Abstract

X-ray luminescence computed tomography (XLCT) has become a promising imaging technology for biological application based on phosphor nanoparticles. There are mainly three kinds of XLCT imaging systems: pencil beam XLCT, narrow beam XLCT and cone beam XLCT. Narrow beam XLCT can be regarded as a balance between the pencil beam mode and the cone-beam mode in terms of imaging efficiency and image quality. The collimated X-ray beams are assumed to be parallel ones in the traditional narrow beam XLCT. However, we observe that the cone beam X-rays are collimated into X-ray beams with fan-shaped broadening instead of parallel ones in our prototype narrow beam XLCT. Hence we incorporate the distribution of the X-ray beams in the physical model and collected the optical data from only two perpendicular directions to further speed up the scanning time. Meanwhile we propose a depth related adaptive regularized split Bregman (DARSB) method in reconstruction. The simulation experiments show that the proposed physical model and method can achieve better results in the location error, dice coefficient, mean square error and the intensity error than the traditional split Bregman method and validate the feasibility of method. The phantom experiment can obtain the location error less than 1.1 mm and validate that the incorporation of fan-shaped X-ray beams in our model can achieve better results than the parallel X-rays.

© 2015 Optical Society of America

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References

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2014 (8)

L. Sudheendra, G. K. Das, C. Li, D. Stark, J. Cena, S. Cherry, and I. M. Kennedy, “Nagdf4: Eu3+ nanoparticles for enhanced x-ray excited optical imaging,” Chem. Mater. 26(5), 1881–1888 (2014).
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[Crossref] [PubMed]

Y. Osakada, G. Pratx, C. Sun, M. Sakamoto, M. Ahmad, O. Volotskova, Q. Ong, T. Teranishi, Y. Harada, L. Xing, and B. Cui, “Hard x-ray-induced optical luminescence via biomolecule-directed metal clusters,” Chem. Commun. 50(27), 3549–3551 (2014).
[Crossref]

X. Liu, Q. Liao, and H. Wang, “Fast x-ray luminescence computed tomography imaging,” IEEE Trans. Biomed. Eng. 61(6), 1621–1627 (2014).
[Crossref] [PubMed]

D. Chen, S. Zhu, X. Chen, T. Chao, X. Cao, F. Zhao, L. Huang, and J. Liang, “Quantitative cone beam x-ray luminescence tomography/x-ray computed tomography imaging,” Appl. Phys. Lett. 105(19), 191104 (2014).
[Crossref]

C. He, C. Hu, W. Zhang, B. Shi, and X. Hu, “Fast total-variation image deconvolution with adaptive parameter estimation via split bregman method,” Math. Probl. Eng. 2014, 617026 (2014).
[Crossref]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating mri structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5(6), 1861–1876 (2014).
[Crossref] [PubMed]

W. Cong, C. Wang, and G. Wang, “Stored luminescence computed tomography,” Appl. Opt. 53(25), 5672–5676 (2014).
[Crossref] [PubMed]

2013 (4)

C. Li, K. Di, J. Bec, and S. R. Cherry, “X-ray luminescence optical tomography imaging: experimental studies,” Opt. Lett. 38(13), 2339–2341 (2013).
[Crossref] [PubMed]

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
[Crossref]

H. Chen, T. Moore, B. Qi, D. C. Colvin, E. K. Jelen, D. A. Hitchcock, J. He, O. T. Mefford, J. C. Gore, F. Alexis, and J. N. Anker, “Monitoring ph-triggered drug release from radioluminescent nanocapsules with x-ray excited optical luminescence,” ACS nano 7(2), 1178–1187 (2013).
[Crossref] [PubMed]

D. Chen, S. Zhu, H. Yi, X. Zhang, D. Chen, J. Liang, and J. Tian, “Cone beam x-ray luminescence computed tomography: A feasibility study,” Med. Phys. 40(3), 031111 (2013).
[Crossref] [PubMed]

2012 (2)

Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the lp regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012).
[Crossref]

J. Feng, C. Qin, K. Jia, S. Zhu, K. Liu, D. Han, X. Yang, Q. Gao, and J. Tian, “Total variation regularization for bioluminescence tomography with the split bregman method,” Appl. Opt. 51(19), 4501–4512 (2012).
[Crossref] [PubMed]

2011 (3)

W. Cong, H. Shen, and G. Wang, “Spectrally resolving and scattering-compensated x-ray luminescence/fluorescence computed tomography,” J. Biomed. Opt. 16(6), 066014 (2011).
[Crossref] [PubMed]

C. Carpenter, G. Pratx, C. Sun, and L. Xing, “Limited-angle x-ray luminescence tomography: methodology and feasibility study,” Phys. Med. Biol. 56(12), 3487 (2011).
[Crossref] [PubMed]

J. J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split bregman method,” Med. Phys. 38(11), 6275–6284 (2011).
[Crossref] [PubMed]

2010 (3)

2009 (3)

D. Hyde, R. Schulz, D. Brooks, E. Miller, and V. Ntziachristos, “Performance dependence of hybrid x-ray computed tomography/fluorescence molecular tomography on the optical forward problem,” J. Opt. Soc. Am. A 26(4), 919–923 (2009).
[Crossref]

N. Zhang, Z.-S. Deng, F. Wang, and X.-Y. Wang, “The effect of different number of diffusion gradients on snr of diffusion tensor-derived measurement maps,” J. Biomed. Sci. Eng. 2(2), 96 (2009).
[Crossref]

T. Goldstein and S. Osher, “The split bregman method for l1-regularized problems,” SIAM J. Imaging Sci. 2(2), 323–343 (2009).
[Crossref]

2008 (4)

W. Yin, S. Osher, D. Goldfarb, and J. Darbon, “Bregman iterative algorithms for l1-minimization with applications to compressed sensing,” SIAM J. Imaging Sci. 1(1), 143–168 (2008).
[Crossref]

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3d multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921 (2008).
[Crossref] [PubMed]

S. Jie, S. L. Dong, and Y. C. Hua, “Luminescent rare earth nanomaterials for bioprobe applications,” Dalton Trans. 42,5687–5697 (2008).

J. Feng, K. Jia, G. Yan, S. Zhu, C. Qin, Y. Lv, and J. Tian, “An optimal permissible source region strategy for multispectral bioluminescence tomography,” Opt. Express 16(20), 15640–15654 (2008).
[Crossref] [PubMed]

2007 (3)

X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15(26), 18300–18317 (2007).
[Crossref] [PubMed]

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3d whole body mouse atlas from ct and cryosection data,” Phy. Med. Biol. 52(3), 577 (2007).
[Crossref]

T. Ying, C. W. He, L. X. Xian, and F. Yao, “Preparation and luminescence property of Gd2O2S: Tb X-ray nano-phosphors using the complex precipitation method,” J. Alloys Compd. 433(1), 313–317 (2007).
[Crossref]

2005 (3)

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202(1), 323–345 (2005).
[Crossref]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of hetero-geneities: study of the normalized born ratio,” IEEE Trans. Medical Imaging 24(10), 1377–1386 (2005).
[Crossref]

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Model. Sim. 4(2), 460–489 (2005).
[Crossref]

1994 (1)

S. C. Eisenstat and H. F. Walker, “Globally convergent inexact newton methods,” SIAM Journal on Optimization 4(2), 393–422 (1994).
[Crossref]

1992 (1)

J. Eckstein and D. P. Bertsekas, On the douglas rachford splitting method and the proximal point algorithm for maximal monotone operators, Math. Program. 55, 293–318 (1992).
[Crossref]

1945 (1)

L. R. Dice, “Measures of the amount of ecologic association between species,” Ecology 26(3), 297–302 (1945).
[Crossref]

Abascal, J. J.

J. J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split bregman method,” Med. Phys. 38(11), 6275–6284 (2011).
[Crossref] [PubMed]

Aguirre, J.

J. J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split bregman method,” Med. Phys. 38(11), 6275–6284 (2011).
[Crossref] [PubMed]

Ahmad, M.

Y. Osakada, G. Pratx, C. Sun, M. Sakamoto, M. Ahmad, O. Volotskova, Q. Ong, T. Teranishi, Y. Harada, L. Xing, and B. Cui, “Hard x-ray-induced optical luminescence via biomolecule-directed metal clusters,” Chem. Commun. 50(27), 3549–3551 (2014).
[Crossref]

C. Wang, O. Volotskova, K. Lu, M. Ahmad, C. Sun, L. Xing, and W. Lin, “Synergistic assembly of heavy metal clusters and luminescent organic bridging ligands in metalCorganic frameworks for highly efficient x-ray scintillation,” J. Am. Chem. Soc. 136(17), 6171–6174 (2014).
[Crossref] [PubMed]

Ahn, S.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3d multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921 (2008).
[Crossref] [PubMed]

Alexis, F.

H. Chen, T. Moore, B. Qi, D. C. Colvin, E. K. Jelen, D. A. Hitchcock, J. He, O. T. Mefford, J. C. Gore, F. Alexis, and J. N. Anker, “Monitoring ph-triggered drug release from radioluminescent nanocapsules with x-ray excited optical luminescence,” ACS nano 7(2), 1178–1187 (2013).
[Crossref] [PubMed]

Anker, J. N.

H. Chen, T. Moore, B. Qi, D. C. Colvin, E. K. Jelen, D. A. Hitchcock, J. He, O. T. Mefford, J. C. Gore, F. Alexis, and J. N. Anker, “Monitoring ph-triggered drug release from radioluminescent nanocapsules with x-ray excited optical luminescence,” ACS nano 7(2), 1178–1187 (2013).
[Crossref] [PubMed]

Arridge, S.

J. J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split bregman method,” Med. Phys. 38(11), 6275–6284 (2011).
[Crossref] [PubMed]

Bai, J.

Barber, W. C.

Bec, J.

Bertsekas, D. P.

J. Eckstein and D. P. Bertsekas, On the douglas rachford splitting method and the proximal point algorithm for maximal monotone operators, Math. Program. 55, 293–318 (1992).
[Crossref]

Bouman, C. A.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3d multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921 (2008).
[Crossref] [PubMed]

Brooks, D.

Burger, M.

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Model. Sim. 4(2), 460–489 (2005).
[Crossref]

Cao, X.

D. Chen, S. Zhu, X. Chen, T. Chao, X. Cao, F. Zhao, L. Huang, and J. Liang, “Quantitative cone beam x-ray luminescence tomography/x-ray computed tomography imaging,” Appl. Phys. Lett. 105(19), 191104 (2014).
[Crossref]

Carpenter, C.

C. Carpenter, G. Pratx, C. Sun, and L. Xing, “Limited-angle x-ray luminescence tomography: methodology and feasibility study,” Phys. Med. Biol. 56(12), 3487 (2011).
[Crossref] [PubMed]

Carpenter, C. M.

Cena, J.

L. Sudheendra, G. K. Das, C. Li, D. Stark, J. Cena, S. Cherry, and I. M. Kennedy, “Nagdf4: Eu3+ nanoparticles for enhanced x-ray excited optical imaging,” Chem. Mater. 26(5), 1881–1888 (2014).
[Crossref] [PubMed]

Chamorro-Servent, J.

J. J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split bregman method,” Med. Phys. 38(11), 6275–6284 (2011).
[Crossref] [PubMed]

Chao, T.

D. Chen, S. Zhu, X. Chen, T. Chao, X. Cao, F. Zhao, L. Huang, and J. Liang, “Quantitative cone beam x-ray luminescence tomography/x-ray computed tomography imaging,” Appl. Phys. Lett. 105(19), 191104 (2014).
[Crossref]

Chatziioannou, A. F.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3d whole body mouse atlas from ct and cryosection data,” Phy. Med. Biol. 52(3), 577 (2007).
[Crossref]

Chaudhari, A. J.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3d multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921 (2008).
[Crossref] [PubMed]

Chen, D.

D. Chen, S. Zhu, X. Chen, T. Chao, X. Cao, F. Zhao, L. Huang, and J. Liang, “Quantitative cone beam x-ray luminescence tomography/x-ray computed tomography imaging,” Appl. Phys. Lett. 105(19), 191104 (2014).
[Crossref]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating mri structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5(6), 1861–1876 (2014).
[Crossref] [PubMed]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating mri structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5(6), 1861–1876 (2014).
[Crossref] [PubMed]

D. Chen, S. Zhu, H. Yi, X. Zhang, D. Chen, J. Liang, and J. Tian, “Cone beam x-ray luminescence computed tomography: A feasibility study,” Med. Phys. 40(3), 031111 (2013).
[Crossref] [PubMed]

D. Chen, S. Zhu, H. Yi, X. Zhang, D. Chen, J. Liang, and J. Tian, “Cone beam x-ray luminescence computed tomography: A feasibility study,” Med. Phys. 40(3), 031111 (2013).
[Crossref] [PubMed]

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H. Chen, T. Moore, B. Qi, D. C. Colvin, E. K. Jelen, D. A. Hitchcock, J. He, O. T. Mefford, J. C. Gore, F. Alexis, and J. N. Anker, “Monitoring ph-triggered drug release from radioluminescent nanocapsules with x-ray excited optical luminescence,” ACS nano 7(2), 1178–1187 (2013).
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A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202(1), 323–345 (2005).
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H. Chen, T. Moore, B. Qi, D. C. Colvin, E. K. Jelen, D. A. Hitchcock, J. He, O. T. Mefford, J. C. Gore, F. Alexis, and J. N. Anker, “Monitoring ph-triggered drug release from radioluminescent nanocapsules with x-ray excited optical luminescence,” ACS nano 7(2), 1178–1187 (2013).
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C. He, C. Hu, W. Zhang, B. Shi, and X. Hu, “Fast total-variation image deconvolution with adaptive parameter estimation via split bregman method,” Math. Probl. Eng. 2014, 617026 (2014).
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S. Jie, S. L. Dong, and Y. C. Hua, “Luminescent rare earth nanomaterials for bioprobe applications,” Dalton Trans. 42,5687–5697 (2008).

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D. Chen, S. Zhu, X. Chen, T. Chao, X. Cao, F. Zhao, L. Huang, and J. Liang, “Quantitative cone beam x-ray luminescence tomography/x-ray computed tomography imaging,” Appl. Phys. Lett. 105(19), 191104 (2014).
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L. Sudheendra, G. K. Das, C. Li, D. Stark, J. Cena, S. Cherry, and I. M. Kennedy, “Nagdf4: Eu3+ nanoparticles for enhanced x-ray excited optical imaging,” Chem. Mater. 26(5), 1881–1888 (2014).
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S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3d multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921 (2008).
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Li, C.

L. Sudheendra, G. K. Das, C. Li, D. Stark, J. Cena, S. Cherry, and I. M. Kennedy, “Nagdf4: Eu3+ nanoparticles for enhanced x-ray excited optical imaging,” Chem. Mater. 26(5), 1881–1888 (2014).
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H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
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H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
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D. Chen, S. Zhu, H. Yi, X. Zhang, D. Chen, J. Liang, and J. Tian, “Cone beam x-ray luminescence computed tomography: A feasibility study,” Med. Phys. 40(3), 031111 (2013).
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Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the lp regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012).
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H. Chen, T. Moore, B. Qi, D. C. Colvin, E. K. Jelen, D. A. Hitchcock, J. He, O. T. Mefford, J. C. Gore, F. Alexis, and J. N. Anker, “Monitoring ph-triggered drug release from radioluminescent nanocapsules with x-ray excited optical luminescence,” ACS nano 7(2), 1178–1187 (2013).
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Miller, E.

Moore, T.

H. Chen, T. Moore, B. Qi, D. C. Colvin, E. K. Jelen, D. A. Hitchcock, J. He, O. T. Mefford, J. C. Gore, F. Alexis, and J. N. Anker, “Monitoring ph-triggered drug release from radioluminescent nanocapsules with x-ray excited optical luminescence,” ACS nano 7(2), 1178–1187 (2013).
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Y. Osakada, G. Pratx, C. Sun, M. Sakamoto, M. Ahmad, O. Volotskova, Q. Ong, T. Teranishi, Y. Harada, L. Xing, and B. Cui, “Hard x-ray-induced optical luminescence via biomolecule-directed metal clusters,” Chem. Commun. 50(27), 3549–3551 (2014).
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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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W. Yin, S. Osher, D. Goldfarb, and J. Darbon, “Bregman iterative algorithms for l1-minimization with applications to compressed sensing,” SIAM J. Imaging Sci. 1(1), 143–168 (2008).
[Crossref]

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Model. Sim. 4(2), 460–489 (2005).
[Crossref]

Pratx, G.

Y. Osakada, G. Pratx, C. Sun, M. Sakamoto, M. Ahmad, O. Volotskova, Q. Ong, T. Teranishi, Y. Harada, L. Xing, and B. Cui, “Hard x-ray-induced optical luminescence via biomolecule-directed metal clusters,” Chem. Commun. 50(27), 3549–3551 (2014).
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G. Pratx, C. M. Carpenter, C. Sun, R. P. Rao, and L. Xing, “Tomographic molecular imaging of x-ray-excitable nanoparticles,” Opt. Lett. 35(20), 3345–3347 (2010).
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H. Chen, T. Moore, B. Qi, D. C. Colvin, E. K. Jelen, D. A. Hitchcock, J. He, O. T. Mefford, J. C. Gore, F. Alexis, and J. N. Anker, “Monitoring ph-triggered drug release from radioluminescent nanocapsules with x-ray excited optical luminescence,” ACS nano 7(2), 1178–1187 (2013).
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Qin, C.

Qu, X.

Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the lp regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012).
[Crossref]

Rao, R. P.

Ripoll, J.

J. J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split bregman method,” Med. Phys. 38(11), 6275–6284 (2011).
[Crossref] [PubMed]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of hetero-geneities: study of the normalized born ratio,” IEEE Trans. Medical Imaging 24(10), 1377–1386 (2005).
[Crossref]

Roeck, W.

Sakamoto, M.

Y. Osakada, G. Pratx, C. Sun, M. Sakamoto, M. Ahmad, O. Volotskova, Q. Ong, T. Teranishi, Y. Harada, L. Xing, and B. Cui, “Hard x-ray-induced optical luminescence via biomolecule-directed metal clusters,” Chem. Commun. 50(27), 3549–3551 (2014).
[Crossref]

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A. Y. Yang, S. S. Sastry, A. Ganesh, and Y. Ma, “Fast l1-minimization algorithms and an application in robust face recognition: A review,” in Image Processing (ICIP), 2010 17th IEEE International Conference on, (IEEE, 2010), pp. 1849–1852.

Schulz, R.

Shen, H.

W. Cong, H. Shen, and G. Wang, “Spectrally resolving and scattering-compensated x-ray luminescence/fluorescence computed tomography,” J. Biomed. Opt. 16(6), 066014 (2011).
[Crossref] [PubMed]

Shi, B.

C. He, C. Hu, W. Zhang, B. Shi, and X. Hu, “Fast total-variation image deconvolution with adaptive parameter estimation via split bregman method,” Math. Probl. Eng. 2014, 617026 (2014).
[Crossref]

Song, X.

Soubret, A.

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of hetero-geneities: study of the normalized born ratio,” IEEE Trans. Medical Imaging 24(10), 1377–1386 (2005).
[Crossref]

Stark, D.

L. Sudheendra, G. K. Das, C. Li, D. Stark, J. Cena, S. Cherry, and I. M. Kennedy, “Nagdf4: Eu3+ nanoparticles for enhanced x-ray excited optical imaging,” Chem. Mater. 26(5), 1881–1888 (2014).
[Crossref] [PubMed]

Stout, D.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3d whole body mouse atlas from ct and cryosection data,” Phy. Med. Biol. 52(3), 577 (2007).
[Crossref]

Sudheendra, L.

L. Sudheendra, G. K. Das, C. Li, D. Stark, J. Cena, S. Cherry, and I. M. Kennedy, “Nagdf4: Eu3+ nanoparticles for enhanced x-ray excited optical imaging,” Chem. Mater. 26(5), 1881–1888 (2014).
[Crossref] [PubMed]

Sun, C.

C. Wang, O. Volotskova, K. Lu, M. Ahmad, C. Sun, L. Xing, and W. Lin, “Synergistic assembly of heavy metal clusters and luminescent organic bridging ligands in metalCorganic frameworks for highly efficient x-ray scintillation,” J. Am. Chem. Soc. 136(17), 6171–6174 (2014).
[Crossref] [PubMed]

Y. Osakada, G. Pratx, C. Sun, M. Sakamoto, M. Ahmad, O. Volotskova, Q. Ong, T. Teranishi, Y. Harada, L. Xing, and B. Cui, “Hard x-ray-induced optical luminescence via biomolecule-directed metal clusters,” Chem. Commun. 50(27), 3549–3551 (2014).
[Crossref]

C. Carpenter, G. Pratx, C. Sun, and L. Xing, “Limited-angle x-ray luminescence tomography: methodology and feasibility study,” Phys. Med. Biol. 56(12), 3487 (2011).
[Crossref] [PubMed]

G. Pratx, C. M. Carpenter, C. Sun, R. P. Rao, and L. Xing, “Tomographic molecular imaging of x-ray-excitable nanoparticles,” Opt. Lett. 35(20), 3345–3347 (2010).
[Crossref] [PubMed]

Sun, L.

Teranishi, T.

Y. Osakada, G. Pratx, C. Sun, M. Sakamoto, M. Ahmad, O. Volotskova, Q. Ong, T. Teranishi, Y. Harada, L. Xing, and B. Cui, “Hard x-ray-induced optical luminescence via biomolecule-directed metal clusters,” Chem. Commun. 50(27), 3549–3551 (2014).
[Crossref]

Tian, J.

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating mri structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5(6), 1861–1876 (2014).
[Crossref] [PubMed]

D. Chen, S. Zhu, H. Yi, X. Zhang, D. Chen, J. Liang, and J. Tian, “Cone beam x-ray luminescence computed tomography: A feasibility study,” Med. Phys. 40(3), 031111 (2013).
[Crossref] [PubMed]

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
[Crossref]

Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the lp regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012).
[Crossref]

J. Feng, C. Qin, K. Jia, S. Zhu, K. Liu, D. Han, X. Yang, Q. Gao, and J. Tian, “Total variation regularization for bioluminescence tomography with the split bregman method,” Appl. Opt. 51(19), 4501–4512 (2012).
[Crossref] [PubMed]

B. Zhang, X. Yang, C. Qin, D. Liu, S. Zhu, J. Feng, L. Sun, K. Liu, D. Han, X. Ma, X. Zhang, J. Zhong, X. Li, X. Yang, and J. Tian, “A trust region method in adaptive finite element framework for bioluminescence tomography,” Opt. Express 18(7), 6477–6491 (2010).
[Crossref] [PubMed]

J. Feng, K. Jia, G. Yan, S. Zhu, C. Qin, Y. Lv, and J. Tian, “An optimal permissible source region strategy for multispectral bioluminescence tomography,” Opt. Express 16(20), 15640–15654 (2008).
[Crossref] [PubMed]

Vaquero, J. J.

J. J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split bregman method,” Med. Phys. 38(11), 6275–6284 (2011).
[Crossref] [PubMed]

Volotskova, O.

Y. Osakada, G. Pratx, C. Sun, M. Sakamoto, M. Ahmad, O. Volotskova, Q. Ong, T. Teranishi, Y. Harada, L. Xing, and B. Cui, “Hard x-ray-induced optical luminescence via biomolecule-directed metal clusters,” Chem. Commun. 50(27), 3549–3551 (2014).
[Crossref]

C. Wang, O. Volotskova, K. Lu, M. Ahmad, C. Sun, L. Xing, and W. Lin, “Synergistic assembly of heavy metal clusters and luminescent organic bridging ligands in metalCorganic frameworks for highly efficient x-ray scintillation,” J. Am. Chem. Soc. 136(17), 6171–6174 (2014).
[Crossref] [PubMed]

Walker, H. F.

S. C. Eisenstat and H. F. Walker, “Globally convergent inexact newton methods,” SIAM Journal on Optimization 4(2), 393–422 (1994).
[Crossref]

Wang, C.

C. Wang, O. Volotskova, K. Lu, M. Ahmad, C. Sun, L. Xing, and W. Lin, “Synergistic assembly of heavy metal clusters and luminescent organic bridging ligands in metalCorganic frameworks for highly efficient x-ray scintillation,” J. Am. Chem. Soc. 136(17), 6171–6174 (2014).
[Crossref] [PubMed]

W. Cong, C. Wang, and G. Wang, “Stored luminescence computed tomography,” Appl. Opt. 53(25), 5672–5676 (2014).
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Wang, D.

Wang, F.

N. Zhang, Z.-S. Deng, F. Wang, and X.-Y. Wang, “The effect of different number of diffusion gradients on snr of diffusion tensor-derived measurement maps,” J. Biomed. Sci. Eng. 2(2), 96 (2009).
[Crossref]

Wang, G.

W. Cong, C. Wang, and G. Wang, “Stored luminescence computed tomography,” Appl. Opt. 53(25), 5672–5676 (2014).
[Crossref] [PubMed]

W. Cong, H. Shen, and G. Wang, “Spectrally resolving and scattering-compensated x-ray luminescence/fluorescence computed tomography,” J. Biomed. Opt. 16(6), 066014 (2011).
[Crossref] [PubMed]

Wang, H.

Wang, Q.

Wang, X.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
[Crossref]

Wang, X.-Y.

N. Zhang, Z.-S. Deng, F. Wang, and X.-Y. Wang, “The effect of different number of diffusion gradients on snr of diffusion tensor-derived measurement maps,” J. Biomed. Sci. Eng. 2(2), 96 (2009).
[Crossref]

Xian, L. X.

T. Ying, C. W. He, L. X. Xian, and F. Yao, “Preparation and luminescence property of Gd2O2S: Tb X-ray nano-phosphors using the complex precipitation method,” J. Alloys Compd. 433(1), 313–317 (2007).
[Crossref]

Xing, L.

C. Wang, O. Volotskova, K. Lu, M. Ahmad, C. Sun, L. Xing, and W. Lin, “Synergistic assembly of heavy metal clusters and luminescent organic bridging ligands in metalCorganic frameworks for highly efficient x-ray scintillation,” J. Am. Chem. Soc. 136(17), 6171–6174 (2014).
[Crossref] [PubMed]

Y. Osakada, G. Pratx, C. Sun, M. Sakamoto, M. Ahmad, O. Volotskova, Q. Ong, T. Teranishi, Y. Harada, L. Xing, and B. Cui, “Hard x-ray-induced optical luminescence via biomolecule-directed metal clusters,” Chem. Commun. 50(27), 3549–3551 (2014).
[Crossref]

C. Carpenter, G. Pratx, C. Sun, and L. Xing, “Limited-angle x-ray luminescence tomography: methodology and feasibility study,” Phys. Med. Biol. 56(12), 3487 (2011).
[Crossref] [PubMed]

G. Pratx, C. M. Carpenter, C. Sun, R. P. Rao, and L. Xing, “Tomographic molecular imaging of x-ray-excitable nanoparticles,” Opt. Lett. 35(20), 3345–3347 (2010).
[Crossref] [PubMed]

Xu, J.

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Model. Sim. 4(2), 460–489 (2005).
[Crossref]

Xue, H.

Yan, G.

Yang, A. Y.

A. Y. Yang, S. S. Sastry, A. Ganesh, and Y. Ma, “Fast l1-minimization algorithms and an application in robust face recognition: A review,” in Image Processing (ICIP), 2010 17th IEEE International Conference on, (IEEE, 2010), pp. 1849–1852.

Yang, X.

Yao, F.

T. Ying, C. W. He, L. X. Xian, and F. Yao, “Preparation and luminescence property of Gd2O2S: Tb X-ray nano-phosphors using the complex precipitation method,” J. Alloys Compd. 433(1), 313–317 (2007).
[Crossref]

Yi, H.

D. Chen, S. Zhu, H. Yi, X. Zhang, D. Chen, J. Liang, and J. Tian, “Cone beam x-ray luminescence computed tomography: A feasibility study,” Med. Phys. 40(3), 031111 (2013).
[Crossref] [PubMed]

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
[Crossref]

Yin, W.

W. Yin, S. Osher, D. Goldfarb, and J. Darbon, “Bregman iterative algorithms for l1-minimization with applications to compressed sensing,” SIAM J. Imaging Sci. 1(1), 143–168 (2008).
[Crossref]

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Model. Sim. 4(2), 460–489 (2005).
[Crossref]

Ying, L.

B. Liu, Y. M. Zou, and L. Ying, “Sparsesense: application of compressed sensing in parallel mri,” in Information Technology and Applications in Biomedicine, 2008. ITAB 2008. International Conference on, (IEEE,), pp. 127–130.

Ying, T.

T. Ying, C. W. He, L. X. Xian, and F. Yao, “Preparation and luminescence property of Gd2O2S: Tb X-ray nano-phosphors using the complex precipitation method,” J. Alloys Compd. 433(1), 313–317 (2007).
[Crossref]

Zhang, B.

Zhang, J.

Zhang, N.

N. Zhang, Z.-S. Deng, F. Wang, and X.-Y. Wang, “The effect of different number of diffusion gradients on snr of diffusion tensor-derived measurement maps,” J. Biomed. Sci. Eng. 2(2), 96 (2009).
[Crossref]

Zhang, Q.

Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the lp regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012).
[Crossref]

Zhang, W.

C. He, C. Hu, W. Zhang, B. Shi, and X. Hu, “Fast total-variation image deconvolution with adaptive parameter estimation via split bregman method,” Math. Probl. Eng. 2014, 617026 (2014).
[Crossref]

Zhang, X.

Zhao, F.

D. Chen, S. Zhu, X. Chen, T. Chao, X. Cao, F. Zhao, L. Huang, and J. Liang, “Quantitative cone beam x-ray luminescence tomography/x-ray computed tomography imaging,” Appl. Phys. Lett. 105(19), 191104 (2014).
[Crossref]

Zhong, J.

Zhu, S.

D. Chen, S. Zhu, X. Chen, T. Chao, X. Cao, F. Zhao, L. Huang, and J. Liang, “Quantitative cone beam x-ray luminescence tomography/x-ray computed tomography imaging,” Appl. Phys. Lett. 105(19), 191104 (2014).
[Crossref]

D. Chen, S. Zhu, H. Yi, X. Zhang, D. Chen, J. Liang, and J. Tian, “Cone beam x-ray luminescence computed tomography: A feasibility study,” Med. Phys. 40(3), 031111 (2013).
[Crossref] [PubMed]

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
[Crossref]

J. Feng, C. Qin, K. Jia, S. Zhu, K. Liu, D. Han, X. Yang, Q. Gao, and J. Tian, “Total variation regularization for bioluminescence tomography with the split bregman method,” Appl. Opt. 51(19), 4501–4512 (2012).
[Crossref] [PubMed]

B. Zhang, X. Yang, C. Qin, D. Liu, S. Zhu, J. Feng, L. Sun, K. Liu, D. Han, X. Ma, X. Zhang, J. Zhong, X. Li, X. Yang, and J. Tian, “A trust region method in adaptive finite element framework for bioluminescence tomography,” Opt. Express 18(7), 6477–6491 (2010).
[Crossref] [PubMed]

J. Feng, K. Jia, G. Yan, S. Zhu, C. Qin, Y. Lv, and J. Tian, “An optimal permissible source region strategy for multispectral bioluminescence tomography,” Opt. Express 16(20), 15640–15654 (2008).
[Crossref] [PubMed]

Zou, Y. M.

B. Liu, Y. M. Zou, and L. Ying, “Sparsesense: application of compressed sensing in parallel mri,” in Information Technology and Applications in Biomedicine, 2008. ITAB 2008. International Conference on, (IEEE,), pp. 127–130.

ACS nano (1)

H. Chen, T. Moore, B. Qi, D. C. Colvin, E. K. Jelen, D. A. Hitchcock, J. He, O. T. Mefford, J. C. Gore, F. Alexis, and J. N. Anker, “Monitoring ph-triggered drug release from radioluminescent nanocapsules with x-ray excited optical luminescence,” ACS nano 7(2), 1178–1187 (2013).
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Adv. Sci. Lett. (1)

Q. Zhang, X. Qu, D. Chen, X. Chen, J. Liang, and J. Tian, “Experimental three-dimensional bioluminescence tomography reconstruction using the lp regularization,” Adv. Sci. Lett. 16(1), 125–129 (2012).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

D. Chen, S. Zhu, X. Chen, T. Chao, X. Cao, F. Zhao, L. Huang, and J. Liang, “Quantitative cone beam x-ray luminescence tomography/x-ray computed tomography imaging,” Appl. Phys. Lett. 105(19), 191104 (2014).
[Crossref]

Biomed. Opt. Express (1)

Chem. Commun. (1)

Y. Osakada, G. Pratx, C. Sun, M. Sakamoto, M. Ahmad, O. Volotskova, Q. Ong, T. Teranishi, Y. Harada, L. Xing, and B. Cui, “Hard x-ray-induced optical luminescence via biomolecule-directed metal clusters,” Chem. Commun. 50(27), 3549–3551 (2014).
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Chem. Mater. (1)

L. Sudheendra, G. K. Das, C. Li, D. Stark, J. Cena, S. Cherry, and I. M. Kennedy, “Nagdf4: Eu3+ nanoparticles for enhanced x-ray excited optical imaging,” Chem. Mater. 26(5), 1881–1888 (2014).
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T. Ying, C. W. He, L. X. Xian, and F. Yao, “Preparation and luminescence property of Gd2O2S: Tb X-ray nano-phosphors using the complex precipitation method,” J. Alloys Compd. 433(1), 313–317 (2007).
[Crossref]

J. Am. Chem. Soc. (1)

C. Wang, O. Volotskova, K. Lu, M. Ahmad, C. Sun, L. Xing, and W. Lin, “Synergistic assembly of heavy metal clusters and luminescent organic bridging ligands in metalCorganic frameworks for highly efficient x-ray scintillation,” J. Am. Chem. Soc. 136(17), 6171–6174 (2014).
[Crossref] [PubMed]

J. Biomed. Opt. (2)

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
[Crossref]

W. Cong, H. Shen, and G. Wang, “Spectrally resolving and scattering-compensated x-ray luminescence/fluorescence computed tomography,” J. Biomed. Opt. 16(6), 066014 (2011).
[Crossref] [PubMed]

J. Biomed. Sci. Eng. (1)

N. Zhang, Z.-S. Deng, F. Wang, and X.-Y. Wang, “The effect of different number of diffusion gradients on snr of diffusion tensor-derived measurement maps,” J. Biomed. Sci. Eng. 2(2), 96 (2009).
[Crossref]

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C. He, C. Hu, W. Zhang, B. Shi, and X. Hu, “Fast total-variation image deconvolution with adaptive parameter estimation via split bregman method,” Math. Probl. Eng. 2014, 617026 (2014).
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J. J. Abascal, J. Chamorro-Servent, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, J. J. Vaquero, and M. Desco, “Fluorescence diffuse optical tomography using the split bregman method,” Med. Phys. 38(11), 6275–6284 (2011).
[Crossref] [PubMed]

D. Chen, S. Zhu, H. Yi, X. Zhang, D. Chen, J. Liang, and J. Tian, “Cone beam x-ray luminescence computed tomography: A feasibility study,” Med. Phys. 40(3), 031111 (2013).
[Crossref] [PubMed]

Multiscale Model. Sim. (1)

S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Model. Sim. 4(2), 460–489 (2005).
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J. Gilles, The Bregman Cookbook (2011).

A. Y. Yang, S. S. Sastry, A. Ganesh, and Y. Ma, “Fast l1-minimization algorithms and an application in robust face recognition: A review,” in Image Processing (ICIP), 2010 17th IEEE International Conference on, (IEEE, 2010), pp. 1849–1852.

B. Liu, Y. M. Zou, and L. Ying, “Sparsesense: application of compressed sensing in parallel mri,” in Information Technology and Applications in Biomedicine, 2008. ITAB 2008. International Conference on, (IEEE,), pp. 127–130.

C. Li, A. M. Davalos, and S. R. Cherry, “Numerical and experimental studies of x-ray luminescence optical tomography for small animal imaging,” in SPIE BiOS, (International Society for Optics and Photonics, 2013), pp. 85781B.

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Figures (5)

Fig. 1
Fig. 1 An overview of the system.
Fig. 2
Fig. 2 (a)Data analysis of the X-ray detection with different distances from the X-ray source (71.5 cm, 69 cm, 66.5 cm, and 64 cm). (b)Relationship between the X-ray beam width and the distances from the X-ray source
Fig. 3
Fig. 3 Reconstruction results of the two methods. (a), (b), (c) and (d) show the configuration of the phantoms in the slice of z = 20 mm. (e), (f), (g) and (h) show the reconstruction results of the proposed method while (i), (j), (k) and (l) show the reconstruction results of the SB method at the corresponding slice.
Fig. 4
Fig. 4 Fusion images of the collected data from one direction. (a)–(n) show the fusion images of the phantom when it moves at the direction parallel to the X-ray source.
Fig. 5
Fig. 5 Reconstruction results of the phantom experiments in the slices of z=21.79 mm and x=42. 67 mm respectively represented by red dotted lines. (a) shows the micro-CT result on the x–z plane. (b) and (c) show the reconstruction results of the traditional SB method with fan-shaped X-rays model and parallel X-rays model respectively while (d) and (e) show the results of the proposed method with fan-shaped X-rays model and parallel X-rays model respectively.

Tables (3)

Tables Icon

Table 1 Reconstruction errors of the two methods

Tables Icon

Table 2 Reconstruction errors of the method of different noise levels

Tables Icon

Table 3 Reconstruction errors of the two methods in different models

Equations (20)

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

X ( r ) = X 0 exp { r 0 r μ t ( τ ) d τ } ,
S ( r ) = ε X ( r ) ρ ( r ) ,
[ D ( r ) Φ ( r ) ] + μ ( r ) Φ ( r ) = S ( r ) r Ω ,
A ρ = Φ , where ρ 0.
Ψ = { 1 if node n is within the X-ray scanning area 0 otherwise ,
min ρ | ρ | 1 + λ 2 A ρ Φ 2 , where ρ 0.
min ρ | ρ ^ | 1 + λ 2 A ρ Φ 2 , where ρ 0.
min ρ , x , y | y | 1 + λ 2 x Φ 2 subject ti A ρ = x , y = ρ ^ .
J ( ρ , x , y ) = { | y | 1 + λ 2 x Φ 2 } ,
D J ( p ρ k , p x k , p y k ) ( ρ , x , y ; ρ k , x k , y k ) = J ( ρ , x , y ) J ( ρ k , x k , y k ) < p ρ k , ρ ρ k > < p x k , x x k > < p y k , y y k > ,
ρ k + 1 = arg min u { β 1 2 x A ρ b k 2 2 + | y | 1 + β 2 2 y d k ρ ^ 2 2 } ,
y k + 1 = arg min y { | y | 1 + β 2 2 y d k ρ ^ 2 2 } ,
x k + 1 = arg min x { λ k + 1 2 x A ρ 2 2 + β 1 2 x A ρ b k 2 2 } ,
b k + 1 = b k + A ρ k + 1 x k + 1 , b k + 1 = b k + ρ ^ k + 1 y k + 1 .
y k + 1 = s h r i n k ( d k + ρ ^ k + 1 , 1 β ) ,
x k + 1 = λ k + 1 Φ + β 1 ( A ρ k + 1 + b k ) λ k + 1 + β 1 , λ k + 1 = β 1 A ρ k + 1 + b k Φ 2 c β 1 .
location error = ( x x 0 ) 2 + ( y y 0 ) 2 + ( z z 0 ) 2
DC = 2 | R S A S | | R S | + | A S | × 100 % ,
M E S = 1 N 1 ( ρ k t ρ k r ) 2 ,
intensity error = 1 N u m ( ρ k t > 0 ) ρ k t > 0 | ρ k r ρ k t | max ( ρ k t ) × 100 %

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