Abstract

In X-ray imaging, it is common practice to normalize the acquired projection data with averaged flat fields taken prior to the scan. Unfortunately, due to source instabilities, vibrating beamline components such as the monochromator, time varying detector properties, or other confounding factors, flat fields are often far from stationary, resulting in significant systematic errors in intensity normalization. In this work, a simple and efficient method is proposed to account for dynamically varying flat fields. Through principal component analysis of a set of flat fields, eigen flat fields are computed. A linear combination of the most important eigen flat fields is then used to individually normalize each X-ray projection. Experiments show that the proposed dynamic flat field correction leads to a substantial reduction of systematic errors in projection intensity normalization compared to conventional flat field correction.

© 2015 Optical Society of America

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References

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  1. L. Tlustos, M. Campbell, E. Heijne, and X. Llopart, “Signal variations in high-granularity Si pixel detectors,” IEEE Trans. Nucl. Sci 51, 3006–3012 (2004).
    [Crossref]
  2. J. Sijbers and A. Postnov, “Reduction of ring artefacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49, N247–N253 (2004).
    [Crossref] [PubMed]
  3. M. Boin and A. Haibel, “Compensation of ring artefacts in synchrotron tomographic images,” Opt. Express 14, 12071–12075 (2006).
    [Crossref] [PubMed]
  4. B. Münch, P. Trtik, F. Marone, and M. Stampanoni, “Stripe and ring artifact removal with combined wavelet-Fourier filtering,” Opt. Express 17, 8567–8591 (2009).
    [Crossref]
  5. J. Baek, B. De Man, D. Harrison, and N. J. Pelc, “Raw data normalization for a multi source inverse geometry CT system,” Opt. Express 23, 7514–7526 (2015).
    [Crossref] [PubMed]
  6. S. R. Stock, Micro Computed Tomography: Methodology and Applications (CRC Press, 2008).
    [Crossref]
  7. R. Tucoulou, G. Martinez-Criado, P. Bleuet, I. Kieffer, P. Cloetens, S. Labouré, T. Martin, C. Guilloud, and J. Susini, “High-resolution angular beam stability monitoring at a nanofocusing beamline,” J. Synchrotron Radiat. 15, 392–398 (2008).
    [Crossref] [PubMed]
  8. V. Titarenko, S. Titarenko, P. J. Withers, F. De Carlo, and X. Xiao, “Improved tomographic reconstructions using adaptive time-dependent intensity normalization,” J. Synchrotron Radiat. 17, 689–699 (2010).
    [Crossref] [PubMed]
  9. J. M. Bauer, J. C. Liu, A. A. Prinz, and S. H. Rokni, “Experiences from first top-off injection at the stanford synchrotron radiation lightsource,” in “5th International Workshop on Radiation Safety at Synchrotron Radiation Sources,” (2009).
  10. S. E. Park, J. G. Kim, M. A. A. Hegazy, M. H. Cho, and S. Y. Lee, “A flat-field correction method for photon-counting-detector-based micro-CT,” Proc. SPIE 9033, 90335 (2014).
    [Crossref]
  11. I. Jolliffe, Principal Component Analysis, 2nd ed. (Springer, 2002).
  12. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
    [Crossref]
  13. M. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cognitive Neurosci. 3, 71–86 (1991).
    [Crossref]
  14. R. B. Cattell, “The scree test for the number of factors,” Multivar. Behav. Res. 1, 245–276 (1966).
    [Crossref]
  15. S. B. Franklin, D. J. Gibson, P. A. Robertson, J. T. Pohlmann, and J. S. Fralish, “Parallel analysis: a method for determining significant principal components,” J. Veg. Sci. 6, 99–106 (1995).
    [Crossref]
  16. K. Dabov and A. Foi, “Image denoising with block-matching and 3D filtering,” Proc. SPIE 6064, 6064A (2006).
  17. D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comput. 24, 647–656 (1970).
    [Crossref]
  18. F. Natterer, The Mathematics of Computerized Tomography (Society for Industrial and Applied Mathematics, 2001).
    [Crossref]
  19. W. J. Palenstijn, K. J. Batenburg, and J. Sijbers, “Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs),” J. Struct. Biol. 176, 250–253 (2011).
    [Crossref] [PubMed]
  20. F. Bleichrodt, T. van Leeuwen, W. J. Palenstijn, W. Van Aarle, J. Sijbers, and K. J. Batenburg, “Easy implementation of advanced tomography algorithms using the astra toolbox with spot operators,” Numer. Algorithms (to be published).
  21. W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA toolbox: a platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
    [Crossref] [PubMed]
  22. A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 60–65.

2015 (2)

J. Baek, B. De Man, D. Harrison, and N. J. Pelc, “Raw data normalization for a multi source inverse geometry CT system,” Opt. Express 23, 7514–7526 (2015).
[Crossref] [PubMed]

W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA toolbox: a platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref] [PubMed]

2014 (1)

S. E. Park, J. G. Kim, M. A. A. Hegazy, M. H. Cho, and S. Y. Lee, “A flat-field correction method for photon-counting-detector-based micro-CT,” Proc. SPIE 9033, 90335 (2014).
[Crossref]

2011 (1)

W. J. Palenstijn, K. J. Batenburg, and J. Sijbers, “Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs),” J. Struct. Biol. 176, 250–253 (2011).
[Crossref] [PubMed]

2010 (1)

V. Titarenko, S. Titarenko, P. J. Withers, F. De Carlo, and X. Xiao, “Improved tomographic reconstructions using adaptive time-dependent intensity normalization,” J. Synchrotron Radiat. 17, 689–699 (2010).
[Crossref] [PubMed]

2009 (1)

2008 (1)

R. Tucoulou, G. Martinez-Criado, P. Bleuet, I. Kieffer, P. Cloetens, S. Labouré, T. Martin, C. Guilloud, and J. Susini, “High-resolution angular beam stability monitoring at a nanofocusing beamline,” J. Synchrotron Radiat. 15, 392–398 (2008).
[Crossref] [PubMed]

2006 (2)

K. Dabov and A. Foi, “Image denoising with block-matching and 3D filtering,” Proc. SPIE 6064, 6064A (2006).

M. Boin and A. Haibel, “Compensation of ring artefacts in synchrotron tomographic images,” Opt. Express 14, 12071–12075 (2006).
[Crossref] [PubMed]

2004 (2)

L. Tlustos, M. Campbell, E. Heijne, and X. Llopart, “Signal variations in high-granularity Si pixel detectors,” IEEE Trans. Nucl. Sci 51, 3006–3012 (2004).
[Crossref]

J. Sijbers and A. Postnov, “Reduction of ring artefacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49, N247–N253 (2004).
[Crossref] [PubMed]

1995 (1)

S. B. Franklin, D. J. Gibson, P. A. Robertson, J. T. Pohlmann, and J. S. Fralish, “Parallel analysis: a method for determining significant principal components,” J. Veg. Sci. 6, 99–106 (1995).
[Crossref]

1992 (1)

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

1991 (1)

M. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cognitive Neurosci. 3, 71–86 (1991).
[Crossref]

1970 (1)

D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comput. 24, 647–656 (1970).
[Crossref]

1966 (1)

R. B. Cattell, “The scree test for the number of factors,” Multivar. Behav. Res. 1, 245–276 (1966).
[Crossref]

Altantzis, T.

W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA toolbox: a platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref] [PubMed]

Baek, J.

Bals, S.

W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA toolbox: a platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref] [PubMed]

Batenburg, K. J.

W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA toolbox: a platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref] [PubMed]

W. J. Palenstijn, K. J. Batenburg, and J. Sijbers, “Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs),” J. Struct. Biol. 176, 250–253 (2011).
[Crossref] [PubMed]

F. Bleichrodt, T. van Leeuwen, W. J. Palenstijn, W. Van Aarle, J. Sijbers, and K. J. Batenburg, “Easy implementation of advanced tomography algorithms using the astra toolbox with spot operators,” Numer. Algorithms (to be published).

Bauer, J. M.

J. M. Bauer, J. C. Liu, A. A. Prinz, and S. H. Rokni, “Experiences from first top-off injection at the stanford synchrotron radiation lightsource,” in “5th International Workshop on Radiation Safety at Synchrotron Radiation Sources,” (2009).

Bleichrodt, F.

F. Bleichrodt, T. van Leeuwen, W. J. Palenstijn, W. Van Aarle, J. Sijbers, and K. J. Batenburg, “Easy implementation of advanced tomography algorithms using the astra toolbox with spot operators,” Numer. Algorithms (to be published).

Bleuet, P.

R. Tucoulou, G. Martinez-Criado, P. Bleuet, I. Kieffer, P. Cloetens, S. Labouré, T. Martin, C. Guilloud, and J. Susini, “High-resolution angular beam stability monitoring at a nanofocusing beamline,” J. Synchrotron Radiat. 15, 392–398 (2008).
[Crossref] [PubMed]

Boin, M.

Buades, A.

A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 60–65.

Campbell, M.

L. Tlustos, M. Campbell, E. Heijne, and X. Llopart, “Signal variations in high-granularity Si pixel detectors,” IEEE Trans. Nucl. Sci 51, 3006–3012 (2004).
[Crossref]

Cattell, R. B.

R. B. Cattell, “The scree test for the number of factors,” Multivar. Behav. Res. 1, 245–276 (1966).
[Crossref]

Cho, M. H.

S. E. Park, J. G. Kim, M. A. A. Hegazy, M. H. Cho, and S. Y. Lee, “A flat-field correction method for photon-counting-detector-based micro-CT,” Proc. SPIE 9033, 90335 (2014).
[Crossref]

Cloetens, P.

R. Tucoulou, G. Martinez-Criado, P. Bleuet, I. Kieffer, P. Cloetens, S. Labouré, T. Martin, C. Guilloud, and J. Susini, “High-resolution angular beam stability monitoring at a nanofocusing beamline,” J. Synchrotron Radiat. 15, 392–398 (2008).
[Crossref] [PubMed]

Coll, B.

A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 60–65.

Dabov, K.

K. Dabov and A. Foi, “Image denoising with block-matching and 3D filtering,” Proc. SPIE 6064, 6064A (2006).

De Beenhouwer, J.

W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA toolbox: a platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref] [PubMed]

De Carlo, F.

V. Titarenko, S. Titarenko, P. J. Withers, F. De Carlo, and X. Xiao, “Improved tomographic reconstructions using adaptive time-dependent intensity normalization,” J. Synchrotron Radiat. 17, 689–699 (2010).
[Crossref] [PubMed]

De Man, B.

Fatemi, E.

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

Foi, A.

K. Dabov and A. Foi, “Image denoising with block-matching and 3D filtering,” Proc. SPIE 6064, 6064A (2006).

Fralish, J. S.

S. B. Franklin, D. J. Gibson, P. A. Robertson, J. T. Pohlmann, and J. S. Fralish, “Parallel analysis: a method for determining significant principal components,” J. Veg. Sci. 6, 99–106 (1995).
[Crossref]

Franklin, S. B.

S. B. Franklin, D. J. Gibson, P. A. Robertson, J. T. Pohlmann, and J. S. Fralish, “Parallel analysis: a method for determining significant principal components,” J. Veg. Sci. 6, 99–106 (1995).
[Crossref]

Gibson, D. J.

S. B. Franklin, D. J. Gibson, P. A. Robertson, J. T. Pohlmann, and J. S. Fralish, “Parallel analysis: a method for determining significant principal components,” J. Veg. Sci. 6, 99–106 (1995).
[Crossref]

Guilloud, C.

R. Tucoulou, G. Martinez-Criado, P. Bleuet, I. Kieffer, P. Cloetens, S. Labouré, T. Martin, C. Guilloud, and J. Susini, “High-resolution angular beam stability monitoring at a nanofocusing beamline,” J. Synchrotron Radiat. 15, 392–398 (2008).
[Crossref] [PubMed]

Haibel, A.

Harrison, D.

Hegazy, M. A. A.

S. E. Park, J. G. Kim, M. A. A. Hegazy, M. H. Cho, and S. Y. Lee, “A flat-field correction method for photon-counting-detector-based micro-CT,” Proc. SPIE 9033, 90335 (2014).
[Crossref]

Heijne, E.

L. Tlustos, M. Campbell, E. Heijne, and X. Llopart, “Signal variations in high-granularity Si pixel detectors,” IEEE Trans. Nucl. Sci 51, 3006–3012 (2004).
[Crossref]

Jolliffe, I.

I. Jolliffe, Principal Component Analysis, 2nd ed. (Springer, 2002).

Kieffer, I.

R. Tucoulou, G. Martinez-Criado, P. Bleuet, I. Kieffer, P. Cloetens, S. Labouré, T. Martin, C. Guilloud, and J. Susini, “High-resolution angular beam stability monitoring at a nanofocusing beamline,” J. Synchrotron Radiat. 15, 392–398 (2008).
[Crossref] [PubMed]

Kim, J. G.

S. E. Park, J. G. Kim, M. A. A. Hegazy, M. H. Cho, and S. Y. Lee, “A flat-field correction method for photon-counting-detector-based micro-CT,” Proc. SPIE 9033, 90335 (2014).
[Crossref]

Labouré, S.

R. Tucoulou, G. Martinez-Criado, P. Bleuet, I. Kieffer, P. Cloetens, S. Labouré, T. Martin, C. Guilloud, and J. Susini, “High-resolution angular beam stability monitoring at a nanofocusing beamline,” J. Synchrotron Radiat. 15, 392–398 (2008).
[Crossref] [PubMed]

Lee, S. Y.

S. E. Park, J. G. Kim, M. A. A. Hegazy, M. H. Cho, and S. Y. Lee, “A flat-field correction method for photon-counting-detector-based micro-CT,” Proc. SPIE 9033, 90335 (2014).
[Crossref]

Liu, J. C.

J. M. Bauer, J. C. Liu, A. A. Prinz, and S. H. Rokni, “Experiences from first top-off injection at the stanford synchrotron radiation lightsource,” in “5th International Workshop on Radiation Safety at Synchrotron Radiation Sources,” (2009).

Llopart, X.

L. Tlustos, M. Campbell, E. Heijne, and X. Llopart, “Signal variations in high-granularity Si pixel detectors,” IEEE Trans. Nucl. Sci 51, 3006–3012 (2004).
[Crossref]

Marone, F.

Martin, T.

R. Tucoulou, G. Martinez-Criado, P. Bleuet, I. Kieffer, P. Cloetens, S. Labouré, T. Martin, C. Guilloud, and J. Susini, “High-resolution angular beam stability monitoring at a nanofocusing beamline,” J. Synchrotron Radiat. 15, 392–398 (2008).
[Crossref] [PubMed]

Martinez-Criado, G.

R. Tucoulou, G. Martinez-Criado, P. Bleuet, I. Kieffer, P. Cloetens, S. Labouré, T. Martin, C. Guilloud, and J. Susini, “High-resolution angular beam stability monitoring at a nanofocusing beamline,” J. Synchrotron Radiat. 15, 392–398 (2008).
[Crossref] [PubMed]

Morel, J.-M.

A. Buades, B. Coll, and J.-M. Morel, “A non-local algorithm for image denoising,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 60–65.

Münch, B.

Natterer, F.

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

Osher, S.

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

Palenstijn, W. J.

W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA toolbox: a platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref] [PubMed]

W. J. Palenstijn, K. J. Batenburg, and J. Sijbers, “Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs),” J. Struct. Biol. 176, 250–253 (2011).
[Crossref] [PubMed]

F. Bleichrodt, T. van Leeuwen, W. J. Palenstijn, W. Van Aarle, J. Sijbers, and K. J. Batenburg, “Easy implementation of advanced tomography algorithms using the astra toolbox with spot operators,” Numer. Algorithms (to be published).

Park, S. E.

S. E. Park, J. G. Kim, M. A. A. Hegazy, M. H. Cho, and S. Y. Lee, “A flat-field correction method for photon-counting-detector-based micro-CT,” Proc. SPIE 9033, 90335 (2014).
[Crossref]

Pelc, N. J.

Pentland, A.

M. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cognitive Neurosci. 3, 71–86 (1991).
[Crossref]

Pohlmann, J. T.

S. B. Franklin, D. J. Gibson, P. A. Robertson, J. T. Pohlmann, and J. S. Fralish, “Parallel analysis: a method for determining significant principal components,” J. Veg. Sci. 6, 99–106 (1995).
[Crossref]

Postnov, A.

J. Sijbers and A. Postnov, “Reduction of ring artefacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49, N247–N253 (2004).
[Crossref] [PubMed]

Prinz, A. A.

J. M. Bauer, J. C. Liu, A. A. Prinz, and S. H. Rokni, “Experiences from first top-off injection at the stanford synchrotron radiation lightsource,” in “5th International Workshop on Radiation Safety at Synchrotron Radiation Sources,” (2009).

Robertson, P. A.

S. B. Franklin, D. J. Gibson, P. A. Robertson, J. T. Pohlmann, and J. S. Fralish, “Parallel analysis: a method for determining significant principal components,” J. Veg. Sci. 6, 99–106 (1995).
[Crossref]

Rokni, S. H.

J. M. Bauer, J. C. Liu, A. A. Prinz, and S. H. Rokni, “Experiences from first top-off injection at the stanford synchrotron radiation lightsource,” in “5th International Workshop on Radiation Safety at Synchrotron Radiation Sources,” (2009).

Rudin, L. I.

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

Shanno, D. F.

D. F. Shanno, “Conditioning of quasi-Newton methods for function minimization,” Math. Comput. 24, 647–656 (1970).
[Crossref]

Sijbers, J.

W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA toolbox: a platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref] [PubMed]

W. J. Palenstijn, K. J. Batenburg, and J. Sijbers, “Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs),” J. Struct. Biol. 176, 250–253 (2011).
[Crossref] [PubMed]

J. Sijbers and A. Postnov, “Reduction of ring artefacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49, N247–N253 (2004).
[Crossref] [PubMed]

F. Bleichrodt, T. van Leeuwen, W. J. Palenstijn, W. Van Aarle, J. Sijbers, and K. J. Batenburg, “Easy implementation of advanced tomography algorithms using the astra toolbox with spot operators,” Numer. Algorithms (to be published).

Stampanoni, M.

Stock, S. R.

S. R. Stock, Micro Computed Tomography: Methodology and Applications (CRC Press, 2008).
[Crossref]

Susini, J.

R. Tucoulou, G. Martinez-Criado, P. Bleuet, I. Kieffer, P. Cloetens, S. Labouré, T. Martin, C. Guilloud, and J. Susini, “High-resolution angular beam stability monitoring at a nanofocusing beamline,” J. Synchrotron Radiat. 15, 392–398 (2008).
[Crossref] [PubMed]

Titarenko, S.

V. Titarenko, S. Titarenko, P. J. Withers, F. De Carlo, and X. Xiao, “Improved tomographic reconstructions using adaptive time-dependent intensity normalization,” J. Synchrotron Radiat. 17, 689–699 (2010).
[Crossref] [PubMed]

Titarenko, V.

V. Titarenko, S. Titarenko, P. J. Withers, F. De Carlo, and X. Xiao, “Improved tomographic reconstructions using adaptive time-dependent intensity normalization,” J. Synchrotron Radiat. 17, 689–699 (2010).
[Crossref] [PubMed]

Tlustos, L.

L. Tlustos, M. Campbell, E. Heijne, and X. Llopart, “Signal variations in high-granularity Si pixel detectors,” IEEE Trans. Nucl. Sci 51, 3006–3012 (2004).
[Crossref]

Trtik, P.

Tucoulou, R.

R. Tucoulou, G. Martinez-Criado, P. Bleuet, I. Kieffer, P. Cloetens, S. Labouré, T. Martin, C. Guilloud, and J. Susini, “High-resolution angular beam stability monitoring at a nanofocusing beamline,” J. Synchrotron Radiat. 15, 392–398 (2008).
[Crossref] [PubMed]

Turk, M.

M. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cognitive Neurosci. 3, 71–86 (1991).
[Crossref]

van Aarle, W.

W. van Aarle, W. J. Palenstijn, J. De Beenhouwer, T. Altantzis, S. Bals, K. J. Batenburg, and J. Sijbers, “The ASTRA toolbox: a platform for advanced algorithm development in electron tomography,” Ultramicroscopy 157, 35–47 (2015).
[Crossref] [PubMed]

F. Bleichrodt, T. van Leeuwen, W. J. Palenstijn, W. Van Aarle, J. Sijbers, and K. J. Batenburg, “Easy implementation of advanced tomography algorithms using the astra toolbox with spot operators,” Numer. Algorithms (to be published).

van Leeuwen, T.

F. Bleichrodt, T. van Leeuwen, W. J. Palenstijn, W. Van Aarle, J. Sijbers, and K. J. Batenburg, “Easy implementation of advanced tomography algorithms using the astra toolbox with spot operators,” Numer. Algorithms (to be published).

Withers, P. J.

V. Titarenko, S. Titarenko, P. J. Withers, F. De Carlo, and X. Xiao, “Improved tomographic reconstructions using adaptive time-dependent intensity normalization,” J. Synchrotron Radiat. 17, 689–699 (2010).
[Crossref] [PubMed]

Xiao, X.

V. Titarenko, S. Titarenko, P. J. Withers, F. De Carlo, and X. Xiao, “Improved tomographic reconstructions using adaptive time-dependent intensity normalization,” J. Synchrotron Radiat. 17, 689–699 (2010).
[Crossref] [PubMed]

IEEE Trans. Nucl. Sci (1)

L. Tlustos, M. Campbell, E. Heijne, and X. Llopart, “Signal variations in high-granularity Si pixel detectors,” IEEE Trans. Nucl. Sci 51, 3006–3012 (2004).
[Crossref]

J. Cognitive Neurosci. (1)

M. Turk and A. Pentland, “Eigenfaces for recognition,” J. Cognitive Neurosci. 3, 71–86 (1991).
[Crossref]

J. Struct. Biol. (1)

W. J. Palenstijn, K. J. Batenburg, and J. Sijbers, “Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs),” J. Struct. Biol. 176, 250–253 (2011).
[Crossref] [PubMed]

J. Synchrotron Radiat. (2)

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Figures (15)

Fig. 1
Fig. 1

Overview of the dynamic FFC algorithm.

Fig. 2
Fig. 2

Sinograms, reconstructions and error images of slice 129 for conventional FFC and dynamic FFC are shown. For the dynamic FFC of the 500 projections, 2 EFFs, based on 100 flat fields, were calculated. The red square in the phantom images indicates the ROI in which the MSE was calculated.

Fig. 3
Fig. 3

(a) Mean posterior flat field of the aluminum peroxide dataset. (b) The first projection of the aluminum peroxide dataset.

Fig. 4
Fig. 4

(a) Mean of the prior and posterior flat fields of the foam dataset. (b) The first projection of the foam dataset.

Fig. 5
Fig. 5

MSE of the projections (left) and the reconstructions (right) for both conventional FFC and dynamic FFC with 1 to 5 EFFs in function of the number of flat fields.

Fig. 6
Fig. 6

MSE of the projections (left) and the reconstructions (right) for both conventional FFC and dynamic FFC (100 flat fields, 2 EFFs) in function of the number of projections.

Fig. 7
Fig. 7

(a)–(e): EFF 1–5 of the aluminum peroxide dataset, respectively.

Fig. 8
Fig. 8

An FFC corrected projection from the aluminum peroxide dataset: (a) conventional FFC, (b)–(f) dynamic FFC with 1 to 5 EFFs, respectively.

Fig. 9
Fig. 9

ROI of the aluminum peroxide sinogram: (a) conventional FFC, (b) dynamic FFC with 3 EFFs. (c) The difference between the conventional and dynamic flat field corrected sinogram.

Fig. 10
Fig. 10

FBP reconstructed slice of the aluminum peroxide dataset with (a) conventional and (b) dynamic FFC with 3 EFFs.

Fig. 11
Fig. 11

(a)–(e): The first five (principal) EFFs of the foam dataset.

Fig. 12
Fig. 12

An FFC corrected projection from the foam dataset: (a) conventional FFC, (b)–(f) dynamic FFC with 1 to 5 EFFs, respectively.

Fig. 13
Fig. 13

Sinogram of a slice of the foam dataset: (a) conventional FFC, (b)–(f) dynamic FFC with 1 to 5 EFFs, respectively. Bands containing artifacts are indicated with red arrows.

Fig. 14
Fig. 14

SIRT reconstruction of a slice (same slice as in Fig. 13) of the foam dataset: (a) conventional FFC, (b) dynamic FFC with 5 EFFs. The broad ring artifacts are indicated with red arrows and correspond to the artifacts indicated on the sinograms (see Fig. 13)

Fig. 15
Fig. 15

FBP reconstruction of a slice (same slice as in Fig. 13) of the foam dataset: (a) conventional FFC, (b) dynamic FFC with 5 EFFs. The broad ring artifacts are indicated with red arrows and correspond to the artifacts indicated on the sinograms (see Fig. 13)

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

p = I 0 exp ( μ ( l ) d l )
μ ( l ) d l = ln ( p I 0 )
n j = p j d f d
n j = p j d ¯ f d ¯
f m f ¯ + k = 1 K w m k u k
A = ( f 1 f ¯ , , f M f ¯ )
f ^ j = f ¯ + k = 1 K w ^ j k u k
{ w ^ j k } = arg min { w j k } c ( { w j k } ) n = 1 N | n j ( { w j k } ) | n
n j ( { w j k } ) = ( p j d ¯ ) / ( f ¯ + k = 1 K w j k u k d ¯ )
c ( { w j k } ) = 1 N n = 1 N ( f ¯ n + k = 1 K w j k u k , n d ¯ n )
p j , sim = f j e n j

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