Abstract

Synchrotron-based X-ray micro-tomography systems often suffer severe ring artifacts in reconstructed images. In sinograms the artifacts appear as straight lines or stripe artifacts. These artifacts are caused by the irregular response of a detecting system giving rise to a variety of observed types of stripes: full stripes, partial stripes, fluctuating stripes, and unresponsive stripes. The use of pre-processing techniques such as distortion correction or phase retrieval blurs and enlarges these stripes. It is impossible for a single approach to remove all types of stripe artifacts. Here, we propose three techniques for tackling all of them. The proposed techniques are easy to implement; do not generate extra stripe artifacts and void-center artifacts; and give superior quality on challenging data sets and in comparison with other techniques. Implementations in Python and a challenging data set are available for download.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (1)

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

2017 (1)

F. Brun, L. Massimi, M. Fratini, D. Dreossi, F. Billé, A. Accardo, R. Pugliese, and A. Cedola, “SYRMEP Tomo Project: a graphical user interface for customizing CT reconstruction workflows,” Adv. Struct. Chem. Imaging 3(1), 4 (2017).
[Crossref] [PubMed]

2016 (2)

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

W. van Aarle, W. J. Palenstijn, J. Cant, E. Janssens, F. Bleichrodt, A. Dabravolski, J. De Beenhouwer, K. Joost Batenburg, and J. Sijbers, “Fast and flexible X-ray tomography using the ASTRA toolbox,” Opt. Express 24(22), 25129–25147 (2016).
[Crossref] [PubMed]

2015 (2)

N. T. Vo, R. C. Atwood, and M. Drakopoulos, “Radial lens distortion correction with sub-pixel accuracy for X-ray micro-tomography,” Opt. Express 23(25), 32859–32868 (2015).
[Crossref] [PubMed]

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

2014 (3)

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, “Tomopy: a framework for the analysis of synchrotron tomographic data,” J. Synchrotron Radiat. 21(Pt 5), 1188–1193 (2014).
[Crossref] [PubMed]

A. Mirone, E. Brun, E. Gouillart, P. Tafforeau, and J. Kieffer, “The PyHST2 hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities,” Nucl. Instrum. Methods Phys. Res. B 324, 41–48 (2014).
[Crossref]

N. T. Vo, M. Drakopoulos, R. C. Atwood, and C. Reinhard, “Reliable method for calculating the center of rotation in parallel-beam tomography,” Opt. Express 22(16), 19078–19086 (2014).
[Crossref] [PubMed]

2011 (2)

S. Titarenko, V. Titarenko, A. Kyrieleis, P. J. Withers, and F. De Carlo, “Suppression of ring artefacts when tomographing anisotropically attenuating samples,” J. Synchrotron Radiat. 18(3), 427–435 (2011).
[Crossref] [PubMed]

T. E. Gureyev, Y. Nesterets, D. Ternovski, D. Thompson, S. Wilkins, A. Stevenson, A. Sakellariou, and J. A. Taylor, “Toolbox for advanced X-ray image processing,” Proc. SPIE 8141, 81410B (2011).

2010 (1)

S. Titarenko, P. J. Withers, and A. Yagola, “An analytical formula for ring artefact suppression in X-ray tomography,” Appl. Math. Lett. 23(12), 1489–1495 (2010).
[Crossref]

2009 (1)

2004 (1)

J. Sijbers and A. Postnov, “Reduction of ring artefacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49(14), N247–N253 (2004).
[Crossref] [PubMed]

2002 (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[Crossref] [PubMed]

1998 (1)

C. Raven, “Numerical Removal of Ring Artifacts in Microtomography,” Rev. Sci. Instrum. 69(8), 2978–2980 (1998).
[Crossref]

1995 (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

1971 (1)

G. N. Ramachandran and A. V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms,” Proc. Natl. Acad. Sci. U.S.A. 68(9), 2236–2240 (1971).
[Crossref] [PubMed]

1962 (1)

D. F. Swinehart, “The Beer-Lambert Law,” J. Chem. Educ. 39(7), 333 (1962).
[Crossref]

Abel, R. L.

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

Accardo, A.

F. Brun, L. Massimi, M. Fratini, D. Dreossi, F. Billé, A. Accardo, R. Pugliese, and A. Cedola, “SYRMEP Tomo Project: a graphical user interface for customizing CT reconstruction workflows,” Adv. Struct. Chem. Imaging 3(1), 4 (2017).
[Crossref] [PubMed]

Albon, J.

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

Arzilli, F.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

Atwood, R.

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Atwood, R. C.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

N. T. Vo, R. C. Atwood, and M. Drakopoulos, “Radial lens distortion correction with sub-pixel accuracy for X-ray micro-tomography,” Opt. Express 23(25), 32859–32868 (2015).
[Crossref] [PubMed]

N. T. Vo, M. Drakopoulos, R. C. Atwood, and C. Reinhard, “Reliable method for calculating the center of rotation in parallel-beam tomography,” Opt. Express 22(16), 19078–19086 (2014).
[Crossref] [PubMed]

Basham, M.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Billé, F.

F. Brun, L. Massimi, M. Fratini, D. Dreossi, F. Billé, A. Accardo, R. Pugliese, and A. Cedola, “SYRMEP Tomo Project: a graphical user interface for customizing CT reconstruction workflows,” Adv. Struct. Chem. Imaging 3(1), 4 (2017).
[Crossref] [PubMed]

Bleichrodt, F.

Brun, E.

A. Mirone, E. Brun, E. Gouillart, P. Tafforeau, and J. Kieffer, “The PyHST2 hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities,” Nucl. Instrum. Methods Phys. Res. B 324, 41–48 (2014).
[Crossref]

Brun, F.

F. Brun, L. Massimi, M. Fratini, D. Dreossi, F. Billé, A. Accardo, R. Pugliese, and A. Cedola, “SYRMEP Tomo Project: a graphical user interface for customizing CT reconstruction workflows,” Adv. Struct. Chem. Imaging 3(1), 4 (2017).
[Crossref] [PubMed]

Burton, M. R.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

Cai, B.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

Campbell, I. C.

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

Cant, J.

Cedola, A.

F. Brun, L. Massimi, M. Fratini, D. Dreossi, F. Billé, A. Accardo, R. Pugliese, and A. Cedola, “SYRMEP Tomo Project: a graphical user interface for customizing CT reconstruction workflows,” Adv. Struct. Chem. Imaging 3(1), 4 (2017).
[Crossref] [PubMed]

Chilingaryan, S.

M. Vogelgesang, S. Chilingaryan, T. d. Rolo, and A. Kopmann, “UFO: a scalable GPU-based image processing framework for on-line monitoring,” in IEEE International Conference on High Performance Computing and Communication & Embedded Software and Systems (2012) pp. 824–829.

Connolley, T.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Connor, L.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Coudrillier, B.

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

Dabravolski, A.

Davies, S.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

De Beenhouwer, J.

De Carlo, F.

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, “Tomopy: a framework for the analysis of synchrotron tomographic data,” J. Synchrotron Radiat. 21(Pt 5), 1188–1193 (2014).
[Crossref] [PubMed]

S. Titarenko, V. Titarenko, A. Kyrieleis, P. J. Withers, and F. De Carlo, “Suppression of ring artefacts when tomographing anisotropically attenuating samples,” J. Synchrotron Radiat. 18(3), 427–435 (2011).
[Crossref] [PubMed]

De Maio, N.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Di Genova, D.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

Drakopoulos, M.

N. T. Vo, R. C. Atwood, and M. Drakopoulos, “Radial lens distortion correction with sub-pixel accuracy for X-ray micro-tomography,” Opt. Express 23(25), 32859–32868 (2015).
[Crossref] [PubMed]

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

N. T. Vo, M. Drakopoulos, R. C. Atwood, and C. Reinhard, “Reliable method for calculating the center of rotation in parallel-beam tomography,” Opt. Express 22(16), 19078–19086 (2014).
[Crossref] [PubMed]

Dreossi, D.

F. Brun, L. Massimi, M. Fratini, D. Dreossi, F. Billé, A. Accardo, R. Pugliese, and A. Cedola, “SYRMEP Tomo Project: a graphical user interface for customizing CT reconstruction workflows,” Adv. Struct. Chem. Imaging 3(1), 4 (2017).
[Crossref] [PubMed]

Ethier, C. R.

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

Foster, A.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Fratini, M.

F. Brun, L. Massimi, M. Fratini, D. Dreossi, F. Billé, A. Accardo, R. Pugliese, and A. Cedola, “SYRMEP Tomo Project: a graphical user interface for customizing CT reconstruction workflows,” Adv. Struct. Chem. Imaging 3(1), 4 (2017).
[Crossref] [PubMed]

Geraldes, D. M.

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

Gouillart, E.

A. Mirone, E. Brun, E. Gouillart, P. Tafforeau, and J. Kieffer, “The PyHST2 hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities,” Nucl. Instrum. Methods Phys. Res. B 324, 41–48 (2014).
[Crossref]

Gureyev, T. E.

T. E. Gureyev, Y. Nesterets, D. Ternovski, D. Thompson, S. Wilkins, A. Stevenson, A. Sakellariou, and J. A. Taylor, “Toolbox for advanced X-ray image processing,” Proc. SPIE 8141, 81410B (2011).

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[Crossref] [PubMed]

Gürsoy, D.

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, “Tomopy: a framework for the analysis of synchrotron tomographic data,” J. Synchrotron Radiat. 21(Pt 5), 1188–1193 (2014).
[Crossref] [PubMed]

Hart, M.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Hartley, M. E.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

Hill, T.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Howell, G.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Humphreys, B.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Jacobsen, C.

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, “Tomopy: a framework for the analysis of synchrotron tomographic data,” J. Synchrotron Radiat. 21(Pt 5), 1188–1193 (2014).
[Crossref] [PubMed]

Janssens, E.

Joost Batenburg, K.

Kieffer, J.

A. Mirone, E. Brun, E. Gouillart, P. Tafforeau, and J. Kieffer, “The PyHST2 hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities,” Nucl. Instrum. Methods Phys. Res. B 324, 41–48 (2014).
[Crossref]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Kopmann, A.

M. Vogelgesang, S. Chilingaryan, T. d. Rolo, and A. Kopmann, “UFO: a scalable GPU-based image processing framework for on-line monitoring,” in IEEE International Conference on High Performance Computing and Communication & Embedded Software and Systems (2012) pp. 824–829.

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Kyrieleis, A.

S. Titarenko, V. Titarenko, A. Kyrieleis, P. J. Withers, and F. De Carlo, “Suppression of ring artefacts when tomographing anisotropically attenuating samples,” J. Synchrotron Radiat. 18(3), 427–435 (2011).
[Crossref] [PubMed]

La Spina, G.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

Lakshminarayanan, A. V.

G. N. Ramachandran and A. V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms,” Proc. Natl. Acad. Sci. U.S.A. 68(9), 2236–2240 (1971).
[Crossref] [PubMed]

Le Gall, N.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

Lee, P. D.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

Llewellin, E. W.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

Magdysyuk, O.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Marone, F.

Massimi, L.

F. Brun, L. Massimi, M. Fratini, D. Dreossi, F. Billé, A. Accardo, R. Pugliese, and A. Cedola, “SYRMEP Tomo Project: a graphical user interface for customizing CT reconstruction workflows,” Adv. Struct. Chem. Imaging 3(1), 4 (2017).
[Crossref] [PubMed]

Mayo, S. C.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[Crossref] [PubMed]

Miller, P. R.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[Crossref] [PubMed]

Mirone, A.

A. Mirone, E. Brun, E. Gouillart, P. Tafforeau, and J. Kieffer, “The PyHST2 hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities,” Nucl. Instrum. Methods Phys. Res. B 324, 41–48 (2014).
[Crossref]

Münch, B.

Nesterets, Y.

T. E. Gureyev, Y. Nesterets, D. Ternovski, D. Thompson, S. Wilkins, A. Stevenson, A. Sakellariou, and J. A. Taylor, “Toolbox for advanced X-ray image processing,” Proc. SPIE 8141, 81410B (2011).

Nonni, S.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

Paganin, D.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[Crossref] [PubMed]

Palenstijn, W. J.

Pedersen, U.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Polacci, M.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

Postnov, A.

J. Sijbers and A. Postnov, “Reduction of ring artefacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49(14), N247–N253 (2004).
[Crossref] [PubMed]

Pugliese, R.

F. Brun, L. Massimi, M. Fratini, D. Dreossi, F. Billé, A. Accardo, R. Pugliese, and A. Cedola, “SYRMEP Tomo Project: a graphical user interface for customizing CT reconstruction workflows,” Adv. Struct. Chem. Imaging 3(1), 4 (2017).
[Crossref] [PubMed]

Raji, Y.

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

Ramachandran, G. N.

G. N. Ramachandran and A. V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms,” Proc. Natl. Acad. Sci. U.S.A. 68(9), 2236–2240 (1971).
[Crossref] [PubMed]

Raven, C.

C. Raven, “Numerical Removal of Ring Artifacts in Microtomography,” Rev. Sci. Instrum. 69(8), 2978–2980 (1998).
[Crossref]

Reinhard, C.

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

N. T. Vo, M. Drakopoulos, R. C. Atwood, and C. Reinhard, “Reliable method for calculating the center of rotation in parallel-beam tomography,” Opt. Express 22(16), 19078–19086 (2014).
[Crossref] [PubMed]

Rolo, T. d.

M. Vogelgesang, S. Chilingaryan, T. d. Rolo, and A. Kopmann, “UFO: a scalable GPU-based image processing framework for on-line monitoring,” in IEEE International Conference on High Performance Computing and Communication & Embedded Software and Systems (2012) pp. 824–829.

Sakellariou, A.

T. E. Gureyev, Y. Nesterets, D. Ternovski, D. Thompson, S. Wilkins, A. Stevenson, A. Sakellariou, and J. A. Taylor, “Toolbox for advanced X-ray image processing,” Proc. SPIE 8141, 81410B (2011).

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Sijbers, J.

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66(12), 5486–5492 (1995).
[Crossref]

Stampanoni, M.

Stevenson, A.

T. E. Gureyev, Y. Nesterets, D. Ternovski, D. Thompson, S. Wilkins, A. Stevenson, A. Sakellariou, and J. A. Taylor, “Toolbox for advanced X-ray image processing,” Proc. SPIE 8141, 81410B (2011).

Swinehart, D. F.

D. F. Swinehart, “The Beer-Lambert Law,” J. Chem. Educ. 39(7), 333 (1962).
[Crossref]

Tafforeau, P.

A. Mirone, E. Brun, E. Gouillart, P. Tafforeau, and J. Kieffer, “The PyHST2 hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities,” Nucl. Instrum. Methods Phys. Res. B 324, 41–48 (2014).
[Crossref]

Taylor, J. A.

T. E. Gureyev, Y. Nesterets, D. Ternovski, D. Thompson, S. Wilkins, A. Stevenson, A. Sakellariou, and J. A. Taylor, “Toolbox for advanced X-ray image processing,” Proc. SPIE 8141, 81410B (2011).

Ternovski, D.

T. E. Gureyev, Y. Nesterets, D. Ternovski, D. Thompson, S. Wilkins, A. Stevenson, A. Sakellariou, and J. A. Taylor, “Toolbox for advanced X-ray image processing,” Proc. SPIE 8141, 81410B (2011).

Thompson, D.

T. E. Gureyev, Y. Nesterets, D. Ternovski, D. Thompson, S. Wilkins, A. Stevenson, A. Sakellariou, and J. A. Taylor, “Toolbox for advanced X-ray image processing,” Proc. SPIE 8141, 81410B (2011).

Titarenko, S.

S. Titarenko, V. Titarenko, A. Kyrieleis, P. J. Withers, and F. De Carlo, “Suppression of ring artefacts when tomographing anisotropically attenuating samples,” J. Synchrotron Radiat. 18(3), 427–435 (2011).
[Crossref] [PubMed]

S. Titarenko, P. J. Withers, and A. Yagola, “An analytical formula for ring artefact suppression in X-ray tomography,” Appl. Math. Lett. 23(12), 1489–1495 (2010).
[Crossref]

Titarenko, V.

S. Titarenko, V. Titarenko, A. Kyrieleis, P. J. Withers, and F. De Carlo, “Suppression of ring artefacts when tomographing anisotropically attenuating samples,” J. Synchrotron Radiat. 18(3), 427–435 (2011).
[Crossref] [PubMed]

Trtik, P.

van Aarle, W.

Vo, N.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Vo, N. T.

M. Polacci, F. Arzilli, G. La Spina, N. Le Gall, B. Cai, M. E. Hartley, D. Di Genova, N. T. Vo, S. Nonni, R. C. Atwood, E. W. Llewellin, P. D. Lee, and M. R. Burton, “Crystallisation in basaltic magmas revealed via in situ 4D synchrotron X-ray microtomography,” Sci. Rep. 8(1), 8377 (2018).
[Crossref] [PubMed]

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

N. T. Vo, R. C. Atwood, and M. Drakopoulos, “Radial lens distortion correction with sub-pixel accuracy for X-ray micro-tomography,” Opt. Express 23(25), 32859–32868 (2015).
[Crossref] [PubMed]

N. T. Vo, M. Drakopoulos, R. C. Atwood, and C. Reinhard, “Reliable method for calculating the center of rotation in parallel-beam tomography,” Opt. Express 22(16), 19078–19086 (2014).
[Crossref] [PubMed]

Vogelgesang, M.

M. Vogelgesang, S. Chilingaryan, T. d. Rolo, and A. Kopmann, “UFO: a scalable GPU-based image processing framework for on-line monitoring,” in IEEE International Conference on High Performance Computing and Communication & Embedded Software and Systems (2012) pp. 824–829.

Wanelik, K.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Wilkin, G.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Wilkins, S.

T. E. Gureyev, Y. Nesterets, D. Ternovski, D. Thompson, S. Wilkins, A. Stevenson, A. Sakellariou, and J. A. Taylor, “Toolbox for advanced X-ray image processing,” Proc. SPIE 8141, 81410B (2011).

Wilkins, S. W.

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[Crossref] [PubMed]

Withers, P. J.

S. Titarenko, V. Titarenko, A. Kyrieleis, P. J. Withers, and F. De Carlo, “Suppression of ring artefacts when tomographing anisotropically attenuating samples,” J. Synchrotron Radiat. 18(3), 427–435 (2011).
[Crossref] [PubMed]

S. Titarenko, P. J. Withers, and A. Yagola, “An analytical formula for ring artefact suppression in X-ray tomography,” Appl. Math. Lett. 23(12), 1489–1495 (2010).
[Crossref]

Xiao, X.

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, “Tomopy: a framework for the analysis of synchrotron tomographic data,” J. Synchrotron Radiat. 21(Pt 5), 1188–1193 (2014).
[Crossref] [PubMed]

Yagola, A.

S. Titarenko, P. J. Withers, and A. Yagola, “An analytical formula for ring artefact suppression in X-ray tomography,” Appl. Math. Lett. 23(12), 1489–1495 (2010).
[Crossref]

Yuan, F.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Adv. Struct. Chem. Imaging (1)

F. Brun, L. Massimi, M. Fratini, D. Dreossi, F. Billé, A. Accardo, R. Pugliese, and A. Cedola, “SYRMEP Tomo Project: a graphical user interface for customizing CT reconstruction workflows,” Adv. Struct. Chem. Imaging 3(1), 4 (2017).
[Crossref] [PubMed]

Appl. Math. Lett. (1)

S. Titarenko, P. J. Withers, and A. Yagola, “An analytical formula for ring artefact suppression in X-ray tomography,” Appl. Math. Lett. 23(12), 1489–1495 (2010).
[Crossref]

IEEE Trans. Med. Imaging (1)

B. Coudrillier, D. M. Geraldes, N. T. Vo, R. Atwood, C. Reinhard, I. C. Campbell, Y. Raji, J. Albon, R. L. Abel, and C. R. Ethier, “Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa,” IEEE Trans. Med. Imaging 35(4), 988–999 (2016).
[Crossref] [PubMed]

J. Chem. Educ. (1)

D. F. Swinehart, “The Beer-Lambert Law,” J. Chem. Educ. 39(7), 333 (1962).
[Crossref]

J. Microsc. (1)

D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002).
[Crossref] [PubMed]

J. Synchrotron Radiat. (3)

D. Gürsoy, F. De Carlo, X. Xiao, and C. Jacobsen, “Tomopy: a framework for the analysis of synchrotron tomographic data,” J. Synchrotron Radiat. 21(Pt 5), 1188–1193 (2014).
[Crossref] [PubMed]

S. Titarenko, V. Titarenko, A. Kyrieleis, P. J. Withers, and F. De Carlo, “Suppression of ring artefacts when tomographing anisotropically attenuating samples,” J. Synchrotron Radiat. 18(3), 427–435 (2011).
[Crossref] [PubMed]

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Nucl. Instrum. Methods Phys. Res. B (1)

A. Mirone, E. Brun, E. Gouillart, P. Tafforeau, and J. Kieffer, “The PyHST2 hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities,” Nucl. Instrum. Methods Phys. Res. B 324, 41–48 (2014).
[Crossref]

Opt. Express (4)

Phys. Med. Biol. (1)

J. Sijbers and A. Postnov, “Reduction of ring artefacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49(14), N247–N253 (2004).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

G. N. Ramachandran and A. V. Lakshminarayanan, “Three-dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms,” Proc. Natl. Acad. Sci. U.S.A. 68(9), 2236–2240 (1971).
[Crossref] [PubMed]

Proc. SPIE (1)

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Supplementary Material (3)

NameDescription
» Visualization 1       Reconstructed slices of a 3D tomographic dataset without ring artifacts suppresion.
» Visualization 2       Reconstructed slices of a 3D tomographic dataset after ring artifacts suppression using the wavelet-FFT-based method.
» Visualization 3       Reconstructed slices of a 3D tomographic dataset after ring artifacts suppression using algorithm 6, algorithm 5, and algorithm 3 of our approaches.

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Figures (25)

Fig. 1
Fig. 1 Impact of defects in a detector system: (a) Stripe artifacts in the sinogram; (b) Ring artifacts in the reconstructed image.
Fig. 2
Fig. 2 Degradation of a scintillator during an experiment: (a) At the beginning of the experiment; (b) After few days of use.
Fig. 3
Fig. 3 Characteristic intensity profile of a defective pixel (red color) in comparison with an adjacent good pixel (blue color) for distinguishing the type of a stripe: (a) Unresponsive stripe; (b) Full stripe; (c) Partial stripe; (d) Fluctuating stripe.
Fig. 4
Fig. 4 (a) Visual demonstration of the S2, S3, and S4 stripe. (b) Magnified view from the blue frame in (a) shows the fluctuating stripe. (c), (d), and (e) Ring artifacts caused by the S2, S3, S4 stripes, respectively.
Fig. 5
Fig. 5 Demonstration of the difference between the flat-field image and the defective pixel map. (a) Flat-field image; (b) Flat-field correction of a sample projection; (c) Defective map showing the intercept values of the linear fit; (d) Magnified view from the rectangular box in (a); (e) Magnified view from the rectangular box in (b); (f) Magnified view from the rectangular box in (c) showing defective regions not visible in (d).
Fig. 6
Fig. 6 Occurrence of the ring artifacts depends on the dynamic range of the incoming intensities. (a) Reconstructed image from the sample giving a low dynamic range of transmitted intensities; (b) Reconstructed image of the same detector row from the sample giving a high dynamic range of transmitted intensities, which shows the partial rings (arrowed).
Fig. 7
Fig. 7 Demonstration of algorithm 3 in which the image contrast is inverted to improve the visibility of stripes. (a) Original sinogram; (b) Sorted sinogram; (c) Smoothed sorted sinogram using the median filter; (d) Corrected sinogram; (e) Difference between (a) and (d).
Fig. 8
Fig. 8 Comparison of reconstructed images before and after using algorithm 3: (a) Reconstructed image from the sinogram in Fig. 7(a); (b) Reconstructed image from the corrected sinogram in Fig. 7(d); (c) Magnified view from the red frame in (a); (d) Magnified view from the red frame in (b).
Fig. 9
Fig. 9 Causes and impact of large stripes. (a) Large defects (vertical arrow) and the areas around the over-exposed blob (horizontal arrows) cause large stripes in the sinogram; (b) Large stripes in the sinogram (arrowed); (c) Large ring artifacts in the reconstructed image come from the large stripes in (b).
Fig. 10
Fig. 10 Demonstration of algorithm 4. (a) Normalized 1D array, i.e. non-uniform background is corrected. (b) Sorted array and fitted array using the middle part of the sorted array.
Fig. 11
Fig. 11 Explanation of step 2 in Table 4. (a) Sorted sinogram where high-frequency edges (indicated by the arrows) can cause false detection of stripes; (b) Horizontal median filter of sinogram (a);
Fig. 12
Fig. 12 Results of removing large ring artifacts in the reconstructed image shown in Fig. 9(c). (a) Corrected image after using step 1, 2, and 3 where some partial rings still remain (arrows); (b) Corrected image at the end; (c) Difference between the image in (b) and the image in Fig. 9(c).
Fig. 13
Fig. 13 Impact of unresponsive stripes and fluctuating stripes. (a) Sinogram having both type of stripes, S1 (arrow) and S4 (red frame); (b) Ring artifacts in the reconstructed image caused by the stripes in sinogram (a); (c) Over-exposed blob on the detector resulting the S1 stripe in (a); (d) Magnified view of the red frame in image (a) showing the S4 stripe; (e) Magnified view of the red frame in (b) showing the streak artifacts (arrows) caused by the S4 stripes.
Fig. 14
Fig. 14 Explanation of steps 1 and 2 of algorithm 6. (a) Averaging the absolute difference between the intensity profiles and their low-pass components (blue profile); and after filtered by the median filter (red profile); (b) Division of two profiles in (a).
Fig. 15
Fig. 15 Results of correcting type S1 and S4 stripes. (a) Corrected sinogram after using algorithm 6 showing a large stripe left; (b) Reconstructed image from the sinogram in (a); (c) Reconstructed image after algorithm 5 is used; (d) Difference between the image in (c) and the image in Fig. 13(b).
Fig. 16
Fig. 16 (a) Sinogram of sample 1 having low dynamic range of transmitted intensities with high-frequency edges (arrows); (b) Sinogram of sample 2 having higher dynamic range of intensities than the sinogram in (a) with a high-absorption area (oval) and some high-frequency edges (arrows).
Fig. 17
Fig. 17 Reconstructed images of sinogram in Fig. 16(a) where the red arrows indicate extra artifacts: (a) After flat-field correction; (b) using method M1; (c) using method M2; (d) using method M3; (e) using method M4; (f) using algorithm 3.
Fig. 18
Fig. 18 Magnified views of the center part of the reconstructed images in Fig. 17: (a) from Fig. 17(a); (b) from Fig. 17(b); (c) from Fig. 17(c); (d) from Fig. 17(d); (e) from Fig. 17(e); (f) from Fig. 17(f).
Fig. 19
Fig. 19 Reconstructed images of sinogram in Fig. 16(b) where the red arrows indicate extra artifacts: (a) After flat-field correction; (b) using method M1; (c) using method M2; (d) using method M3; (e) using method M4; (f) using algorithm 3.
Fig. 20
Fig. 20 Magnified views of the center part of the reconstructed images in Fig. 19: (a) From Fig. 19(a); (b) from Fig. 19(b); (c) from Fig. 19(c); (d) from Fig. 19(d); (e) from Fig. 19(e); (f) from Fig. 19(f).
Fig. 21
Fig. 21 Partial stripes caused by the high dynamic range of the incoming intensities. (a) Sinogram of a sample in rectangular shape; (b)-(c) Magnified view of the red frames at the top and bottom in image (a) showing partial stripes; (d) Reconstructed image from sinogram (a); (e) Magnified view of the red frame in image (d).
Fig. 22
Fig. 22 Magnified views of the reconstructed images from method M1-M4 and algorithm 3 using different parameters. The first row shows the results of method M1 (a.1), method M2 (b.1), method M3 (c.1), method M4 (d.1), and algorithm 3 (e.1) in which the same parameters as in the first test are used. The second row shows the results of method M1 (a.2), method M2 (b.2), method M3 (c.2), method M4 (d.2), and algorithm 3 (e.2) using different parameters.
Fig. 23
Fig. 23 Blurry stripes caused by using a pre-processing method on the 2D projections and results of removing them using algorithm 1. (a)-(b) Sinogram at the same row of the detector before and after the pre-processing method was used; (c) Reconstructed image from sinogram in (b); (d) Result of step 1 of algorithm 1 using the polynomial order of 3; (e) Corrected sinogram after a strong 2D low-pass filter is used; (f) Reconstructed image from sinogram in (e).
Fig. 24
Fig. 24 Reconstructed images using method M1-M4 showing extra artifacts indicated by the arrows. (a) Method M1 (σ = 121); (b) method M2 (α = 0.00001); (c) method M3 (u = 2, v = 1, n = 10); (d) method M4 (order = 11, level = 3, σ = 10).
Fig. 25
Fig. 25 (a) Reconstructed slices with ring artifacts (see Visualization 1). (b) Reconstructed slices after using the wavelet-FFT-based method where the parameters are the same as used in Fig. 17(e) (see Visualization 2). (c) Reconstructed slices after using algorithm 6, algorithm 5, and algorithm 3 (see Visualization 3).

Tables (5)

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Table 1 Classification of stripes

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Table 2 Algorithms for removing stripes of type S2 and S3

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Table 3 Steps of the algorithm for detecting defects (called algorithm 4)

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Table 4 Algorithm for removing large stripes (called algorithm 5)

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Table 5 Steps of algorithm 6 for removing unresponsive stripes and fluctuating stripes.

Equations (2)

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T L = F 0 ( F 1 F 0 )×R/2
T U = F 1 +( F 1 F 0 )×R/2

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