey, “Acoustic measurements of pore-scale displacements,” Geophys. Res. Lett. 30, 1901 (2003).
[Crossref]

IEEE Trans. Image Process. (2)

K. Lange and J. A. Fessler, “Globally convergent algorithms for maximum a posteriori transmission tomography,” IEEE Trans. Image Process. 4, 1430–1438 (1995).
[Crossref] [PubMed]

C. A. Bouman and K. Sauer, “A unified approach to statistical tomography using coordinate descent optimization,” IEEE Trans. Image Process. 5, 480–492 (1996).
[Crossref] [PubMed]

J. Agr. Sci. (1)

W. B. Haines, “Studies in the physical properties of soil. v. the hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith,” J. Agr. Sci. 20, 97–116 (1930).
[Crossref]

J. R. Soc. Interface (1)

S. Dubsky, S. B. Hooper, K. K. W. Siu, and A. Fouras, “Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement,” J. R. Soc. Interface 9, 2213–2224 (2012).
[Crossref] [PubMed]

Magn. Reson. Med. (1)

R. L. OHalloran, Z. Wen, J. H. Holmes, and S. B. Fain, “Iterative projection reconstruction of time-resolved images using highly-constrained back-projection (hypr),” Magn. Reson. Med. 59, 132–139 (2008).
[Crossref]

Med. Phys. (4)

C. A. Mistretta, “Sub-nyquist acquisition and constrained reconstruction in time resolved angiography,” Med. Phys. 38, 2975–2985 (2011).
[Crossref] [PubMed]

Z. Tian, X. Jia, B. Dong, Y. Lou, and S. B. Jiang, “Low-dose 4DCT reconstruction via temporal nonlocal means,” Med. Phys. 38, 1359 (2011).
[Crossref] [PubMed]

J.-B. Thibault, K. D. Sauer, C. A. Bouman, and J. Hsieh, “A three-dimensional statistical approach to improved image quality for multislice helical CT,” Med. Phys. 34, 4526 (2007).
[Crossref] [PubMed]

A. Kingston, A. Sakellariou, T. Varslot, G. R. Myers, and A. Sheppard, “Reliable automatic alignment of tomographic projection data by passive auto-focus,” Med. Phys. 38, 4934 (2011).
[Crossref] [PubMed]

Med. Phys. Lett. (1)

G. 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. Lett. 35, 660–663 (2008).

Nucl. Instrum. Meth. B (2)

H. Derluyn, J. Dewanckele, M. N. Boone, V. Cnudde, D. Derome, and J. Carmeliet, “Crystallization of hydrated and anhydrous salts in porous limestone resolved by synchrotron X-ray microtomography,” Nucl. Instrum. Meth. B 324, 102–112 (2014).
[Crossref]

A. Sheppard, S. Latham, J. Middleton, A. Kingston, G. Myers, T. Varslot, A. Fogden, T. Sawkins, R. Cruikshank, M. Saadatfar, N. Francois, C. Arns, and T. Senden, “Techniques in helical scanning, dynamic imaging and image segmentation for improved quantitative analysis with x-ray micro-ct,” Nucl. Instrum. Meth. B 324, 49–56 (2014).
[Crossref]

Opt. Lett. (1)

Pattern Recognition (1)

K. J. Batenburg and J. Sijbers, “Adaptive thresholding of tomograms by projection distance minimization,” Pattern Recognition 42, 2297–2305 (2009).
[Crossref]

Proc. Nat. Acad. Sci. (1)

S. Berg, H. Ott, S. A. Klapp, A. Schwing, R. Neiteler, N. Brussee, A. Makurat, L. Leu, F. Enzmann, J. O. Schwarz, M. Kersten, S. Irvine, and M. Stampanoni, “Real-time 3d imaging of haines jumps in porous media flow,” Proc. Nat. Acad. Sci. 110, 3755–3759 (2013).
[Crossref] [PubMed]

Proc. SPIE (2)

G. Myers, M. Geleta, A. Kingston, B. Recur, and A. Sheppard, “Improving dynamic tomography, through maximum a posteriori estimation,” Proc. SPIE,  9212, 921211 (2014).
[Crossref]

G. Myers, T. Varslot, A. Kingston, A. Herring, and A. Sheppard, “Ground-truth verification of dynamic x-ray micro-tomography images of fluid displacement,” Proc. SPIE,  8506, 85060P (2012).
[Crossref]

SPE Reservoir Eng. (1)

K. K. Mohanty, H. T. Davis, and L. E. Scriven, “Physics of oil entrapment in water-wet rock,” SPE Reservoir Eng. 2, 113–128 (1987).
[Crossref]

Other (6)

C. Caubit, G. Hamon, A. P. Sheppard, and P. E. Øren, “Evaluation of the reliability of prediction of petrophysical data through imagery and pore network modelling,” in “22nd International Symposium of the Society of Core Analysts,” (Society of Core Analysts, Abu Dhabi, UAE, 2008). SCA2008-33.

G. Myers, A. Kingston, T. Varslot, M. Turner, and A. Sheppard, “Dynamic x-ray micro-tomography for real time imaging of drainage and imbibition processes at the pore scale,” in Procedings of the International Symposium of the Society of Core Analysts 20112011, SCA2011–27 (2011).

S. V. Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and-Play priors for model based reconstruction,” in “IEEE Global Conference on Signal and Information Processing (GlobalSIP)” (2013), pp. 945–948.

F. Natterer, The Mathematics of Computerized Tomography (Society for Industrial and Applied Mathematics, 2001).
[Crossref]

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001).
[Crossref]

Y. Shi and W. C. Karl, “Level set methods for dynamic tomography,” in IEEE International Symposium on Biomedical Imaging (2004), pp. 620–623.

Supplementary Material (2)

NameDescription
» Visualization 1: MP4 (9702 KB)      Ground-truth FBP reconstruction.
» Visualization 2: MP4 (7695 KB)      Bayesian reconstruction, from 10x under-sampled data.

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Figures (4)

Fig. 1
Fig. 1 3D renderings of five sequential volume frames (proceeding top-to-bottom). Each frame is calculated as a difference image between the initial and current reconstructed states of the sample [i.e. μ(x, t)]: in a drainage experiment this difference is primarily due to air infiltrating the pore space. The middle column shows the results of the reference FBP reconstruction ( Visualization 1). The left column shows the reconstruction produced by our empirical SIRT-based algorithm [4]. The right column shows reconstructions performed using Eq. (5) ( Visualization 2).
Fig. 2
Fig. 2 Reconstructed 2D (right) and 3D (left) slices through a Bentheimer sandstone during drainage, calculated as a difference image between the initial and current reconstructed states of the sample [i.e. μ(x, t)]. 2D slices are a 480×400 pixels (6.7×5.6mm), taken normal to the rotation axis. Middle row: a reference reconstruction from full data, using FBP. In the upper right is a pore which displays partial volume effects. This violates our assumption that the rock is present at only a single grey level. Top row: reconstruction from every 10th viewing angle, using an empirical SIRT-based 2-phase flow algorithm [4]. Bottom row: reconstruction from every 10th viewing angle, using MLTR-like algorithm [Eq. (5)]. Note successful reconstruction of partial volume effects.
Fig. 3
Fig. 3 Left: a 292×292 pixel slice through the synthetic 420-pixel diameter, 4-material object, taken normal to the rotation axis when the time-evolution was roughly 50% complete. The immobile rock phase is in dark grey, and the three mobile fluid phases are black, light grey and white respectively. Right: a time-resolved reconstruction from simulated data, using 72 radiographs per time-step. The majority of thin-film structures are correctly reconstructed.
Fig. 4
Fig. 4 3D renderings showing the time-evolution of the slice shown in figure 3. Time evolution occurs along the vertical axis, proceeding from bottom to top. The two non-air fluid phases are rendered in brown and red respectively. Left: the numerical phantom used to generate the data. Right: a time-resolved reconstruction from simulated data, using 72 radiographs per time-step.

Equations (15)

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μ ^ ( x , t T μ ) = argmax μ ( x , t T μ ) P [ μ ( x , t T μ ) | I ( r , θ , t T i ) , μ s ( x ) ] .
f ( n ) ( μ | μ ( n ) , I , μ s ) = τ m P ( τ , m | μ ( n ) , I , μ s ) ln [ P ( τ , m , I , μ s | μ ) ] , μ ( n + 1 ) = argmax μ [ f ( n ) ( μ | μ ( n ) , I , μ s ) + ln [ P ( μ ) ] ] ,
μ ( n + 1 ) = argmax μ τ P ( τ | I , μ ( n ) ) ln [ P ( I | τ , μ ) ] + τ P ( τ | I , μ ( n ) ) ln [ P ( τ | μ ) ] + m P ( m | μ s , μ ( n ) ) ln [ P ( m | μ s , μ ) ] + ln [ P ( μ s | μ ) ] + ln [ P ( μ ) ] ,
P [ I ( r , θ , t 0 T i ) | τ ( t 0 , t 1 T μ ) , μ ( x , t T μ ) ] { I s ( r , θ ) exp [ ( 𝒫 θ μ ) ( r , t 1 ) ] } I s ( r , θ ) I ( r , θ , t 0 ) [ I s ( r , θ ) I ( r , θ , t 0 ) ] ! × exp { I s ( r , θ ) exp [ ( 𝒫 θ μ ) ( r , t 1 ) ] } ,
I s ( r , θ ) exp [ ( 𝒫 θ μ s ) ( r ) ] .
P [ τ ( t 0 T i , t 1 T μ ) | I , μ ( n ) ] = Γ ( t 0 , t 1 ) , 1 Γ ( t 0 , t 1 ) | t 0 t 1 | , if t 0 and t 1 are not separated by a large Haines jump , Γ ( t 0 , t 1 ) = 0 , otherwise .
P [ m | μ s , μ ( n ) ] exp [ ( μ s μ rock ) 2 2 σ s 2 μ ( n ) 2 2 σ 2 ] , if m = rock , exp [ μ s 2 2 σ s 2 ( μ ( n ) μ m ) 2 2 σ 2 ] , otherwise .
ln P ( μ s | μ ) μ 2 2 σ 2 exp [ ( μ s μ rock ) 2 2 σ s 2 ] .
P [ μ ( x , t T μ ) ] exp [ | μ ( x , t T μ ) | a ] .
μ ( n : l + 0.5 ) ( x , t 1 T μ ) = μ ( n : l ) ( x , t 1 ) α 1 t 0 T i Γ ( t 0 , t 1 ) { I s ( r , θ ) [ I ( r , θ , t 0 ) t 1 T μ Γ ( t 0 , t 1 ) e ( P θ μ ( n : l ) ) ( r , t 1 ) } α 2 μ σ 2 exp [ ( μ s μ rock ) 2 2 σ s 2 μ ( n ) 2 2 σ 2 ] α 3 μ σ 2 exp [ ( μ s μ rock ) 2 2 σ s 2 ] . α 2 m rock μ μ m σ 2 exp [ μ s 2 2 σ s 2 ( μ ( n ) μ m ) 2 2 σ 2 ] .
μ ( n : l + 1 ) ( x , t 1 T μ ) = [ 𝒯 μ ( n : l + 0.5 ) ] ( x , t 1 ) .
μ ( n + 1 : l = 0 ) ( x , t 1 T μ ) = μ ( n : l ) ( x , t 1 T μ )
P [ I ( r , θ , t 0 T i ) | τ ( t 0 , t 1 T μ ) , μ ( x , t T μ ) ] exp { [ ln I ( r , θ , t 0 ) ( 𝒫 θ μ ) ( r , t 1 ) ] 2 2 σ 2 } ,
P [ τ ( t 0 T i , t 1 T μ ) | I , μ ( n ) ] max ( 0 , Δ | t 1 t 0 | ) .
ln [ P ( μ s | μ ) ] + m P [ m | μ s , μ ( n ) ] ln [ P ( m | μ s , μ ) ] μ ( x , t T μ ) 2 , if x Ω or μ ( x , t T μ ) < ε , { Ω μ ( x , t T μ ) d x d t Ω d x d t μ ( x , t T μ ) } 2 , otherwise .

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