Abstract

We present a pixel-specific, measurement-driven correction that effectively reduces errors in detector response that give rise to the ring artifacts commonly seen in X-ray computed tomography (CT) scans. This correction is easy to implement, suppresses CT artifacts significantly, and is effective enough for use with both absorption and phase contrast imaging. It can be used as a standalone correction or in conjunction with existing ring artifact removal algorithms to further improve image quality. We validate this method using two X-ray CT data sets acquired using monochromatic sources, showing post-correction signal-to-noise increases of up to 55%, and we define an image quality metric to use specifically for the assessment of ring artifact suppression.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (1)

2018 (6)

T. Zhou, H. Wang, T. Connolley, S. Scott, N. Baker, and K. Sawhney, “Development of an x-ray imaging system to prevent scintillator degradation for white synchrotron radiation,” J. Synchrotron Radiat. 25, 801–807 (2018).
[Crossref] [PubMed]

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast x-ray brain CT,” Sci. Rep. 8, 11412:1–12 (2018).
[Crossref]

L. Massimi, F. Brun, M. Fratini, I. Bukreeva, and A. Cedola, “An improved ring removal procedure for in-line x-ray phase contrast tomography,” Phys. Med. Biol. 63, 045007 (2018).
[Crossref] [PubMed]

N. T. Vo, R. C. Atwood, and M. Drakopoulos, “Superior techniques for eliminating ring artifacts in x-ray micro-tomography,” Opt. Express 26, 28396–28412 (2018).
[Crossref] [PubMed]

M. Hubert, A. Pacureanu, C. Guilloud, Y. Yang, J. C. da Silva, J. Laurencin, F. Lefebvre-Joud, and P. Cloetens, “Efficient correction of wavefront inhomogeneities in x-ray holographic nanotomography by random sample displacement,” Appl. Phys. Lett. 112, 203704 (2018).
[Crossref]

D. M. Pelt and D. Y. Parkinson, “Ring artifact reduction in synchrotron x-ray tomography through helical acquisition,” Meas. Sci. Technol. 29, 034002 (2018).
[Crossref]

2017 (6)

C. Jailin, J.-Y. Buffière, F. Hild, M. Poncelet, and S. Roux, “On the use of flat-fields for tomographic reconstruction,” J. Synchrotron Radiat. 24, 220–231 (2017).
[Crossref]

D.-J. Ji, G.-R. Qu, C.-H. Hu, B.-D. Liu, J.-B. Jian, and X.-K. Guo, “Anisotropic total variation minimization approach in in-line phase-contrast tomography and its application to correction of ring artifacts,” Chin. Phys. B 26, 060701 (2017).
[Crossref]

X. Liang, Z. Zhang, T. Niu, S. Yu, S. Wu, Z. Li, H. Zhang, and Y. Xie, “Iterative image-domain ring artifact removal in cone-beam CT,” Phys. Med. Biol. 62, 5276–5292 (2017).
[Crossref] [PubMed]

M. J. Kitchen, G. A. Buckley, T. E. Gureyev, M. J. Wallace, N. Andres-Thio, K. Uesugi, N. Yagi, and S. B. Hooper, “CT dose reduction factors in the thousands using x-ray phase contrast,” Sci. Rep. 7, 15953:1–9 (2017).
[Crossref]

W. Vågberg, J. C. Larsson, and H. M. Hertz, “Removal of ring artifacts in microtomography by characterization of scintillator variations,” Opt. Express 25, 23191–23198 (2017).
[Crossref] [PubMed]

T. E. Gureyev, Y. I. Nesterets, A. Kozlov, D. M. Paganin, and H. M. Quiney, “On the “unreasonable” effectiveness of transport of intensity imaging and optical deconvolution,” J. Opt. Soc. Am. A 34, 2251–2260 (2017).
[Crossref]

2016 (3)

D. M. Pelt, D. Gürsoy, W. J. Palenstijn, J. Sijbers, F. De Carlo, and K. J. Batenburg, “Integration of TomoPy and the ASTRA toolbox for advanced processing and reconstruction of tomographic synchrotron data,” J. Synchrotron Radiat. 23, 842–849 (2016).
[Crossref] [PubMed]

V. Titarenko, “1-D filter for ring artifact suppression,” IEEE Signal Process. Lett. 23, 800–804 (2016).
[Crossref]

L. Yan, T. Wu, S. Zhong, and Q. Zhang, “A variation-based ring artifact correction method with sparse constraint for flat-detector CT,” Phys. Med. Biol. 61, 1278–1292 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (6)

D. Jha, H. O. Sørensen, S. Dobberschütz, R. Feidenhans’l, and S. L. S. Stipp, “Adaptive center determination for effective suppression of ring artifacts in tomography images,” Appl. Phys. Lett. 105, 143107 (2014).
[Crossref]

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]

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

Y. I. Nesterets and T. E. Gureyev, “Noise propagation in x-ray phase-contrast imaging and computed tomography,” J. Phys. D: Appl. Phys. 47, 105402 (2014).
[Crossref]

T. E. Gureyev, S. C. Mayo, Y. I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli, K. M. Pavlov, M. J. Kitchen, F. Zanconati, C. Dullin, and G. Tromba, “Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography,” J. Phys. D: Appl. Phys. 47, 365401 (2014).
[Crossref]

E. X. Miqueles, J. Rinkel, F. O’Dowd, and J. S. V. Bermúdez, “Generalized Titarenko’s algorithm for ring artefacts reduction,” J. Synchrotron Radiat. 21, 1333–1346 (2014).
[Crossref] [PubMed]

2011 (1)

M. A. Beltran, D. M. Paganin, K. K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[Crossref] [PubMed]

2010 (2)

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[Crossref] [PubMed]

M. A. Yousuf and M. Asaduzzaman, “An efficient ring artifact reduction method based on projection data for micro-CT images,” J. Sci. Res. 2, 37–45 (2010).
[Crossref]

2009 (1)

2008 (1)

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[Crossref] [PubMed]

2006 (1)

2004 (1)

J. Sijbers and A. Postnov, “Reduction of ring artefacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49, N247 (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, 33–40 (2002).
[Crossref] [PubMed]

1998 (1)

C. Raven, “Numerical removal of ring artifacts in microtomography,” Rev. Sci. Instrum. 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. Methods Phys. Res. A 394, 157–162 (1997).
[Crossref]

1996 (1)

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

1995 (1)

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

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]

Andres-Thio, N.

M. J. Kitchen, G. A. Buckley, T. E. Gureyev, M. J. Wallace, N. Andres-Thio, K. Uesugi, N. Yagi, and S. B. Hooper, “CT dose reduction factors in the thousands using x-ray phase contrast,” Sci. Rep. 7, 15953:1–9 (2017).
[Crossref]

Arfelli, F.

T. E. Gureyev, S. C. Mayo, Y. I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli, K. M. Pavlov, M. J. Kitchen, F. Zanconati, C. Dullin, and G. Tromba, “Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography,” J. Phys. D: Appl. Phys. 47, 365401 (2014).
[Crossref]

Asaduzzaman, M.

M. A. Yousuf and M. Asaduzzaman, “An efficient ring artifact reduction method based on projection data for micro-CT images,” J. Sci. Res. 2, 37–45 (2010).
[Crossref]

Atwood, R. C.

Baker, N.

T. Zhou, H. Wang, T. Connolley, S. Scott, N. Baker, and K. Sawhney, “Development of an x-ray imaging system to prevent scintillator degradation for white synchrotron radiation,” J. Synchrotron Radiat. 25, 801–807 (2018).
[Crossref] [PubMed]

Barrett, R.

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

Baruchel, J.

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

Batenburg, K. J.

D. M. Pelt, D. Gürsoy, W. J. Palenstijn, J. Sijbers, F. De Carlo, and K. J. Batenburg, “Integration of TomoPy and the ASTRA toolbox for advanced processing and reconstruction of tomographic synchrotron data,” J. Synchrotron Radiat. 23, 842–849 (2016).
[Crossref] [PubMed]

Beltran, M. A.

M. A. Beltran, D. M. Paganin, K. K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[Crossref] [PubMed]

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[Crossref] [PubMed]

Bermúdez, J. S. V.

E. X. Miqueles, J. Rinkel, F. O’Dowd, and J. S. V. Bermúdez, “Generalized Titarenko’s algorithm for ring artefacts reduction,” J. Synchrotron Radiat. 21, 1333–1346 (2014).
[Crossref] [PubMed]

Boin, M.

Brun, F.

L. Massimi, F. Brun, M. Fratini, I. Bukreeva, and A. Cedola, “An improved ring removal procedure for in-line x-ray phase contrast tomography,” Phys. Med. Biol. 63, 045007 (2018).
[Crossref] [PubMed]

Buckley, G. A.

M. J. Kitchen, G. A. Buckley, T. E. Gureyev, M. J. Wallace, N. Andres-Thio, K. Uesugi, N. Yagi, and S. B. Hooper, “CT dose reduction factors in the thousands using x-ray phase contrast,” Sci. Rep. 7, 15953:1–9 (2017).
[Crossref]

Buffière, J.-Y.

C. Jailin, J.-Y. Buffière, F. Hild, M. Poncelet, and S. Roux, “On the use of flat-fields for tomographic reconstruction,” J. Synchrotron Radiat. 24, 220–231 (2017).
[Crossref]

Bukreeva, I.

L. Massimi, F. Brun, M. Fratini, I. Bukreeva, and A. Cedola, “An improved ring removal procedure for in-line x-ray phase contrast tomography,” Phys. Med. Biol. 63, 045007 (2018).
[Crossref] [PubMed]

Cedola, A.

L. Massimi, F. Brun, M. Fratini, I. Bukreeva, and A. Cedola, “An improved ring removal procedure for in-line x-ray phase contrast tomography,” Phys. Med. Biol. 63, 045007 (2018).
[Crossref] [PubMed]

Cloetens, P.

M. Hubert, A. Pacureanu, C. Guilloud, Y. Yang, J. C. da Silva, J. Laurencin, F. Lefebvre-Joud, and P. Cloetens, “Efficient correction of wavefront inhomogeneities in x-ray holographic nanotomography by random sample displacement,” Appl. Phys. Lett. 112, 203704 (2018).
[Crossref]

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[Crossref] [PubMed]

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

Connolley, T.

T. Zhou, H. Wang, T. Connolley, S. Scott, N. Baker, and K. Sawhney, “Development of an x-ray imaging system to prevent scintillator degradation for white synchrotron radiation,” J. Synchrotron Radiat. 25, 801–807 (2018).
[Crossref] [PubMed]

Crossley, K. J.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast x-ray brain CT,” Sci. Rep. 8, 11412:1–12 (2018).
[Crossref]

Croton, L. C. P.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast x-ray brain CT,” Sci. Rep. 8, 11412:1–12 (2018).
[Crossref]

da Silva, J. C.

M. Hubert, A. Pacureanu, C. Guilloud, Y. Yang, J. C. da Silva, J. Laurencin, F. Lefebvre-Joud, and P. Cloetens, “Efficient correction of wavefront inhomogeneities in x-ray holographic nanotomography by random sample displacement,” Appl. Phys. Lett. 112, 203704 (2018).
[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. Methods Phys. Res. A 394, 157–162 (1997).
[Crossref]

De Beenhouwer, J.

De Carlo, F.

D. M. Pelt, D. Gürsoy, W. J. Palenstijn, J. Sijbers, F. De Carlo, and K. J. Batenburg, “Integration of TomoPy and the ASTRA toolbox for advanced processing and reconstruction of tomographic synchrotron data,” J. Synchrotron Radiat. 23, 842–849 (2016).
[Crossref] [PubMed]

V. Van Nieuwenhove, J. De Beenhouwer, F. De Carlo, L. Mancini, F. Marone, and J. Sijbers, “Dynamic intensity normalization using eigen flat fields in x-ray imaging,” Opt. Express 23, 27975–27989 (2015).
[Crossref] [PubMed]

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

Dobberschütz, S.

D. Jha, H. O. Sørensen, S. Dobberschütz, R. Feidenhans’l, and S. L. S. Stipp, “Adaptive center determination for effective suppression of ring artifacts in tomography images,” Appl. Phys. Lett. 105, 143107 (2014).
[Crossref]

Drakopoulos, M.

Dullin, C.

T. E. Gureyev, S. C. Mayo, Y. I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli, K. M. Pavlov, M. J. Kitchen, F. Zanconati, C. Dullin, and G. Tromba, “Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography,” J. Phys. D: Appl. Phys. 47, 365401 (2014).
[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. Methods Phys. Res. A 394, 157–162 (1997).
[Crossref]

Feidenhans’l, R.

D. Jha, H. O. Sørensen, S. Dobberschütz, R. Feidenhans’l, and S. L. S. Stipp, “Adaptive center determination for effective suppression of ring artifacts in tomography images,” Appl. Phys. Lett. 105, 143107 (2014).
[Crossref]

Fouras, A.

M. A. Beltran, D. M. Paganin, K. K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[Crossref] [PubMed]

Fratini, M.

L. Massimi, F. Brun, M. Fratini, I. Bukreeva, and A. Cedola, “An improved ring removal procedure for in-line x-ray phase contrast tomography,” Phys. Med. Biol. 63, 045007 (2018).
[Crossref] [PubMed]

Guigay, J.

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

Guigay, J. P.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[Crossref] [PubMed]

Guilloud, C.

M. Hubert, A. Pacureanu, C. Guilloud, Y. Yang, J. C. da Silva, J. Laurencin, F. Lefebvre-Joud, and P. Cloetens, “Efficient correction of wavefront inhomogeneities in x-ray holographic nanotomography by random sample displacement,” Appl. Phys. Lett. 112, 203704 (2018).
[Crossref]

Guo, X.-K.

D.-J. Ji, G.-R. Qu, C.-H. Hu, B.-D. Liu, J.-B. Jian, and X.-K. Guo, “Anisotropic total variation minimization approach in in-line phase-contrast tomography and its application to correction of ring artifacts,” Chin. Phys. B 26, 060701 (2017).
[Crossref]

Gureyev, T. E.

M. J. Kitchen, G. A. Buckley, T. E. Gureyev, M. J. Wallace, N. Andres-Thio, K. Uesugi, N. Yagi, and S. B. Hooper, “CT dose reduction factors in the thousands using x-ray phase contrast,” Sci. Rep. 7, 15953:1–9 (2017).
[Crossref]

T. E. Gureyev, Y. I. Nesterets, A. Kozlov, D. M. Paganin, and H. M. Quiney, “On the “unreasonable” effectiveness of transport of intensity imaging and optical deconvolution,” J. Opt. Soc. Am. A 34, 2251–2260 (2017).
[Crossref]

Y. I. Nesterets and T. E. Gureyev, “Noise propagation in x-ray phase-contrast imaging and computed tomography,” J. Phys. D: Appl. Phys. 47, 105402 (2014).
[Crossref]

T. E. Gureyev, S. C. Mayo, Y. I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli, K. M. Pavlov, M. J. Kitchen, F. Zanconati, C. Dullin, and G. Tromba, “Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography,” J. Phys. D: Appl. Phys. 47, 365401 (2014).
[Crossref]

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, 33–40 (2002).
[Crossref] [PubMed]

Gürsoy, D.

D. M. Pelt, D. Gürsoy, W. J. Palenstijn, J. Sijbers, F. De Carlo, and K. J. Batenburg, “Integration of TomoPy and the ASTRA toolbox for advanced processing and reconstruction of tomographic synchrotron data,” J. Synchrotron Radiat. 23, 842–849 (2016).
[Crossref] [PubMed]

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

Haibel, A.

Hertz, H. M.

Hild, F.

C. Jailin, J.-Y. Buffière, F. Hild, M. Poncelet, and S. Roux, “On the use of flat-fields for tomographic reconstruction,” J. Synchrotron Radiat. 24, 220–231 (2017).
[Crossref]

Hooper, S. B.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast x-ray brain CT,” Sci. Rep. 8, 11412:1–12 (2018).
[Crossref]

M. J. Kitchen, G. A. Buckley, T. E. Gureyev, M. J. Wallace, N. Andres-Thio, K. Uesugi, N. Yagi, and S. B. Hooper, “CT dose reduction factors in the thousands using x-ray phase contrast,” Sci. Rep. 7, 15953:1–9 (2017).
[Crossref]

M. A. Beltran, D. M. Paganin, K. K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[Crossref] [PubMed]

Hu, C.-H.

D.-J. Ji, G.-R. Qu, C.-H. Hu, B.-D. Liu, J.-B. Jian, and X.-K. Guo, “Anisotropic total variation minimization approach in in-line phase-contrast tomography and its application to correction of ring artifacts,” Chin. Phys. B 26, 060701 (2017).
[Crossref]

Hubert, M.

M. Hubert, A. Pacureanu, C. Guilloud, Y. Yang, J. C. da Silva, J. Laurencin, F. Lefebvre-Joud, and P. Cloetens, “Efficient correction of wavefront inhomogeneities in x-ray holographic nanotomography by random sample displacement,” Appl. Phys. Lett. 112, 203704 (2018).
[Crossref]

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, 1188–1193 (2014).
[Crossref] [PubMed]

Jailin, C.

C. Jailin, J.-Y. Buffière, F. Hild, M. Poncelet, and S. Roux, “On the use of flat-fields for tomographic reconstruction,” J. Synchrotron Radiat. 24, 220–231 (2017).
[Crossref]

Jha, D.

D. Jha, H. O. Sørensen, S. Dobberschütz, R. Feidenhans’l, and S. L. S. Stipp, “Adaptive center determination for effective suppression of ring artifacts in tomography images,” Appl. Phys. Lett. 105, 143107 (2014).
[Crossref]

Ji, D.-J.

D.-J. Ji, G.-R. Qu, C.-H. Hu, B.-D. Liu, J.-B. Jian, and X.-K. Guo, “Anisotropic total variation minimization approach in in-line phase-contrast tomography and its application to correction of ring artifacts,” Chin. Phys. B 26, 060701 (2017).
[Crossref]

Jian, J.-B.

D.-J. Ji, G.-R. Qu, C.-H. Hu, B.-D. Liu, J.-B. Jian, and X.-K. Guo, “Anisotropic total variation minimization approach in in-line phase-contrast tomography and its application to correction of ring artifacts,” Chin. Phys. B 26, 060701 (2017).
[Crossref]

Kerr, L. T.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast x-ray brain CT,” Sci. Rep. 8, 11412:1–12 (2018).
[Crossref]

Kitchen, M. J.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast x-ray brain CT,” Sci. Rep. 8, 11412:1–12 (2018).
[Crossref]

M. J. Kitchen, G. A. Buckley, T. E. Gureyev, M. J. Wallace, N. Andres-Thio, K. Uesugi, N. Yagi, and S. B. Hooper, “CT dose reduction factors in the thousands using x-ray phase contrast,” Sci. Rep. 7, 15953:1–9 (2017).
[Crossref]

T. E. Gureyev, S. C. Mayo, Y. I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli, K. M. Pavlov, M. J. Kitchen, F. Zanconati, C. Dullin, and G. Tromba, “Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography,” J. Phys. D: Appl. Phys. 47, 365401 (2014).
[Crossref]

M. A. Beltran, D. M. Paganin, K. K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[Crossref] [PubMed]

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[Crossref] [PubMed]

Kohn, V.

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

Kozlov, A.

Kuznetsov, S.

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

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]

Langer, M.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[Crossref] [PubMed]

Larsson, J. C.

Laurencin, J.

M. Hubert, A. Pacureanu, C. Guilloud, Y. Yang, J. C. da Silva, J. Laurencin, F. Lefebvre-Joud, and P. Cloetens, “Efficient correction of wavefront inhomogeneities in x-ray holographic nanotomography by random sample displacement,” Appl. Phys. Lett. 112, 203704 (2018).
[Crossref]

Lefebvre-Joud, F.

M. Hubert, A. Pacureanu, C. Guilloud, Y. Yang, J. C. da Silva, J. Laurencin, F. Lefebvre-Joud, and P. Cloetens, “Efficient correction of wavefront inhomogeneities in x-ray holographic nanotomography by random sample displacement,” Appl. Phys. Lett. 112, 203704 (2018).
[Crossref]

Li, Z.

X. Liang, Z. Zhang, T. Niu, S. Yu, S. Wu, Z. Li, H. Zhang, and Y. Xie, “Iterative image-domain ring artifact removal in cone-beam CT,” Phys. Med. Biol. 62, 5276–5292 (2017).
[Crossref] [PubMed]

Liang, X.

X. Liang, Z. Zhang, T. Niu, S. Yu, S. Wu, Z. Li, H. Zhang, and Y. Xie, “Iterative image-domain ring artifact removal in cone-beam CT,” Phys. Med. Biol. 62, 5276–5292 (2017).
[Crossref] [PubMed]

Lifton, J.

Liu, B.-D.

D.-J. Ji, G.-R. Qu, C.-H. Hu, B.-D. Liu, J.-B. Jian, and X.-K. Guo, “Anisotropic total variation minimization approach in in-line phase-contrast tomography and its application to correction of ring artifacts,” Chin. Phys. B 26, 060701 (2017).
[Crossref]

Liu, T.

Lockie, D.

T. E. Gureyev, S. C. Mayo, Y. I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli, K. M. Pavlov, M. J. Kitchen, F. Zanconati, C. Dullin, and G. Tromba, “Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography,” J. Phys. D: Appl. Phys. 47, 365401 (2014).
[Crossref]

Mancini, L.

Marone, F.

Massimi, L.

L. Massimi, F. Brun, M. Fratini, I. Bukreeva, and A. Cedola, “An improved ring removal procedure for in-line x-ray phase contrast tomography,” Phys. Med. Biol. 63, 045007 (2018).
[Crossref] [PubMed]

Mayo, S. C.

T. E. Gureyev, S. C. Mayo, Y. I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli, K. M. Pavlov, M. J. Kitchen, F. Zanconati, C. Dullin, and G. Tromba, “Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography,” J. Phys. D: Appl. Phys. 47, 365401 (2014).
[Crossref]

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, 33–40 (2002).
[Crossref] [PubMed]

Menk, R. H.

T. E. Gureyev, S. C. Mayo, Y. I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli, K. M. Pavlov, M. J. Kitchen, F. Zanconati, C. Dullin, and G. Tromba, “Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography,” J. Phys. D: Appl. Phys. 47, 365401 (2014).
[Crossref]

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, 33–40 (2002).
[Crossref] [PubMed]

Miller, S. L.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast x-ray brain CT,” Sci. Rep. 8, 11412:1–12 (2018).
[Crossref]

Miqueles, E. X.

E. X. Miqueles, J. Rinkel, F. O’Dowd, and J. S. V. Bermúdez, “Generalized Titarenko’s algorithm for ring artefacts reduction,” J. Synchrotron Radiat. 21, 1333–1346 (2014).
[Crossref] [PubMed]

Mirone, A.

P. Paleo and A. Mirone, “Ring artifacts correction in compressed sensing tomographic reconstruction,” J. Synchrotron Radiat. 22, 1268–1278 (2015).
[Crossref] [PubMed]

Mohammadi, S.

T. E. Gureyev, S. C. Mayo, Y. I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli, K. M. Pavlov, M. J. Kitchen, F. Zanconati, C. Dullin, and G. Tromba, “Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography,” J. Phys. D: Appl. Phys. 47, 365401 (2014).
[Crossref]

Morgan, K. S.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast x-ray brain CT,” Sci. Rep. 8, 11412:1–12 (2018).
[Crossref]

Münch, B.

Nesterets, Y. I.

T. E. Gureyev, Y. I. Nesterets, A. Kozlov, D. M. Paganin, and H. M. Quiney, “On the “unreasonable” effectiveness of transport of intensity imaging and optical deconvolution,” J. Opt. Soc. Am. A 34, 2251–2260 (2017).
[Crossref]

T. E. Gureyev, S. C. Mayo, Y. I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli, K. M. Pavlov, M. J. Kitchen, F. Zanconati, C. Dullin, and G. Tromba, “Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography,” J. Phys. D: Appl. Phys. 47, 365401 (2014).
[Crossref]

Y. I. Nesterets and T. E. Gureyev, “Noise propagation in x-ray phase-contrast imaging and computed tomography,” J. Phys. D: Appl. Phys. 47, 105402 (2014).
[Crossref]

Niu, T.

X. Liang, Z. Zhang, T. Niu, S. Yu, S. Wu, Z. Li, H. Zhang, and Y. Xie, “Iterative image-domain ring artifact removal in cone-beam CT,” Phys. Med. Biol. 62, 5276–5292 (2017).
[Crossref] [PubMed]

O’Dowd, F.

E. X. Miqueles, J. Rinkel, F. O’Dowd, and J. S. V. Bermúdez, “Generalized Titarenko’s algorithm for ring artefacts reduction,” J. Synchrotron Radiat. 21, 1333–1346 (2014).
[Crossref] [PubMed]

Pacureanu, A.

M. Hubert, A. Pacureanu, C. Guilloud, Y. Yang, J. C. da Silva, J. Laurencin, F. Lefebvre-Joud, and P. Cloetens, “Efficient correction of wavefront inhomogeneities in x-ray holographic nanotomography by random sample displacement,” Appl. Phys. Lett. 112, 203704 (2018).
[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 homogeneous object,” J. Microsc. 206, 33–40 (2002).
[Crossref] [PubMed]

Paganin, D. M.

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast x-ray brain CT,” Sci. Rep. 8, 11412:1–12 (2018).
[Crossref]

T. E. Gureyev, Y. I. Nesterets, A. Kozlov, D. M. Paganin, and H. M. Quiney, “On the “unreasonable” effectiveness of transport of intensity imaging and optical deconvolution,” J. Opt. Soc. Am. A 34, 2251–2260 (2017).
[Crossref]

M. A. Beltran, D. M. Paganin, K. K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[Crossref] [PubMed]

M. A. Beltran, D. M. Paganin, K. Uesugi, and M. J. Kitchen, “2D and 3D x-ray phase retrieval of multi-material objects using a single defocus distance,” Opt. Express 18, 6423–6436 (2010).
[Crossref] [PubMed]

Palenstijn, W. J.

D. M. Pelt, D. Gürsoy, W. J. Palenstijn, J. Sijbers, F. De Carlo, and K. J. Batenburg, “Integration of TomoPy and the ASTRA toolbox for advanced processing and reconstruction of tomographic synchrotron data,” J. Synchrotron Radiat. 23, 842–849 (2016).
[Crossref] [PubMed]

Paleo, P.

P. Paleo and A. Mirone, “Ring artifacts correction in compressed sensing tomographic reconstruction,” J. Synchrotron Radiat. 22, 1268–1278 (2015).
[Crossref] [PubMed]

Parkinson, D. Y.

D. M. Pelt and D. Y. Parkinson, “Ring artifact reduction in synchrotron x-ray tomography through helical acquisition,” Meas. Sci. Technol. 29, 034002 (2018).
[Crossref]

Pavlov, K. M.

T. E. Gureyev, S. C. Mayo, Y. I. Nesterets, S. Mohammadi, D. Lockie, R. H. Menk, F. Arfelli, K. M. Pavlov, M. J. Kitchen, F. Zanconati, C. Dullin, and G. Tromba, “Investigation of the imaging quality of synchrotron-based phase-contrast mammographic tomography,” J. Phys. D: Appl. Phys. 47, 365401 (2014).
[Crossref]

Pelt, D. M.

D. M. Pelt and D. Y. Parkinson, “Ring artifact reduction in synchrotron x-ray tomography through helical acquisition,” Meas. Sci. Technol. 29, 034002 (2018).
[Crossref]

D. M. Pelt, D. Gürsoy, W. J. Palenstijn, J. Sijbers, F. De Carlo, and K. J. Batenburg, “Integration of TomoPy and the ASTRA toolbox for advanced processing and reconstruction of tomographic synchrotron data,” J. Synchrotron Radiat. 23, 842–849 (2016).
[Crossref] [PubMed]

Peyrin, F.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[Crossref] [PubMed]

Poncelet, M.

C. Jailin, J.-Y. Buffière, F. Hild, M. Poncelet, and S. Roux, “On the use of flat-fields for tomographic reconstruction,” J. Synchrotron Radiat. 24, 220–231 (2017).
[Crossref]

Postnov, A.

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

Qu, G.-R.

D.-J. Ji, G.-R. Qu, C.-H. Hu, B.-D. Liu, J.-B. Jian, and X.-K. Guo, “Anisotropic total variation minimization approach in in-line phase-contrast tomography and its application to correction of ring artifacts,” Chin. Phys. B 26, 060701 (2017).
[Crossref]

Quiney, H. M.

Raven, C.

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

Reser, D. H.

M. A. Beltran, D. M. Paganin, K. K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[Crossref] [PubMed]

Rinkel, J.

E. X. Miqueles, J. Rinkel, F. O’Dowd, and J. S. V. Bermúdez, “Generalized Titarenko’s algorithm for ring artefacts reduction,” J. Synchrotron Radiat. 21, 1333–1346 (2014).
[Crossref] [PubMed]

Roux, S.

C. Jailin, J.-Y. Buffière, F. Hild, M. Poncelet, and S. Roux, “On the use of flat-fields for tomographic reconstruction,” J. Synchrotron Radiat. 24, 220–231 (2017).
[Crossref]

Sawhney, K.

T. Zhou, H. Wang, T. Connolley, S. Scott, N. Baker, and K. Sawhney, “Development of an x-ray imaging system to prevent scintillator degradation for white synchrotron radiation,” J. Synchrotron Radiat. 25, 801–807 (2018).
[Crossref] [PubMed]

Schlenker, M.

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

Scott, S.

T. Zhou, H. Wang, T. Connolley, S. Scott, N. Baker, and K. Sawhney, “Development of an x-ray imaging system to prevent scintillator degradation for white synchrotron radiation,” J. Synchrotron Radiat. 25, 801–807 (2018).
[Crossref] [PubMed]

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.

D. M. Pelt, D. Gürsoy, W. J. Palenstijn, J. Sijbers, F. De Carlo, and K. J. Batenburg, “Integration of TomoPy and the ASTRA toolbox for advanced processing and reconstruction of tomographic synchrotron data,” J. Synchrotron Radiat. 23, 842–849 (2016).
[Crossref] [PubMed]

V. Van Nieuwenhove, J. De Beenhouwer, F. De Carlo, L. Mancini, F. Marone, and J. Sijbers, “Dynamic intensity normalization using eigen flat fields in x-ray imaging,” Opt. Express 23, 27975–27989 (2015).
[Crossref] [PubMed]

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

Siu, K. K. W.

M. A. Beltran, D. M. Paganin, K. K. W. Siu, A. Fouras, S. B. Hooper, D. H. Reser, and M. J. Kitchen, “Interface-specific x-ray phase retrieval tomography of complex biological organs,” Phys. Med. Biol. 56, 7353–7369 (2011).
[Crossref] [PubMed]

Smith, S. W.

S. W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing (California Technical Publishing, 1997).

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, and S. Kuznetsov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instruments 66, 5486–5492 (1995).
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Sci. Rep. (2)

M. J. Kitchen, G. A. Buckley, T. E. Gureyev, M. J. Wallace, N. Andres-Thio, K. Uesugi, N. Yagi, and S. B. Hooper, “CT dose reduction factors in the thousands using x-ray phase contrast,” Sci. Rep. 7, 15953:1–9 (2017).
[Crossref]

L. C. P. Croton, K. S. Morgan, D. M. Paganin, L. T. Kerr, M. J. Wallace, K. J. Crossley, S. L. Miller, N. Yagi, K. Uesugi, S. B. Hooper, and M. J. Kitchen, “In situ phase contrast x-ray brain CT,” Sci. Rep. 8, 11412:1–12 (2018).
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Figures (8)

Fig. 1
Fig. 1 A flow chart of the correction algorithm. (1) The detector is swept through the X-ray beam while an image sequence is acquired. (2) The sequence is dark-corrected and stacked into a 3D volume. (3) A second volume is created to estimate the ‘true’ intensity of the beam by smoothing each image in the volume. (4) and (5) The measured intensity is fit as a function of the ‘true’ intensity for every pixel, yielding detector gain and dark-current offset maps. (6) For a CT data set, projections are corrected using these maps, after dark-current correction. (7) The mean of the flat-field images acquired with the CT data is dark-corrected, and the resultant image is smoothed using the same smoothing kernel as that used in step 3. (8) The corrected projection images are then flat-field corrected using the smoothed flat-field image, if necessary with scaling for beam injections. *The residual correction (7) and beam injection scaling (RP/RF) may be omitted if not required.
Fig. 2
Fig. 2 The experimental set-up, shown for an incident beam with a parabolic intensity profile. When sweeping vertically, the detector is positioned high enough above the beam to achieve the desired minimum number of incident counts. A sequence of images is then acquired while the detector is translated downward through the beam to the equivalent position below the beam. Three images are shown near the middle of the sequence, along with intensity profiles taken vertically through the center of the images. The extreme ends of the sequence (not shown) contain only traces of the edge of the incident beam. Note that the direction of transverse translation is not important; it is equally valid to acquire an image sequence while translating the detector horizontally through the beam.
Fig. 3
Fig. 3 a) The counts measured at a single pixel in a stack of images taken while the detector was swept vertically through the beam three times; the beam was centered first on the horizontal left, then center, and finally the right side of the detector. Note that the highest peak for this particular pixel corresponds to the sweep across the centre of the detector, with the next highest peak corresponding to the right, indicating that this pixel is located just to the right of the horizontal centre of the detector. b) The ‘true’ (i.e. smoothed) counts for the same pixel as in (a) as a function of the measured counts.
Fig. 4
Fig. 4 The detector gain (α) and offset (β) maps are shown in (a) and (b), respectively, for the Hamamatsu detector used at SPring-8. (c) and (d) show those for the pco.edge detector used at IMBL. Spatial scale bars are 1 mm in length. Numerous features can be seen to affect the response. These are labeled with white letters and are described at the end of section 3.
Fig. 5
Fig. 5 Top row: Phase-retrieved, reconstructed slices of a region near the cerebellum of the rabbit kitten head with different corrections applied. (a) Standard dark-current and flat-field correction. (b) The beam injection correction from section 5, step 8. (c) The primary response correction only. (d) The primary response and residual corrections. (e) The primary response, residual, and beam injection corrections. Bottom row: (f) The sinogram corresponding to the standard corrections. (g) - (j) The difference between (f) and the sinograms corresponding to each of the corrections in the top row.
Fig. 6
Fig. 6 (a), (b), (e), (f) Reconstructed tomograms of a rabbit kitten head in agarose and (c), (d), (g), (h) rabbit kitten lungs in agarose with MICROFIL contrast agent. Also shown are reconstructed slices of sample-free regions from both the (i), (j) head and (k), (l) lung data sets, containing only agarose. All data are shown without (first and third columns) and with (second and fourth columns) the correction detailed in this paper. Top row: Phase contrast tomograms of rabbit kitten head and lungs, no phase retrieval. Middle row: Tomograms of the same rabbit kitten head and lungs, after two-material phase retrieval [25, 27]. Bottom row: Phase-retrieved tomograms of sample-free regions from rabbit kitten head and lung data sets. First and third columns: Standard dark-current and flat-field correction. Second and fourth columns: Beam sweep response correction.
Fig. 7
Fig. 7 a) Azimuthally-averaged radial profiles for the sample-free region in Figs. 6(i) and 6(j). The decrease in the variance between the uncorrected and corrected images can be clearly seen, particularly at smaller radii, where the effects of the ring artifacts are strongest. b) The reconstruction region used for averaging (Hamamatsu ORCA Flash 4.0). Since the CT was acquired over 180°, the artifacts for individual pixels occur only in the top or the bottom half of the image. c) Azimuthally-averaged radial profiles for the sample-free region in Figs. 6(k) and 6(l). d) The reconstruction region used for averaging (pco.edge 5.5). The images in (b) and (d) are the uncorrected tomograms.
Fig. 8
Fig. 8 A phase-retrieved tomogram of a rabbit kitten brain in situ, with five different ring artifact correction methods applied, as labeled. The image on the upper left is the uncorrected image, with only a standard dark-current and flat-field correction applied, before phase retrieval. The image on the lower right has been corrected following the procedure outlined in this paper.

Equations (3)

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I s ( i , j , k ) = α [ I ( i , j , k ) D ( i , j ) ] + β .
P c ( i , j , k ) = α [ P ( i , j , k ) D ( i , j ) ] + β .
RASP = ( 1 σ c σ u ) × 100 % = ( 1 1 N j = 1 N ( x c , j μ c , j ) 2 1 N j = 1 N ( x u , j μ u , j ) 2 ) × 100 % .

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