Abstract

Ring artifacts reduce image quality in tomography, and arise from faulty detector calibration. In microtomography, we have identified that ring artifacts can arise due to high-spatial frequency variations in the scintillator thickness. Such variations are normally removed by a flat-field correction. However, as the spectrum changes, e.g. due to beam hardening, the detector response varies non-uniformly introducing ring artifacts that persist after flat-field correction. In this paper, we present a method to correct for ring artifacts from variations in scintillator thickness by using a simple method to characterize the local scintillator response. The method addresses the actual physical cause of the ring artifacts, in contrary to many other ring artifact removal methods which rely only on image post-processing. By applying the technique to an experimental phantom tomography, we show that ring artifacts are strongly reduced compared to only making a flat-field correction.

© 2017 Optical Society of America

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References

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  1. C. Raven, “Numerical removal of ring artifacts in microtomography,” Rev. Sci. Inst. 69, 2978–2980 (1998).
    [Crossref]
  2. K. Hasan, F. Sadi, and S. Y. Lee, “Removal of ring artifacts in micro-CT imaging using iterative morphological filters,” Signal Image Video P. 6, 41–53 (2010).
    [Crossref]
  3. S. Rashid, S. Y. Lee, and K. Hasan, “An improved method for the removal of ring artifacts in high resolution CT imaging,” EURASIP J. Adv. Sig. Pr. 2012:93 (2012).
    [Crossref]
  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. Sijbers and A. Postnov, “Reduction of ring artefacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49, N247–N253 (2004).
    [Crossref] [PubMed]
  6. M. Axelsson, S. Svensson, and G. Borgefors, “Reduction of Ring Artifacts in High Resolution X-Ray Microtomography Images,” in Pattern Recognition. DAGM 2006. Lecture Notes in Computer Science, K. Franke, KR. Müller, B. Nickolay, and R. Schäfer, eds. (Springer, 2006).
  7. G. R. Davis and J. C. Elliott, “X-ray microtomography scanner using time-delay integration for elimination of ring artefacts in the reconstructed image,” Nucl. Instrum. Meth. A 394, 157–162 (1997).
    [Crossref]
  8. Y. Zhu, M. Zhao, H. Li, and P. Zhang, “Micro-CT artifacts reduction based on detector random shifting and fast data inpainting,” Med. Phys. 40, 031114 (2013).
    [Crossref] [PubMed]
  9. D. W. Davidson, C. Fröjdh, V. O’Shea, H-E. Nilsson, and M. Rahman, “Limitations to flat-field correction methods when using an X-ray spectrum,” Nucl. Instrum. Meth. A 509, 146–150 (2003).
    [Crossref]
  10. Y. Yu and J. Wang, “Beam hardening-respecting flat field correction of digital X-ray detectors,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2012) pp. 2085–2088.
  11. C. Altunbas, C-J. Lai, Y. Zhong, and C. C. Shaw, “Reduction of ring artifacts in CBCT: Detection and correction of pixel gain variations in flat panel detectors,” Med. Phys. 41, 091913 (2014).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  14. D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
    [Crossref] [PubMed]
  15. 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 homogenous object,” J. Microsc. 206, 33–40 (2002).
    [Crossref] [PubMed]
  16. J. Hsieh, Computed Tomography: Principles, Design, Artifacts, and Recent Advances (SPIE Press, 2009), Chap. 7.
  17. J. F. Barrett and N. Keat, “Artifacts in CT: Recognition and avoidance,” Radiographics 24, 1679–1691 (2004).
    [Crossref] [PubMed]
  18. D. H. Larsson, U. Lundström, U. K. Westermark, M. Arsenian Henriksson, A Burvall, and H. M. Hertz, “First application of liquid-metal-jet sources for small-animal imaging: High-resolution CT and phase-contrast tumor demarcation,” Med. Phys. 40, 021909 (2013).
    [Crossref] [PubMed]
  19. W. Vågberg, D. H. Larsson, M. Li, A. Arner, and H. M. Hertz, “X-ray phase-contrast tomography for high-spatial resolution zebrafish muscle imaging,” Sci. Rep. 5, 16625 (2015).
    [Crossref]

2016 (1)

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
[Crossref] [PubMed]

2015 (1)

W. Vågberg, D. H. Larsson, M. Li, A. Arner, and H. M. Hertz, “X-ray phase-contrast tomography for high-spatial resolution zebrafish muscle imaging,” Sci. Rep. 5, 16625 (2015).
[Crossref]

2014 (1)

C. Altunbas, C-J. Lai, Y. Zhong, and C. C. Shaw, “Reduction of ring artifacts in CBCT: Detection and correction of pixel gain variations in flat panel detectors,” Med. Phys. 41, 091913 (2014).
[Crossref] [PubMed]

2013 (2)

D. H. Larsson, U. Lundström, U. K. Westermark, M. Arsenian Henriksson, A Burvall, and H. M. Hertz, “First application of liquid-metal-jet sources for small-animal imaging: High-resolution CT and phase-contrast tumor demarcation,” Med. Phys. 40, 021909 (2013).
[Crossref] [PubMed]

Y. Zhu, M. Zhao, H. Li, and P. Zhang, “Micro-CT artifacts reduction based on detector random shifting and fast data inpainting,” Med. Phys. 40, 031114 (2013).
[Crossref] [PubMed]

2012 (1)

S. Rashid, S. Y. Lee, and K. Hasan, “An improved method for the removal of ring artifacts in high resolution CT imaging,” EURASIP J. Adv. Sig. Pr. 2012:93 (2012).
[Crossref]

2010 (1)

K. Hasan, F. Sadi, and S. Y. Lee, “Removal of ring artifacts in micro-CT imaging using iterative morphological filters,” Signal Image Video P. 6, 41–53 (2010).
[Crossref]

2009 (1)

2004 (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]

J. F. Barrett and N. Keat, “Artifacts in CT: Recognition and avoidance,” Radiographics 24, 1679–1691 (2004).
[Crossref] [PubMed]

2003 (1)

D. W. Davidson, C. Fröjdh, V. O’Shea, H-E. Nilsson, and M. Rahman, “Limitations to flat-field correction methods when using an X-ray spectrum,” Nucl. Instrum. Meth. A 509, 146–150 (2003).
[Crossref]

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 homogenous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

1998 (1)

C. Raven, “Numerical removal of ring artifacts in microtomography,” Rev. Sci. Inst. 69, 2978–2980 (1998).
[Crossref]

1997 (1)

G. R. Davis and J. C. Elliott, “X-ray microtomography scanner using time-delay integration for elimination of ring artefacts in the reconstructed image,” Nucl. Instrum. Meth. A 394, 157–162 (1997).
[Crossref]

1973 (1)

Altunbas, C.

C. Altunbas, C-J. Lai, Y. Zhong, and C. C. Shaw, “Reduction of ring artifacts in CBCT: Detection and correction of pixel gain variations in flat panel detectors,” Med. Phys. 41, 091913 (2014).
[Crossref] [PubMed]

Arner, A.

W. Vågberg, D. H. Larsson, M. Li, A. Arner, and H. M. Hertz, “X-ray phase-contrast tomography for high-spatial resolution zebrafish muscle imaging,” Sci. Rep. 5, 16625 (2015).
[Crossref]

Arsenian Henriksson, M.

D. H. Larsson, U. Lundström, U. K. Westermark, M. Arsenian Henriksson, A Burvall, and H. M. Hertz, “First application of liquid-metal-jet sources for small-animal imaging: High-resolution CT and phase-contrast tumor demarcation,” Med. Phys. 40, 021909 (2013).
[Crossref] [PubMed]

Axelsson, M.

M. Axelsson, S. Svensson, and G. Borgefors, “Reduction of Ring Artifacts in High Resolution X-Ray Microtomography Images,” in Pattern Recognition. DAGM 2006. Lecture Notes in Computer Science, K. Franke, KR. Müller, B. Nickolay, and R. Schäfer, eds. (Springer, 2006).

Barrett, J. F.

J. F. Barrett and N. Keat, “Artifacts in CT: Recognition and avoidance,” Radiographics 24, 1679–1691 (2004).
[Crossref] [PubMed]

Borgefors, G.

M. Axelsson, S. Svensson, and G. Borgefors, “Reduction of Ring Artifacts in High Resolution X-Ray Microtomography Images,” in Pattern Recognition. DAGM 2006. Lecture Notes in Computer Science, K. Franke, KR. Müller, B. Nickolay, and R. Schäfer, eds. (Springer, 2006).

Burvall, A

D. H. Larsson, U. Lundström, U. K. Westermark, M. Arsenian Henriksson, A Burvall, and H. M. Hertz, “First application of liquid-metal-jet sources for small-animal imaging: High-resolution CT and phase-contrast tumor demarcation,” Med. Phys. 40, 021909 (2013).
[Crossref] [PubMed]

Davidson, D. W.

D. W. Davidson, C. Fröjdh, V. O’Shea, H-E. Nilsson, and M. Rahman, “Limitations to flat-field correction methods when using an X-ray spectrum,” Nucl. Instrum. Meth. A 509, 146–150 (2003).
[Crossref]

Davis, G. R.

G. R. Davis and J. C. Elliott, “X-ray microtomography scanner using time-delay integration for elimination of ring artefacts in the reconstructed image,” Nucl. Instrum. Meth. A 394, 157–162 (1997).
[Crossref]

Elliott, J. C.

G. R. Davis and J. C. Elliott, “X-ray microtomography scanner using time-delay integration for elimination of ring artefacts in the reconstructed image,” Nucl. Instrum. Meth. A 394, 157–162 (1997).
[Crossref]

Fröjdh, C.

D. W. Davidson, C. Fröjdh, V. O’Shea, H-E. Nilsson, and M. Rahman, “Limitations to flat-field correction methods when using an X-ray spectrum,” Nucl. Instrum. Meth. A 509, 146–150 (2003).
[Crossref]

Gureyev, T. E.

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 homogenous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

Hasan, K.

S. Rashid, S. Y. Lee, and K. Hasan, “An improved method for the removal of ring artifacts in high resolution CT imaging,” EURASIP J. Adv. Sig. Pr. 2012:93 (2012).
[Crossref]

K. Hasan, F. Sadi, and S. Y. Lee, “Removal of ring artifacts in micro-CT imaging using iterative morphological filters,” Signal Image Video P. 6, 41–53 (2010).
[Crossref]

Hertz, H. M.

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
[Crossref] [PubMed]

W. Vågberg, D. H. Larsson, M. Li, A. Arner, and H. M. Hertz, “X-ray phase-contrast tomography for high-spatial resolution zebrafish muscle imaging,” Sci. Rep. 5, 16625 (2015).
[Crossref]

D. H. Larsson, U. Lundström, U. K. Westermark, M. Arsenian Henriksson, A Burvall, and H. M. Hertz, “First application of liquid-metal-jet sources for small-animal imaging: High-resolution CT and phase-contrast tumor demarcation,” Med. Phys. 40, 021909 (2013).
[Crossref] [PubMed]

Hsieh, J.

J. Hsieh, Computed Tomography: Principles, Design, Artifacts, and Recent Advances (SPIE Press, 2009), Chap. 7.

Keat, N.

J. F. Barrett and N. Keat, “Artifacts in CT: Recognition and avoidance,” Radiographics 24, 1679–1691 (2004).
[Crossref] [PubMed]

Lai, C-J.

C. Altunbas, C-J. Lai, Y. Zhong, and C. C. Shaw, “Reduction of ring artifacts in CBCT: Detection and correction of pixel gain variations in flat panel detectors,” Med. Phys. 41, 091913 (2014).
[Crossref] [PubMed]

Larsson, D. H.

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
[Crossref] [PubMed]

W. Vågberg, D. H. Larsson, M. Li, A. Arner, and H. M. Hertz, “X-ray phase-contrast tomography for high-spatial resolution zebrafish muscle imaging,” Sci. Rep. 5, 16625 (2015).
[Crossref]

D. H. Larsson, U. Lundström, U. K. Westermark, M. Arsenian Henriksson, A Burvall, and H. M. Hertz, “First application of liquid-metal-jet sources for small-animal imaging: High-resolution CT and phase-contrast tumor demarcation,” Med. Phys. 40, 021909 (2013).
[Crossref] [PubMed]

Lee, S. Y.

S. Rashid, S. Y. Lee, and K. Hasan, “An improved method for the removal of ring artifacts in high resolution CT imaging,” EURASIP J. Adv. Sig. Pr. 2012:93 (2012).
[Crossref]

K. Hasan, F. Sadi, and S. Y. Lee, “Removal of ring artifacts in micro-CT imaging using iterative morphological filters,” Signal Image Video P. 6, 41–53 (2010).
[Crossref]

Li, H.

Y. Zhu, M. Zhao, H. Li, and P. Zhang, “Micro-CT artifacts reduction based on detector random shifting and fast data inpainting,” Med. Phys. 40, 031114 (2013).
[Crossref] [PubMed]

Li, M.

W. Vågberg, D. H. Larsson, M. Li, A. Arner, and H. M. Hertz, “X-ray phase-contrast tomography for high-spatial resolution zebrafish muscle imaging,” Sci. Rep. 5, 16625 (2015).
[Crossref]

Lundström, U.

D. H. Larsson, U. Lundström, U. K. Westermark, M. Arsenian Henriksson, A Burvall, and H. M. Hertz, “First application of liquid-metal-jet sources for small-animal imaging: High-resolution CT and phase-contrast tumor demarcation,” Med. Phys. 40, 021909 (2013).
[Crossref] [PubMed]

Marone, F.

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 homogenous object,” J. Microsc. 206, 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 homogenous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

Münch, B.

Nilsson, H-E.

D. W. Davidson, C. Fröjdh, V. O’Shea, H-E. Nilsson, and M. Rahman, “Limitations to flat-field correction methods when using an X-ray spectrum,” Nucl. Instrum. Meth. A 509, 146–150 (2003).
[Crossref]

O’Shea, V.

D. W. Davidson, C. Fröjdh, V. O’Shea, H-E. Nilsson, and M. Rahman, “Limitations to flat-field correction methods when using an X-ray spectrum,” Nucl. Instrum. Meth. A 509, 146–150 (2003).
[Crossref]

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 homogenous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

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]

Rahman, M.

D. W. Davidson, C. Fröjdh, V. O’Shea, H-E. Nilsson, and M. Rahman, “Limitations to flat-field correction methods when using an X-ray spectrum,” Nucl. Instrum. Meth. A 509, 146–150 (2003).
[Crossref]

Rashid, S.

S. Rashid, S. Y. Lee, and K. Hasan, “An improved method for the removal of ring artifacts in high resolution CT imaging,” EURASIP J. Adv. Sig. Pr. 2012:93 (2012).
[Crossref]

Raven, C.

C. Raven, “Numerical removal of ring artifacts in microtomography,” Rev. Sci. Inst. 69, 2978–2980 (1998).
[Crossref]

Sadi, F.

K. Hasan, F. Sadi, and S. Y. Lee, “Removal of ring artifacts in micro-CT imaging using iterative morphological filters,” Signal Image Video P. 6, 41–53 (2010).
[Crossref]

Shaw, C. C.

C. Altunbas, C-J. Lai, Y. Zhong, and C. C. Shaw, “Reduction of ring artifacts in CBCT: Detection and correction of pixel gain variations in flat panel detectors,” Med. Phys. 41, 091913 (2014).
[Crossref] [PubMed]

Sijbers, J.

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

Stampanoni, M.

Svensson, S.

M. Axelsson, S. Svensson, and G. Borgefors, “Reduction of Ring Artifacts in High Resolution X-Ray Microtomography Images,” in Pattern Recognition. DAGM 2006. Lecture Notes in Computer Science, K. Franke, KR. Müller, B. Nickolay, and R. Schäfer, eds. (Springer, 2006).

Swank, R. K.

Trtik, P.

Vågberg, W.

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
[Crossref] [PubMed]

W. Vågberg, D. H. Larsson, M. Li, A. Arner, and H. M. Hertz, “X-ray phase-contrast tomography for high-spatial resolution zebrafish muscle imaging,” Sci. Rep. 5, 16625 (2015).
[Crossref]

Wang, J.

Y. Yu and J. Wang, “Beam hardening-respecting flat field correction of digital X-ray detectors,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2012) pp. 2085–2088.

Westermark, U. K.

D. H. Larsson, U. Lundström, U. K. Westermark, M. Arsenian Henriksson, A Burvall, and H. M. Hertz, “First application of liquid-metal-jet sources for small-animal imaging: High-resolution CT and phase-contrast tumor demarcation,” Med. Phys. 40, 021909 (2013).
[Crossref] [PubMed]

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 homogenous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

Yaroshenko, A.

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
[Crossref] [PubMed]

Yildirim, A. Ö.

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
[Crossref] [PubMed]

Yu, Y.

Y. Yu and J. Wang, “Beam hardening-respecting flat field correction of digital X-ray detectors,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2012) pp. 2085–2088.

Zhang, P.

Y. Zhu, M. Zhao, H. Li, and P. Zhang, “Micro-CT artifacts reduction based on detector random shifting and fast data inpainting,” Med. Phys. 40, 031114 (2013).
[Crossref] [PubMed]

Zhao, M.

Y. Zhu, M. Zhao, H. Li, and P. Zhang, “Micro-CT artifacts reduction based on detector random shifting and fast data inpainting,” Med. Phys. 40, 031114 (2013).
[Crossref] [PubMed]

Zhong, Y.

C. Altunbas, C-J. Lai, Y. Zhong, and C. C. Shaw, “Reduction of ring artifacts in CBCT: Detection and correction of pixel gain variations in flat panel detectors,” Med. Phys. 41, 091913 (2014).
[Crossref] [PubMed]

Zhu, Y.

Y. Zhu, M. Zhao, H. Li, and P. Zhang, “Micro-CT artifacts reduction based on detector random shifting and fast data inpainting,” Med. Phys. 40, 031114 (2013).
[Crossref] [PubMed]

Appl. Opt. (1)

EURASIP J. Adv. Sig. Pr. (1)

S. Rashid, S. Y. Lee, and K. Hasan, “An improved method for the removal of ring artifacts in high resolution CT imaging,” EURASIP J. Adv. Sig. Pr. 2012:93 (2012).
[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 homogenous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

Med. Phys. (3)

D. H. Larsson, U. Lundström, U. K. Westermark, M. Arsenian Henriksson, A Burvall, and H. M. Hertz, “First application of liquid-metal-jet sources for small-animal imaging: High-resolution CT and phase-contrast tumor demarcation,” Med. Phys. 40, 021909 (2013).
[Crossref] [PubMed]

C. Altunbas, C-J. Lai, Y. Zhong, and C. C. Shaw, “Reduction of ring artifacts in CBCT: Detection and correction of pixel gain variations in flat panel detectors,” Med. Phys. 41, 091913 (2014).
[Crossref] [PubMed]

Y. Zhu, M. Zhao, H. Li, and P. Zhang, “Micro-CT artifacts reduction based on detector random shifting and fast data inpainting,” Med. Phys. 40, 031114 (2013).
[Crossref] [PubMed]

Nucl. Instrum. Meth. A (2)

D. W. Davidson, C. Fröjdh, V. O’Shea, H-E. Nilsson, and M. Rahman, “Limitations to flat-field correction methods when using an X-ray spectrum,” Nucl. Instrum. Meth. A 509, 146–150 (2003).
[Crossref]

G. R. Davis and J. C. Elliott, “X-ray microtomography scanner using time-delay integration for elimination of ring artefacts in the reconstructed image,” Nucl. Instrum. Meth. A 394, 157–162 (1997).
[Crossref]

Opt. Express (1)

Phys. Med. Biol. (1)

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

Radiographics (1)

J. F. Barrett and N. Keat, “Artifacts in CT: Recognition and avoidance,” Radiographics 24, 1679–1691 (2004).
[Crossref] [PubMed]

Rev. Sci. Inst. (1)

C. Raven, “Numerical removal of ring artifacts in microtomography,” Rev. Sci. Inst. 69, 2978–2980 (1998).
[Crossref]

Sci. Rep. (2)

W. Vågberg, D. H. Larsson, M. Li, A. Arner, and H. M. Hertz, “X-ray phase-contrast tomography for high-spatial resolution zebrafish muscle imaging,” Sci. Rep. 5, 16625 (2015).
[Crossref]

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
[Crossref] [PubMed]

Signal Image Video P. (1)

K. Hasan, F. Sadi, and S. Y. Lee, “Removal of ring artifacts in micro-CT imaging using iterative morphological filters,” Signal Image Video P. 6, 41–53 (2010).
[Crossref]

Other (4)

J. H. Hubbell and S. M. Seltzer, “Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest,” https://www.nist.gov/pml/x-ray-mass-attenuation-coefficients .

M. Axelsson, S. Svensson, and G. Borgefors, “Reduction of Ring Artifacts in High Resolution X-Ray Microtomography Images,” in Pattern Recognition. DAGM 2006. Lecture Notes in Computer Science, K. Franke, KR. Müller, B. Nickolay, and R. Schäfer, eds. (Springer, 2006).

Y. Yu and J. Wang, “Beam hardening-respecting flat field correction of digital X-ray detectors,” in Proceedings of IEEE International Conference on Image Processing (IEEE, 2012) pp. 2085–2088.

J. Hsieh, Computed Tomography: Principles, Design, Artifacts, and Recent Advances (SPIE Press, 2009), Chap. 7.

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Fig. 1
Fig. 1

The scintillator thickness measured with the proposed method. The scintillator thickness measurements with the proposed method. (a) Thickness map of the mean of all four measurements. For visibility of the small structures, we only show a smaller region (500×500 pixels).(b) Histograms of measured thickness, for the four different measurements. (c) Histograms of the difference between each measurement and the mean of all four measurements.

Fig. 2
Fig. 2

A tomography of a PET phantom with air-filled holes, reconstructed with three different data processing methods. (a) Reconstructed after flat-field correction without filter. (b) Reconstructed after flat-field correction with 1800 μm Al absorber in the flat-fields. (c) Reconstructed with the proposed correction method and wrong material (Al). (d) Reconstructed with the proposed correction method and correct material (PET). Profiles are taken along the black lines, averaged over 30 pixel lines to reduce noise. The numbers are the standard deviations within the gray areas, relative to the contrast between air and PET. Scale bar is 5 mm. I–IV indicate the four domains, as described in the text.

Fig. 3
Fig. 3

A simulation to calculate the deviation between true spectrum and the estimated spectrum from camera intensity. (a) The 5 mm water phantom diameter water cylinder used in the simulation, with 0.2 mm and 1 mm diameter aluminum and air inserts. (b) The mean energies of the true spectrum in the simulation and the local spectrum estimation in the simulation using four different materials. The estimate is based on water absorption. The method gives slight errors from wrong material or where there is phase contrast. The deviations between the estimated mean energies and the true mean energy is shown in (c).

Tables (1)

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Table 1 Filter thicknesses and exposure times for the scintillator measurements. The total exposure time is 5.6 hours. This was repeated four times to assess the measurement precision.

Equations (4)

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R ( T f , T s , t ) = g t S ( E ) exp ( μ f ( E ) T f ) G ( T s , E ) d E + R d
R ( T obj , T s , t ) = g t S ( E ) exp ( μ obj ( E ) T obj ) G ( T s , E ) d E + R d
R ( 0 , T s , t ) = g t S ( E ) G ( T s , E ) d E + R d
R ( T obj , T s , t ) R d R ( 0 , T s , t ) R d = S ( E ) exp ( μ obj ( E ) T obj ) G ( T s , E ) d E S ( E ) G ( T s , E ) d E

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