Abstract

Dynamic computed tomography (CT) is usually employed to image motion objects, such as beating heart, coronary artery and cerebral perfusion, etc. Recently, to further improve the temporal resolution for aperiodic industrial process imaging, the swinging multi-source CT (SMCT) systems and the corresponding swinging multi-source prior image constrained compressed sensing (SM-PICCS) method were developed. Since the SM-PICCS uses the L1-norm of image gradient, the edge structures in the reconstructed images are blurred and motion artifacts are still present. Inspired by the advantages in terms of image edge preservation and fine structure recovering, the L0-norm of image gradient is incorporated into the prior image constrained compressed sensing, leading to an L0-PICCS Algorithm 1

Tables Icon

Table 1. The parameters of L0-PICCS (δ1,δ2,λ1*,λ2*) for numerical simulation.

. The experimental results confirm that the L0-PICCS outperforms the SM-PICCS in both visual inspection and quantitative analysis.

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

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2018 (5)

M. Holbrook, D. P. Clark, and C. T. Badea, “Low-dose 4D cardiac imaging in small animals using dual source micro-CT,” Phys. Med. Biol. 63(2), 025009 (2018).
[PubMed]

L. Zhang, L. Zeng, and Y. Guo, “l0 regularization based on a prior image incorporated non-local means for limited-angle X-ray CT reconstruction,” J. XRay Sci. Technol. 26(3), 481–498 (2018).
[Crossref] [PubMed]

W. Wu, Y. Zhang, Q. Wang, F. Liu, P. Chen, and H. Yu, “Low-dose spectral CT reconstruction using ℓ0 image gradient and tensor dictionary,” Appl. Math. Model. 63, 538–557 (2018).
[Crossref]

C. Gong, L. Zeng, C. Wang, and L. Ran, “Design and Simulation Study of a CNT-Based Multisource Cubical CT System for Dynamic Objects,” Scanning 2018, 6985698 (2018).
[Crossref] [PubMed]

W. Wu, Y. Zhang, Q. Wang, F. Liu, F. Luo, and H. Yu, “Spatial-spectral cube matching frame for spectral CT reconstruction,” Inverse Probl. 34(10), 104003 (2018).
[Crossref]

2017 (5)

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

M. Nakano, A. Haga, J. Kotoku, T. Magome, Y. Masutani, S. Hanaoka, S. Kida, and K. Nakagawa, “Cone-beam CT reconstruction for non-periodic organ motion using time-ordered chain graph model,” Radiat. Oncol. 12(1), 145 (2017).
[Crossref] [PubMed]

P. FitzGerald, P. Edic, H. Gao, Y. Jin, J. Wang, G. Wang, and B. Man, “Quest for the ultimate cardiac CT scanner,” Med. Phys. 44(9), 4506–4524 (2017).
[Crossref] [PubMed]

W. Wu, H. Yu, C. Gong, and F. Liu, “Swinging multi-source industrial CT systems for aperiodic dynamic imaging,” Opt. Express 25(20), 24215–24235 (2017).
[Crossref] [PubMed]

W. Yu, C. Wang, and M. Huang, “Edge-preserving reconstruction from sparse projections of limited-angle computed tomography using ℓ0-regularized gradient prior,” Rev. Sci. Instrum. 88(4), 043703 (2017).
[Crossref] [PubMed]

2016 (3)

R. Schwarze and J. Klostermann, “Computational Fluid Dynamic (CFD) Simulations of Liquid Steel Infiltration in Porous Ceramic Structures: Dynamics of the Penetrating Melt Surface,” Steel Res. Int. 87(4), 465–471 (2016).
[Crossref]

M. Li, C. Zhang, C. Peng, Y. Guan, P. Xu, M. Sun, and J. Zheng, “Smoothed l0 Norm Regularization for Sparse-View X-Ray CT Reconstruction,” BioMed Res. Int. 2016, 2180457 (2016).
[Crossref] [PubMed]

L. Zeng and C. Wang, “Error bounds and stability in the l0 regularized for CT reconstruction from small projections,” Inverse Probl. Imaging (Springfield) 10(3), 829–853 (2016).
[Crossref]

2015 (2)

S. Kim, Y. Chang, and J. B. Ra, “Cardiac motion correction based on partial angle reconstructed images in x-ray CT,” Med. Phys. 42(5), 2560–2571 (2015).
[PubMed]

W. M. Thompson, W. R. B. Lionheart, E. J. Morton, M. Cunningham, and R. D. Luggar, “High speed imaging of dynamic processes with a switched source x-ray CT system,” Meas. Sci. Technol. 26(5), 55401 (2015).
[Crossref]

2014 (3)

A. Bauereiß, T. Scharowsky, and C. Körner, “Defect generation and propagation mechanism during additive manufacturing by selective beam melting,” J. Mater. Process Tech. 214(11), 2522–2528 (2014).
[Crossref]

E. Y. Sidky, R. Chartrand, J. M. Boone, and X. Pan, “Constrained TpV Minimization for Enhanced Exploitation of Gradient Sparsity: Application to CT Image Reconstruction,” IEEE J. Transl. Eng. Health Med. 2, 1–18 (2014).
[Crossref] [PubMed]

Y. Sun and J. Tao, “Image reconstruction from few views by l(0)-norm optimization,” Chinese Phys. B 23(7), 078703 (2014).
[Crossref]

2012 (1)

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

2011 (2)

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, “Nonconvex prior image constrained compressed sensing (NCPICCS): theory and simulations on perfusion CT,” Med. Phys. 38(4), 2157–2167 (2011).
[Crossref] [PubMed]

B. Liu, G. Wang, E. L. Ritman, G. Cao, J. Lu, O. Zhou, L. Zeng, and H. Yu, “Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems,” Phys. Med. Biol. 56(19), 6337–6357 (2011).
[Crossref] [PubMed]

2009 (3)

G. H. Chen, J. Tang, and J. Hsieh, “Temporal resolution improvement using PICCS in MDCT cardiac imaging,” Med. Phys. 36(6), 2130–2135 (2009).
[Crossref] [PubMed]

J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l(0) -minimization,” IEEE Trans. Med. Imaging 28(1), 106–121 (2009).
[Crossref] [PubMed]

T. Goldstein and S. Osher, “The Split Bregman Method for L1-Regularized Problems,” SIAM J. Imaging Sci. 2(2), 323–343 (2009).
[Crossref]

2008 (3)

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53(17), 4777–4807 (2008).
[Crossref] [PubMed]

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53(17), 4777–4807 (2008).
[Crossref] [PubMed]

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

2007 (1)

R. Chartrand, “Exact Reconstruction of Sparse Signals via Nonconvex Minimization,” IEEE Signal Proc. Lett. 14(10), 707–710 (2007).
[Crossref]

2001 (1)

Y. Liu, H. Liu, Y. Wang, and G. Wang, “Half-scan cone-beam CT fluoroscopy with multiple x-ray sources,” Med. Phys. 28(7), 1466–1471 (2001).
[Crossref] [PubMed]

2000 (1)

P. R. Johnston and R. M. Gulrajani, “Selecting the corner in the L-curve approach to Tikhonov regularization,” IEEE Trans. Biomed. Eng. 47(9), 1293–1296 (2000).
[Crossref] [PubMed]

1983 (1)

R. A. Robb, E. A. Hoffman, L. J. Sinak, L. D. Harris, and E. L. Ritman, “High-speed three-dimensional X-ray computed tomography: The dynamic spatial reconstructor,” Proc. IEEE 71(3), 308–319 (1983).
[Crossref]

1970 (1)

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29(3), 471–481 (1970).
[PubMed]

Badea, C. T.

M. Holbrook, D. P. Clark, and C. T. Badea, “Low-dose 4D cardiac imaging in small animals using dual source micro-CT,” Phys. Med. Biol. 63(2), 025009 (2018).
[PubMed]

Bauereiß, A.

A. Bauereiß, T. Scharowsky, and C. Körner, “Defect generation and propagation mechanism during additive manufacturing by selective beam melting,” J. Mater. Process Tech. 214(11), 2522–2528 (2014).
[Crossref]

Bender, R.

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29(3), 471–481 (1970).
[PubMed]

Bert, C.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

Bevins, N.

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

Boone, J. M.

E. Y. Sidky, R. Chartrand, J. M. Boone, and X. Pan, “Constrained TpV Minimization for Enhanced Exploitation of Gradient Sparsity: Application to CT Image Reconstruction,” IEEE J. Transl. Eng. Health Med. 2, 1–18 (2014).
[Crossref] [PubMed]

Cao, G.

B. Liu, G. Wang, E. L. Ritman, G. Cao, J. Lu, O. Zhou, L. Zeng, and H. Yu, “Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems,” Phys. Med. Biol. 56(19), 6337–6357 (2011).
[Crossref] [PubMed]

Chang, Y.

S. Kim, Y. Chang, and J. B. Ra, “Cardiac motion correction based on partial angle reconstructed images in x-ray CT,” Med. Phys. 42(5), 2560–2571 (2015).
[PubMed]

Chartrand, R.

E. Y. Sidky, R. Chartrand, J. M. Boone, and X. Pan, “Constrained TpV Minimization for Enhanced Exploitation of Gradient Sparsity: Application to CT Image Reconstruction,” IEEE J. Transl. Eng. Health Med. 2, 1–18 (2014).
[Crossref] [PubMed]

R. Chartrand, “Exact Reconstruction of Sparse Signals via Nonconvex Minimization,” IEEE Signal Proc. Lett. 14(10), 707–710 (2007).
[Crossref]

E. Y. Sidky, R. Chartrand, and X. Pan, “Image reconstruction from few views by non-convex optimization,” in IEEE Nuclear Science Symposium Conference Record (2007), p. 3526.
[Crossref]

Chen, G. H.

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

G. H. Chen, J. Tang, and J. Hsieh, “Temporal resolution improvement using PICCS in MDCT cardiac imaging,” Med. Phys. 36(6), 2130–2135 (2009).
[Crossref] [PubMed]

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Chen, P.

W. Wu, Y. Zhang, Q. Wang, F. Liu, P. Chen, and H. Yu, “Low-dose spectral CT reconstruction using ℓ0 image gradient and tensor dictionary,” Appl. Math. Model. 63, 538–557 (2018).
[Crossref]

Clark, D. P.

M. Holbrook, D. P. Clark, and C. T. Badea, “Low-dose 4D cardiac imaging in small animals using dual source micro-CT,” Phys. Med. Biol. 63(2), 025009 (2018).
[PubMed]

Constantinescu, A. M.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

Cunningham, M.

W. M. Thompson, W. R. B. Lionheart, E. J. Morton, M. Cunningham, and R. D. Luggar, “High speed imaging of dynamic processes with a switched source x-ray CT system,” Meas. Sci. Technol. 26(5), 55401 (2015).
[Crossref]

Durante, M.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

Edic, P.

P. FitzGerald, P. Edic, H. Gao, Y. Jin, J. Wang, G. Wang, and B. Man, “Quest for the ultimate cardiac CT scanner,” Med. Phys. 44(9), 4506–4524 (2017).
[Crossref] [PubMed]

Eichhorn, A.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

FitzGerald, P.

P. FitzGerald, P. Edic, H. Gao, Y. Jin, J. Wang, G. Wang, and B. Man, “Quest for the ultimate cardiac CT scanner,” Med. Phys. 44(9), 4506–4524 (2017).
[Crossref] [PubMed]

Gao, H.

P. FitzGerald, P. Edic, H. Gao, Y. Jin, J. Wang, G. Wang, and B. Man, “Quest for the ultimate cardiac CT scanner,” Med. Phys. 44(9), 4506–4524 (2017).
[Crossref] [PubMed]

Goldstein, T.

T. Goldstein and S. Osher, “The Split Bregman Method for L1-Regularized Problems,” SIAM J. Imaging Sci. 2(2), 323–343 (2009).
[Crossref]

Gong, C.

C. Gong, L. Zeng, C. Wang, and L. Ran, “Design and Simulation Study of a CNT-Based Multisource Cubical CT System for Dynamic Objects,” Scanning 2018, 6985698 (2018).
[Crossref] [PubMed]

W. Wu, H. Yu, C. Gong, and F. Liu, “Swinging multi-source industrial CT systems for aperiodic dynamic imaging,” Opt. Express 25(20), 24215–24235 (2017).
[Crossref] [PubMed]

Gordon, R.

R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29(3), 471–481 (1970).
[PubMed]

Graeff, C.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

Guan, Y.

M. Li, C. Zhang, C. Peng, Y. Guan, P. Xu, M. Sun, and J. Zheng, “Smoothed l0 Norm Regularization for Sparse-View X-Ray CT Reconstruction,” BioMed Res. Int. 2016, 2180457 (2016).
[Crossref] [PubMed]

Gulrajani, R. M.

P. R. Johnston and R. M. Gulrajani, “Selecting the corner in the L-curve approach to Tikhonov regularization,” IEEE Trans. Biomed. Eng. 47(9), 1293–1296 (2000).
[Crossref] [PubMed]

Guo, Y.

L. Zhang, L. Zeng, and Y. Guo, “l0 regularization based on a prior image incorporated non-local means for limited-angle X-ray CT reconstruction,” J. XRay Sci. Technol. 26(3), 481–498 (2018).
[Crossref] [PubMed]

Haga, A.

M. Nakano, A. Haga, J. Kotoku, T. Magome, Y. Masutani, S. Hanaoka, S. Kida, and K. Nakagawa, “Cone-beam CT reconstruction for non-periodic organ motion using time-ordered chain graph model,” Radiat. Oncol. 12(1), 145 (2017).
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Hanaoka, S.

M. Nakano, A. Haga, J. Kotoku, T. Magome, Y. Masutani, S. Hanaoka, S. Kida, and K. Nakagawa, “Cone-beam CT reconstruction for non-periodic organ motion using time-ordered chain graph model,” Radiat. Oncol. 12(1), 145 (2017).
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R. A. Robb, E. A. Hoffman, L. J. Sinak, L. D. Harris, and E. L. Ritman, “High-speed three-dimensional X-ray computed tomography: The dynamic spatial reconstructor,” Proc. IEEE 71(3), 308–319 (1983).
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R. A. Robb, E. A. Hoffman, L. J. Sinak, L. D. Harris, and E. L. Ritman, “High-speed three-dimensional X-ray computed tomography: The dynamic spatial reconstructor,” Proc. IEEE 71(3), 308–319 (1983).
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M. Holbrook, D. P. Clark, and C. T. Badea, “Low-dose 4D cardiac imaging in small animals using dual source micro-CT,” Phys. Med. Biol. 63(2), 025009 (2018).
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G. H. Chen, J. Tang, and J. Hsieh, “Temporal resolution improvement using PICCS in MDCT cardiac imaging,” Med. Phys. 36(6), 2130–2135 (2009).
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Huang, M.

W. Yu, C. Wang, and M. Huang, “Edge-preserving reconstruction from sparse projections of limited-angle computed tomography using ℓ0-regularized gradient prior,” Rev. Sci. Instrum. 88(4), 043703 (2017).
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Jia, J.

L. Xu, C. Lu, Y. Xu, and J. Jia, “Image smoothing via L0 gradient minimization,” in SIGGRAPH Asia Conference (2011), p. 174.

Jin, Y.

P. FitzGerald, P. Edic, H. Gao, Y. Jin, J. Wang, G. Wang, and B. Man, “Quest for the ultimate cardiac CT scanner,” Med. Phys. 44(9), 4506–4524 (2017).
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D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
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Kida, S.

M. Nakano, A. Haga, J. Kotoku, T. Magome, Y. Masutani, S. Hanaoka, S. Kida, and K. Nakagawa, “Cone-beam CT reconstruction for non-periodic organ motion using time-ordered chain graph model,” Radiat. Oncol. 12(1), 145 (2017).
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S. Kim, Y. Chang, and J. B. Ra, “Cardiac motion correction based on partial angle reconstructed images in x-ray CT,” Med. Phys. 42(5), 2560–2571 (2015).
[PubMed]

Klostermann, J.

R. Schwarze and J. Klostermann, “Computational Fluid Dynamic (CFD) Simulations of Liquid Steel Infiltration in Porous Ceramic Structures: Dynamics of the Penetrating Melt Surface,” Steel Res. Int. 87(4), 465–471 (2016).
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Körner, C.

A. Bauereiß, T. Scharowsky, and C. Körner, “Defect generation and propagation mechanism during additive manufacturing by selective beam melting,” J. Mater. Process Tech. 214(11), 2522–2528 (2014).
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Kotoku, J.

M. Nakano, A. Haga, J. Kotoku, T. Magome, Y. Masutani, S. Hanaoka, S. Kida, and K. Nakagawa, “Cone-beam CT reconstruction for non-periodic organ motion using time-ordered chain graph model,” Radiat. Oncol. 12(1), 145 (2017).
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Lehmann, H. I.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
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Leng, S.

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, “Nonconvex prior image constrained compressed sensing (NCPICCS): theory and simulations on perfusion CT,” Med. Phys. 38(4), 2157–2167 (2011).
[Crossref] [PubMed]

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Li, M.

M. Li, C. Zhang, C. Peng, Y. Guan, P. Xu, M. Sun, and J. Zheng, “Smoothed l0 Norm Regularization for Sparse-View X-Ray CT Reconstruction,” BioMed Res. Int. 2016, 2180457 (2016).
[Crossref] [PubMed]

Lionheart, W. R. B.

W. M. Thompson, W. R. B. Lionheart, E. J. Morton, M. Cunningham, and R. D. Luggar, “High speed imaging of dynamic processes with a switched source x-ray CT system,” Meas. Sci. Technol. 26(5), 55401 (2015).
[Crossref]

Liu, B.

B. Liu, G. Wang, E. L. Ritman, G. Cao, J. Lu, O. Zhou, L. Zeng, and H. Yu, “Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems,” Phys. Med. Biol. 56(19), 6337–6357 (2011).
[Crossref] [PubMed]

Liu, F.

W. Wu, Y. Zhang, Q. Wang, F. Liu, P. Chen, and H. Yu, “Low-dose spectral CT reconstruction using ℓ0 image gradient and tensor dictionary,” Appl. Math. Model. 63, 538–557 (2018).
[Crossref]

W. Wu, Y. Zhang, Q. Wang, F. Liu, F. Luo, and H. Yu, “Spatial-spectral cube matching frame for spectral CT reconstruction,” Inverse Probl. 34(10), 104003 (2018).
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W. Wu, H. Yu, C. Gong, and F. Liu, “Swinging multi-source industrial CT systems for aperiodic dynamic imaging,” Opt. Express 25(20), 24215–24235 (2017).
[Crossref] [PubMed]

W. Wu, F. Liu, Y. Zhang, Q. Wang, and H. Yu, “Non-local Low-rank Cube-based Tensor Factorization for Spectral CT Reconstruction,” IEEE Trans. Med. Imaging1 (2018).

Liu, H.

Y. Liu, H. Liu, Y. Wang, and G. Wang, “Half-scan cone-beam CT fluoroscopy with multiple x-ray sources,” Med. Phys. 28(7), 1466–1471 (2001).
[Crossref] [PubMed]

Liu, Y.

Y. Liu, H. Liu, Y. Wang, and G. Wang, “Half-scan cone-beam CT fluoroscopy with multiple x-ray sources,” Med. Phys. 28(7), 1466–1471 (2001).
[Crossref] [PubMed]

Lu, C.

L. Xu, C. Lu, Y. Xu, and J. Jia, “Image smoothing via L0 gradient minimization,” in SIGGRAPH Asia Conference (2011), p. 174.

Lu, J.

B. Liu, G. Wang, E. L. Ritman, G. Cao, J. Lu, O. Zhou, L. Zeng, and H. Yu, “Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems,” Phys. Med. Biol. 56(19), 6337–6357 (2011).
[Crossref] [PubMed]

Lugenbiel, P.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

Luggar, R. D.

W. M. Thompson, W. R. B. Lionheart, E. J. Morton, M. Cunningham, and R. D. Luggar, “High speed imaging of dynamic processes with a switched source x-ray CT system,” Meas. Sci. Technol. 26(5), 55401 (2015).
[Crossref]

Luo, F.

W. Wu, Y. Zhang, Q. Wang, F. Liu, F. Luo, and H. Yu, “Spatial-spectral cube matching frame for spectral CT reconstruction,” Inverse Probl. 34(10), 104003 (2018).
[Crossref]

Magome, T.

M. Nakano, A. Haga, J. Kotoku, T. Magome, Y. Masutani, S. Hanaoka, S. Kida, and K. Nakagawa, “Cone-beam CT reconstruction for non-periodic organ motion using time-ordered chain graph model,” Radiat. Oncol. 12(1), 145 (2017).
[Crossref] [PubMed]

Man, B.

P. FitzGerald, P. Edic, H. Gao, Y. Jin, J. Wang, G. Wang, and B. Man, “Quest for the ultimate cardiac CT scanner,” Med. Phys. 44(9), 4506–4524 (2017).
[Crossref] [PubMed]

Manduca, A.

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, “Nonconvex prior image constrained compressed sensing (NCPICCS): theory and simulations on perfusion CT,” Med. Phys. 38(4), 2157–2167 (2011).
[Crossref] [PubMed]

J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l(0) -minimization,” IEEE Trans. Med. Imaging 28(1), 106–121 (2009).
[Crossref] [PubMed]

Masutani, Y.

M. Nakano, A. Haga, J. Kotoku, T. Magome, Y. Masutani, S. Hanaoka, S. Kida, and K. Nakagawa, “Cone-beam CT reconstruction for non-periodic organ motion using time-ordered chain graph model,” Radiat. Oncol. 12(1), 145 (2017).
[Crossref] [PubMed]

McCollough, C. H.

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, “Nonconvex prior image constrained compressed sensing (NCPICCS): theory and simulations on perfusion CT,” Med. Phys. 38(4), 2157–2167 (2011).
[Crossref] [PubMed]

Morton, E. J.

W. M. Thompson, W. R. B. Lionheart, E. J. Morton, M. Cunningham, and R. D. Luggar, “High speed imaging of dynamic processes with a switched source x-ray CT system,” Meas. Sci. Technol. 26(5), 55401 (2015).
[Crossref]

Nakagawa, K.

M. Nakano, A. Haga, J. Kotoku, T. Magome, Y. Masutani, S. Hanaoka, S. Kida, and K. Nakagawa, “Cone-beam CT reconstruction for non-periodic organ motion using time-ordered chain graph model,” Radiat. Oncol. 12(1), 145 (2017).
[Crossref] [PubMed]

Nakano, M.

M. Nakano, A. Haga, J. Kotoku, T. Magome, Y. Masutani, S. Hanaoka, S. Kida, and K. Nakagawa, “Cone-beam CT reconstruction for non-periodic organ motion using time-ordered chain graph model,” Radiat. Oncol. 12(1), 145 (2017).
[Crossref] [PubMed]

Nett, B.

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

Osher, S.

T. Goldstein and S. Osher, “The Split Bregman Method for L1-Regularized Problems,” SIAM J. Imaging Sci. 2(2), 323–343 (2009).
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Packer, D. L.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

Pan, X.

E. Y. Sidky, R. Chartrand, J. M. Boone, and X. Pan, “Constrained TpV Minimization for Enhanced Exploitation of Gradient Sparsity: Application to CT Image Reconstruction,” IEEE J. Transl. Eng. Health Med. 2, 1–18 (2014).
[Crossref] [PubMed]

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53(17), 4777–4807 (2008).
[Crossref] [PubMed]

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53(17), 4777–4807 (2008).
[Crossref] [PubMed]

E. Y. Sidky, R. Chartrand, and X. Pan, “Image reconstruction from few views by non-convex optimization,” in IEEE Nuclear Science Symposium Conference Record (2007), p. 3526.
[Crossref]

Peng, C.

M. Li, C. Zhang, C. Peng, Y. Guan, P. Xu, M. Sun, and J. Zheng, “Smoothed l0 Norm Regularization for Sparse-View X-Ray CT Reconstruction,” BioMed Res. Int. 2016, 2180457 (2016).
[Crossref] [PubMed]

Prall, M.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

Qi, Z.

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

Ra, J. B.

S. Kim, Y. Chang, and J. B. Ra, “Cardiac motion correction based on partial angle reconstructed images in x-ray CT,” Med. Phys. 42(5), 2560–2571 (2015).
[PubMed]

Ramirez-Giraldo, J. C.

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, “Nonconvex prior image constrained compressed sensing (NCPICCS): theory and simulations on perfusion CT,” Med. Phys. 38(4), 2157–2167 (2011).
[Crossref] [PubMed]

Ran, L.

C. Gong, L. Zeng, C. Wang, and L. Ran, “Design and Simulation Study of a CNT-Based Multisource Cubical CT System for Dynamic Objects,” Scanning 2018, 6985698 (2018).
[Crossref] [PubMed]

Raval, A.

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

Reeder, S.

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

Richter, D.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

Ritman, E. L.

B. Liu, G. Wang, E. L. Ritman, G. Cao, J. Lu, O. Zhou, L. Zeng, and H. Yu, “Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems,” Phys. Med. Biol. 56(19), 6337–6357 (2011).
[Crossref] [PubMed]

R. A. Robb, E. A. Hoffman, L. J. Sinak, L. D. Harris, and E. L. Ritman, “High-speed three-dimensional X-ray computed tomography: The dynamic spatial reconstructor,” Proc. IEEE 71(3), 308–319 (1983).
[Crossref]

Robb, R. A.

R. A. Robb, E. A. Hoffman, L. J. Sinak, L. D. Harris, and E. L. Ritman, “High-speed three-dimensional X-ray computed tomography: The dynamic spatial reconstructor,” Proc. IEEE 71(3), 308–319 (1983).
[Crossref]

Rowley, H.

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

Scharowsky, T.

A. Bauereiß, T. Scharowsky, and C. Körner, “Defect generation and propagation mechanism during additive manufacturing by selective beam melting,” J. Mater. Process Tech. 214(11), 2522–2528 (2014).
[Crossref]

Schwarze, R.

R. Schwarze and J. Klostermann, “Computational Fluid Dynamic (CFD) Simulations of Liquid Steel Infiltration in Porous Ceramic Structures: Dynamics of the Penetrating Melt Surface,” Steel Res. Int. 87(4), 465–471 (2016).
[Crossref]

Sidky, E. Y.

E. Y. Sidky, R. Chartrand, J. M. Boone, and X. Pan, “Constrained TpV Minimization for Enhanced Exploitation of Gradient Sparsity: Application to CT Image Reconstruction,” IEEE J. Transl. Eng. Health Med. 2, 1–18 (2014).
[Crossref] [PubMed]

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53(17), 4777–4807 (2008).
[Crossref] [PubMed]

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53(17), 4777–4807 (2008).
[Crossref] [PubMed]

E. Y. Sidky, R. Chartrand, and X. Pan, “Image reconstruction from few views by non-convex optimization,” in IEEE Nuclear Science Symposium Conference Record (2007), p. 3526.
[Crossref]

Sinak, L. J.

R. A. Robb, E. A. Hoffman, L. J. Sinak, L. D. Harris, and E. L. Ritman, “High-speed three-dimensional X-ray computed tomography: The dynamic spatial reconstructor,” Proc. IEEE 71(3), 308–319 (1983).
[Crossref]

Sun, M.

M. Li, C. Zhang, C. Peng, Y. Guan, P. Xu, M. Sun, and J. Zheng, “Smoothed l0 Norm Regularization for Sparse-View X-Ray CT Reconstruction,” BioMed Res. Int. 2016, 2180457 (2016).
[Crossref] [PubMed]

Sun, Y.

Y. Sun and J. Tao, “Image reconstruction from few views by l(0)-norm optimization,” Chinese Phys. B 23(7), 078703 (2014).
[Crossref]

Takami, M.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

Tang, J.

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

G. H. Chen, J. Tang, and J. Hsieh, “Temporal resolution improvement using PICCS in MDCT cardiac imaging,” Med. Phys. 36(6), 2130–2135 (2009).
[Crossref] [PubMed]

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
[Crossref] [PubMed]

Tao, J.

Y. Sun and J. Tao, “Image reconstruction from few views by l(0)-norm optimization,” Chinese Phys. B 23(7), 078703 (2014).
[Crossref]

Theriault-Lauzier, P.

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

Thomas, D.

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
[Crossref] [PubMed]

Thompson, W. M.

W. M. Thompson, W. R. B. Lionheart, E. J. Morton, M. Cunningham, and R. D. Luggar, “High speed imaging of dynamic processes with a switched source x-ray CT system,” Meas. Sci. Technol. 26(5), 55401 (2015).
[Crossref]

Trzasko, J.

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, “Nonconvex prior image constrained compressed sensing (NCPICCS): theory and simulations on perfusion CT,” Med. Phys. 38(4), 2157–2167 (2011).
[Crossref] [PubMed]

J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l(0) -minimization,” IEEE Trans. Med. Imaging 28(1), 106–121 (2009).
[Crossref] [PubMed]

Wang, C.

C. Gong, L. Zeng, C. Wang, and L. Ran, “Design and Simulation Study of a CNT-Based Multisource Cubical CT System for Dynamic Objects,” Scanning 2018, 6985698 (2018).
[Crossref] [PubMed]

W. Yu, C. Wang, and M. Huang, “Edge-preserving reconstruction from sparse projections of limited-angle computed tomography using ℓ0-regularized gradient prior,” Rev. Sci. Instrum. 88(4), 043703 (2017).
[Crossref] [PubMed]

L. Zeng and C. Wang, “Error bounds and stability in the l0 regularized for CT reconstruction from small projections,” Inverse Probl. Imaging (Springfield) 10(3), 829–853 (2016).
[Crossref]

Wang, G.

P. FitzGerald, P. Edic, H. Gao, Y. Jin, J. Wang, G. Wang, and B. Man, “Quest for the ultimate cardiac CT scanner,” Med. Phys. 44(9), 4506–4524 (2017).
[Crossref] [PubMed]

B. Liu, G. Wang, E. L. Ritman, G. Cao, J. Lu, O. Zhou, L. Zeng, and H. Yu, “Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems,” Phys. Med. Biol. 56(19), 6337–6357 (2011).
[Crossref] [PubMed]

Y. Liu, H. Liu, Y. Wang, and G. Wang, “Half-scan cone-beam CT fluoroscopy with multiple x-ray sources,” Med. Phys. 28(7), 1466–1471 (2001).
[Crossref] [PubMed]

Wang, J.

P. FitzGerald, P. Edic, H. Gao, Y. Jin, J. Wang, G. Wang, and B. Man, “Quest for the ultimate cardiac CT scanner,” Med. Phys. 44(9), 4506–4524 (2017).
[Crossref] [PubMed]

Wang, Q.

W. Wu, Y. Zhang, Q. Wang, F. Liu, P. Chen, and H. Yu, “Low-dose spectral CT reconstruction using ℓ0 image gradient and tensor dictionary,” Appl. Math. Model. 63, 538–557 (2018).
[Crossref]

W. Wu, Y. Zhang, Q. Wang, F. Liu, F. Luo, and H. Yu, “Spatial-spectral cube matching frame for spectral CT reconstruction,” Inverse Probl. 34(10), 104003 (2018).
[Crossref]

W. Wu, F. Liu, Y. Zhang, Q. Wang, and H. Yu, “Non-local Low-rank Cube-based Tensor Factorization for Spectral CT Reconstruction,” IEEE Trans. Med. Imaging1 (2018).

Wang, Y.

Y. Liu, H. Liu, Y. Wang, and G. Wang, “Half-scan cone-beam CT fluoroscopy with multiple x-ray sources,” Med. Phys. 28(7), 1466–1471 (2001).
[Crossref] [PubMed]

Wu, W.

W. Wu, Y. Zhang, Q. Wang, F. Liu, P. Chen, and H. Yu, “Low-dose spectral CT reconstruction using ℓ0 image gradient and tensor dictionary,” Appl. Math. Model. 63, 538–557 (2018).
[Crossref]

W. Wu, Y. Zhang, Q. Wang, F. Liu, F. Luo, and H. Yu, “Spatial-spectral cube matching frame for spectral CT reconstruction,” Inverse Probl. 34(10), 104003 (2018).
[Crossref]

W. Wu, H. Yu, C. Gong, and F. Liu, “Swinging multi-source industrial CT systems for aperiodic dynamic imaging,” Opt. Express 25(20), 24215–24235 (2017).
[Crossref] [PubMed]

W. Wu, F. Liu, Y. Zhang, Q. Wang, and H. Yu, “Non-local Low-rank Cube-based Tensor Factorization for Spectral CT Reconstruction,” IEEE Trans. Med. Imaging1 (2018).

Xu, L.

L. Xu, C. Lu, Y. Xu, and J. Jia, “Image smoothing via L0 gradient minimization,” in SIGGRAPH Asia Conference (2011), p. 174.

Xu, P.

M. Li, C. Zhang, C. Peng, Y. Guan, P. Xu, M. Sun, and J. Zheng, “Smoothed l0 Norm Regularization for Sparse-View X-Ray CT Reconstruction,” BioMed Res. Int. 2016, 2180457 (2016).
[Crossref] [PubMed]

Xu, Y.

L. Xu, C. Lu, Y. Xu, and J. Jia, “Image smoothing via L0 gradient minimization,” in SIGGRAPH Asia Conference (2011), p. 174.

Yu, H.

W. Wu, Y. Zhang, Q. Wang, F. Liu, P. Chen, and H. Yu, “Low-dose spectral CT reconstruction using ℓ0 image gradient and tensor dictionary,” Appl. Math. Model. 63, 538–557 (2018).
[Crossref]

W. Wu, Y. Zhang, Q. Wang, F. Liu, F. Luo, and H. Yu, “Spatial-spectral cube matching frame for spectral CT reconstruction,” Inverse Probl. 34(10), 104003 (2018).
[Crossref]

W. Wu, H. Yu, C. Gong, and F. Liu, “Swinging multi-source industrial CT systems for aperiodic dynamic imaging,” Opt. Express 25(20), 24215–24235 (2017).
[Crossref] [PubMed]

B. Liu, G. Wang, E. L. Ritman, G. Cao, J. Lu, O. Zhou, L. Zeng, and H. Yu, “Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems,” Phys. Med. Biol. 56(19), 6337–6357 (2011).
[Crossref] [PubMed]

W. Wu, F. Liu, Y. Zhang, Q. Wang, and H. Yu, “Non-local Low-rank Cube-based Tensor Factorization for Spectral CT Reconstruction,” IEEE Trans. Med. Imaging1 (2018).

Yu, L.

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, “Nonconvex prior image constrained compressed sensing (NCPICCS): theory and simulations on perfusion CT,” Med. Phys. 38(4), 2157–2167 (2011).
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Yu, W.

W. Yu, C. Wang, and M. Huang, “Edge-preserving reconstruction from sparse projections of limited-angle computed tomography using ℓ0-regularized gradient prior,” Rev. Sci. Instrum. 88(4), 043703 (2017).
[Crossref] [PubMed]

Zambelli, J.

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

Zeng, L.

L. Zhang, L. Zeng, and Y. Guo, “l0 regularization based on a prior image incorporated non-local means for limited-angle X-ray CT reconstruction,” J. XRay Sci. Technol. 26(3), 481–498 (2018).
[Crossref] [PubMed]

C. Gong, L. Zeng, C. Wang, and L. Ran, “Design and Simulation Study of a CNT-Based Multisource Cubical CT System for Dynamic Objects,” Scanning 2018, 6985698 (2018).
[Crossref] [PubMed]

L. Zeng and C. Wang, “Error bounds and stability in the l0 regularized for CT reconstruction from small projections,” Inverse Probl. Imaging (Springfield) 10(3), 829–853 (2016).
[Crossref]

B. Liu, G. Wang, E. L. Ritman, G. Cao, J. Lu, O. Zhou, L. Zeng, and H. Yu, “Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems,” Phys. Med. Biol. 56(19), 6337–6357 (2011).
[Crossref] [PubMed]

Zhang, C.

M. Li, C. Zhang, C. Peng, Y. Guan, P. Xu, M. Sun, and J. Zheng, “Smoothed l0 Norm Regularization for Sparse-View X-Ray CT Reconstruction,” BioMed Res. Int. 2016, 2180457 (2016).
[Crossref] [PubMed]

Zhang, L.

L. Zhang, L. Zeng, and Y. Guo, “l0 regularization based on a prior image incorporated non-local means for limited-angle X-ray CT reconstruction,” J. XRay Sci. Technol. 26(3), 481–498 (2018).
[Crossref] [PubMed]

Zhang, Y.

W. Wu, Y. Zhang, Q. Wang, F. Liu, P. Chen, and H. Yu, “Low-dose spectral CT reconstruction using ℓ0 image gradient and tensor dictionary,” Appl. Math. Model. 63, 538–557 (2018).
[Crossref]

W. Wu, Y. Zhang, Q. Wang, F. Liu, F. Luo, and H. Yu, “Spatial-spectral cube matching frame for spectral CT reconstruction,” Inverse Probl. 34(10), 104003 (2018).
[Crossref]

W. Wu, F. Liu, Y. Zhang, Q. Wang, and H. Yu, “Non-local Low-rank Cube-based Tensor Factorization for Spectral CT Reconstruction,” IEEE Trans. Med. Imaging1 (2018).

Zheng, J.

M. Li, C. Zhang, C. Peng, Y. Guan, P. Xu, M. Sun, and J. Zheng, “Smoothed l0 Norm Regularization for Sparse-View X-Ray CT Reconstruction,” BioMed Res. Int. 2016, 2180457 (2016).
[Crossref] [PubMed]

Zhou, O.

B. Liu, G. Wang, E. L. Ritman, G. Cao, J. Lu, O. Zhou, L. Zeng, and H. Yu, “Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems,” Phys. Med. Biol. 56(19), 6337–6357 (2011).
[Crossref] [PubMed]

Appl. Math. Model. (1)

W. Wu, Y. Zhang, Q. Wang, F. Liu, P. Chen, and H. Yu, “Low-dose spectral CT reconstruction using ℓ0 image gradient and tensor dictionary,” Appl. Math. Model. 63, 538–557 (2018).
[Crossref]

BioMed Res. Int. (1)

M. Li, C. Zhang, C. Peng, Y. Guan, P. Xu, M. Sun, and J. Zheng, “Smoothed l0 Norm Regularization for Sparse-View X-Ray CT Reconstruction,” BioMed Res. Int. 2016, 2180457 (2016).
[Crossref] [PubMed]

Chinese Phys. B (1)

Y. Sun and J. Tao, “Image reconstruction from few views by l(0)-norm optimization,” Chinese Phys. B 23(7), 078703 (2014).
[Crossref]

IEEE J. Transl. Eng. Health Med. (1)

E. Y. Sidky, R. Chartrand, J. M. Boone, and X. Pan, “Constrained TpV Minimization for Enhanced Exploitation of Gradient Sparsity: Application to CT Image Reconstruction,” IEEE J. Transl. Eng. Health Med. 2, 1–18 (2014).
[Crossref] [PubMed]

IEEE Signal Proc. Lett. (1)

R. Chartrand, “Exact Reconstruction of Sparse Signals via Nonconvex Minimization,” IEEE Signal Proc. Lett. 14(10), 707–710 (2007).
[Crossref]

IEEE Trans. Biomed. Eng. (1)

P. R. Johnston and R. M. Gulrajani, “Selecting the corner in the L-curve approach to Tikhonov regularization,” IEEE Trans. Biomed. Eng. 47(9), 1293–1296 (2000).
[Crossref] [PubMed]

IEEE Trans. Med. Imaging (2)

J. Trzasko and A. Manduca, “Highly undersampled magnetic resonance image reconstruction via homotopic l(0) -minimization,” IEEE Trans. Med. Imaging 28(1), 106–121 (2009).
[Crossref] [PubMed]

G. H. Chen, P. Theriault-Lauzier, J. Tang, B. Nett, S. Leng, J. Zambelli, Z. Qi, N. Bevins, A. Raval, S. Reeder, and H. Rowley, “Time-resolved interventional cardiac C-arm cone-beam CT: an application of the PICCS algorithm,” IEEE Trans. Med. Imaging 31(4), 907–923 (2012).
[Crossref] [PubMed]

Inverse Probl. (1)

W. Wu, Y. Zhang, Q. Wang, F. Liu, F. Luo, and H. Yu, “Spatial-spectral cube matching frame for spectral CT reconstruction,” Inverse Probl. 34(10), 104003 (2018).
[Crossref]

Inverse Probl. Imaging (Springfield) (1)

L. Zeng and C. Wang, “Error bounds and stability in the l0 regularized for CT reconstruction from small projections,” Inverse Probl. Imaging (Springfield) 10(3), 829–853 (2016).
[Crossref]

J. Mater. Process Tech. (1)

A. Bauereiß, T. Scharowsky, and C. Körner, “Defect generation and propagation mechanism during additive manufacturing by selective beam melting,” J. Mater. Process Tech. 214(11), 2522–2528 (2014).
[Crossref]

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R. Gordon, R. Bender, and G. T. Herman, “Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography,” J. Theor. Biol. 29(3), 471–481 (1970).
[PubMed]

J. XRay Sci. Technol. (1)

L. Zhang, L. Zeng, and Y. Guo, “l0 regularization based on a prior image incorporated non-local means for limited-angle X-ray CT reconstruction,” J. XRay Sci. Technol. 26(3), 481–498 (2018).
[Crossref] [PubMed]

Meas. Sci. Technol. (1)

W. M. Thompson, W. R. B. Lionheart, E. J. Morton, M. Cunningham, and R. D. Luggar, “High speed imaging of dynamic processes with a switched source x-ray CT system,” Meas. Sci. Technol. 26(5), 55401 (2015).
[Crossref]

Med. Phys. (6)

Y. Liu, H. Liu, Y. Wang, and G. Wang, “Half-scan cone-beam CT fluoroscopy with multiple x-ray sources,” Med. Phys. 28(7), 1466–1471 (2001).
[Crossref] [PubMed]

J. C. Ramirez-Giraldo, J. Trzasko, S. Leng, L. Yu, A. Manduca, and C. H. McCollough, “Nonconvex prior image constrained compressed sensing (NCPICCS): theory and simulations on perfusion CT,” Med. Phys. 38(4), 2157–2167 (2011).
[Crossref] [PubMed]

G. H. Chen, J. Tang, and S. Leng, “Prior image constrained compressed sensing (PICCS): a method to accurately reconstruct dynamic CT images from highly undersampled projection data sets,” Med. Phys. 35(2), 660–663 (2008).
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G. H. Chen, J. Tang, and J. Hsieh, “Temporal resolution improvement using PICCS in MDCT cardiac imaging,” Med. Phys. 36(6), 2130–2135 (2009).
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Opt. Express (1)

Phys. Med. Biol. (5)

D. Richter, H. I. Lehmann, A. Eichhorn, A. M. Constantinescu, R. Kaderka, M. Prall, P. Lugenbiel, M. Takami, D. Thomas, C. Bert, M. Durante, D. L. Packer, and C. Graeff, “ECG-based 4D-dose reconstruction of cardiac arrhythmia ablation with carbon ion beams: application in a porcine model,” Phys. Med. Biol. 62(17), 6869–6883 (2017).
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E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53(17), 4777–4807 (2008).
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B. Liu, G. Wang, E. L. Ritman, G. Cao, J. Lu, O. Zhou, L. Zeng, and H. Yu, “Image reconstruction from limited angle projections collected by multisource interior x-ray imaging systems,” Phys. Med. Biol. 56(19), 6337–6357 (2011).
[Crossref] [PubMed]

E. Y. Sidky and X. Pan, “Image reconstruction in circular cone-beam computed tomography by constrained, total-variation minimization,” Phys. Med. Biol. 53(17), 4777–4807 (2008).
[Crossref] [PubMed]

M. Holbrook, D. P. Clark, and C. T. Badea, “Low-dose 4D cardiac imaging in small animals using dual source micro-CT,” Phys. Med. Biol. 63(2), 025009 (2018).
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R. A. Robb, E. A. Hoffman, L. J. Sinak, L. D. Harris, and E. L. Ritman, “High-speed three-dimensional X-ray computed tomography: The dynamic spatial reconstructor,” Proc. IEEE 71(3), 308–319 (1983).
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Radiat. Oncol. (1)

M. Nakano, A. Haga, J. Kotoku, T. Magome, Y. Masutani, S. Hanaoka, S. Kida, and K. Nakagawa, “Cone-beam CT reconstruction for non-periodic organ motion using time-ordered chain graph model,” Radiat. Oncol. 12(1), 145 (2017).
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Rev. Sci. Instrum. (1)

W. Yu, C. Wang, and M. Huang, “Edge-preserving reconstruction from sparse projections of limited-angle computed tomography using ℓ0-regularized gradient prior,” Rev. Sci. Instrum. 88(4), 043703 (2017).
[Crossref] [PubMed]

Scanning (1)

C. Gong, L. Zeng, C. Wang, and L. Ran, “Design and Simulation Study of a CNT-Based Multisource Cubical CT System for Dynamic Objects,” Scanning 2018, 6985698 (2018).
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T. Goldstein and S. Osher, “The Split Bregman Method for L1-Regularized Problems,” SIAM J. Imaging Sci. 2(2), 323–343 (2009).
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Steel Res. Int. (1)

R. Schwarze and J. Klostermann, “Computational Fluid Dynamic (CFD) Simulations of Liquid Steel Infiltration in Porous Ceramic Structures: Dynamics of the Penetrating Melt Surface,” Steel Res. Int. 87(4), 465–471 (2016).
[Crossref]

Other (3)

E. Y. Sidky, R. Chartrand, and X. Pan, “Image reconstruction from few views by non-convex optimization,” in IEEE Nuclear Science Symposium Conference Record (2007), p. 3526.
[Crossref]

L. Xu, C. Lu, Y. Xu, and J. Jia, “Image smoothing via L0 gradient minimization,” in SIGGRAPH Asia Conference (2011), p. 174.

W. Wu, F. Liu, Y. Zhang, Q. Wang, and H. Yu, “Non-local Low-rank Cube-based Tensor Factorization for Spectral CT Reconstruction,” IEEE Trans. Med. Imaging1 (2018).

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Figures (10)

Fig. 1
Fig. 1 A representative SMCT system ( Q = 5 ).
Fig. 2
Fig. 2 The fan-beam geometry of the SMCT system in Fig. 1.
Fig. 3
Fig. 3 From left to right columns represent the statues of the casting cooling process at 0.1s, 0.6s and 5.0s, respectively.
Fig. 4
Fig. 4 Reconstructed results of the time frame 6 from the noisy projections acquired with 5 X-ray sources. The 1st −3rd rows represents the reconstructed results of the undersampling factors 10, 25, 50, respectively. 1st-3rd columns are the results reconstructed by ART, TVM-SD, SM-PICCS, L0-PICCS methods, respectively. The display window is [0.04,0.1].
Fig. 5
Fig. 5 The difference images between reconstructed images in Fig. 4 and true image. The display window is [0.04,0.1].
Fig. 6
Fig. 6 The 3D structure of the specimen reconstructed by FDK algorithm (left) and extracted 50 reconstructed slices (right).
Fig. 7
Fig. 7 50 reconstructed slices from 50 FPD slices by using FBP and each reconstructed slice consists of 256 × 256 pixels. The display window is [0 0.05].
Fig. 8
Fig. 8 Reconstructed results of the time frame 6 from realistic data set acquired with 5 X-ray sources. The 1st-3rd rows represents the reconstructed results of the undersampling factors 10, 18 and 30, respectively. 1st-3rd columns are the results reconstructed by ART, TVM-SD, SM-PICCS, L0-PICCS methods, respectively. The display window is [0,0.05].
Fig. 9
Fig. 9 Same as Fig. 8 but for 7 X-ray sources.
Fig. 10
Fig. 10 RMSEs v.s. different parameters settings. (a)-(d) represent δ 1 , λ 1 * , δ 2 , λ 2 * respectively.

Tables (7)

Tables Icon

Table 1 The parameters of L0-PICCS ( δ 1 , δ 2 , λ 1 * , λ 2 * ) for numerical simulation.

Tables Icon

Table 2 Algorithm 1: L0-PICCS

Tables Icon

Table 2 The parameters of L0-PICCS ( δ 1 , δ 2 , λ 1 * , λ 2 * ) for realistic simulation.

Tables Icon

Table 3 Numerical simulation parameters

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Table 4 Quantitative results in terms of RMSEs

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Table 5 Quantitative results in terms of PSNRs

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Table 6 Quantitative results in terms of SSIMs

Equations (23)

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A f = P ,
arg min f | | A f P | | 2 2 + γ R ( f ) ,
a r g min f κ T V ( f ) + ( 1 κ ) T V ( f f p ) , s . t . A f = P ,
T V ( f ) = i = 2 I j = 2 J f i , j f i 1 , j 2 + f i , j f i , j 1 2 ,
|| f | | 0 = i = 2 I j = 2 J φ ( | f i , j f i 1 , j | + | f i , j f i , j 1 | ) ,
φ ( | f i , j f i 1 , j | + | f i , j f i , j 1 | ) = { 1 | f i , j f i 1 , j | + | f i , j f i , j 1 | 0 0 otherwise .
arg min f κ | | f | | 0 + ( 1 κ ) | | ( f f p ) | | 0 s . t . A f = P .
arg min f 1 2 | | A f P | | 2 2 + λ ( κ | | f | | 0 + ( 1 κ ) | | ( f f p ) | | 0 ) .
arg min f 1 2 || A f P | | 2 2 + λ ( κ | | u 1 | | 0 + ( 1 κ ) | | u 2 | | 0 ) s . t . u 1 = f , u 2 = f f p .
arg min f , u 1 , u 2 , t 1 . t 2 { 1 2 || A f P | | 2 2 + λ ( κ | | u 1 | | 0 + ( 1 κ ) | | u 2 | | 0 ) + δ 1 2 | | f u 1 t 1 | | 2 2 + δ 2 2 | | f f p u 2 t 2 | | 2 2 } ,
f ( k + 1 ) = arg min f 1 2 | | A f P | | 2 2 + δ 1 2 | | f u 1 ( k ) t 1 ( k ) | | 2 2 + δ 2 2 | | f f p u 2 ( k ) t 2 ( k ) | | 2 2 .
u 1 ( k + 1 ) = arg min u 1 δ 1 2 | | f ( k + 1 ) u 1 t 1 ( k ) | | 2 2 + λ κ | | u 1 | | 0 ,
u 2 ( k + 1 ) = arg min u 2 δ 2 2 | | f ( k + 1 ) f p u 2 t 2 ( k ) | | 2 2 + λ ( 1 κ ) | | u 2 | | 0 .
t 1 ( k + 1 ) = t 1 ( k ) ( f ( k + 1 ) u 1 ( k + 1 ) ) ,
t 2 ( k + 1 ) = t 2 ( k ) ( f ( k + 1 ) f p u 2 ( k + 1 ) ) .
A T ( A f P ) + δ 1 ( f u 1 ( k ) t 1 ( k ) ) + δ 2 ( f f p u 2 ( k ) t 2 ( k ) ) = 0 ,
( A T A + δ 1 I + δ 2 I ) f = A T P + δ 1 ( u 1 ( k ) + t 1 ( k ) ) + δ 2 ( f p + u 2 ( k ) + t 2 ( k ) ) .
( A T A + δ 1 I + δ 2 I ) f = ( A T A + δ 1 I + δ 2 I ) f ( k ) ( A T A + δ 1 I + δ 2 I ) f ( k ) + A T P + δ 1 ( u 1 ( k ) + t 1 ( k ) ) + δ 2 ( f p + u 2 ( k ) + t 2 ( k ) ) ,
f ( k +1 ) = f ( k ) ( A T A + δ 1 I + δ 2 I ) 1 × [ A T ( A f ( k ) P ) + δ 1 ( f ( k ) u 1 ( k ) t 1 ( k ) ) + δ 2 ( f ( k ) u 2 ( k ) t 2 ( k ) f p ) ] .
u 1 ( k + 1 ) = arg min u 1 | | f ( k + 1 ) u 1 t 1 ( k ) | | 2 2 + 2 λ κ δ 1 | | u 1 | | 0 .
arg min u 1 , { h n , v n } | | f ( k + 1 ) u 1 t 1 ( k ) | | 2 2 + λ 1 * | | u 1 | | 0 + β 1 ( ( ( x u 1 ) n h n ) 2 + ( ( y u 1 ) n v n ) 2 ) ,
{ ( h n ) ( i + 1 ) , ( v n ) ( i + 1 ) } = { ( 0 , 0 ) ( ( ( x ( u 1 ) ) n ) ( i ) ) 2 + ( ( ( y ( u 1 ) ) n ) ( i ) ) 2 λ 1 * / β 1 { ( ( x ( u 1 ) ) n ) ( i ) , ( ( y ( u 1 ) ) n ) ( i ) } otherwise ,
u 1 ( i + 1 ) = F 1 { F ( f ( i + 1 ) d ( i ) ) + β 1 ( F * ( x ) F ( h ( i + 1 ) ) + F * ( y ) F ( v ( i + 1 ) ) ) F ( 1 ) + β 1 ( F * ( x ) F ( x ) + F * ( y ) F ( y ) ) } ,

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