Abstract

Cone beam X-ray luminescence computed tomography (CB-XLCT) has been proposed as a promising hybrid imaging technique. Though it has the advantage of fast imaging, the inverse problem of CB-XLCT is seriously ill-conditioned, making the image quality quite poor, especially for imaging multi-targets. To achieve fast imaging of multi-targets, which is essential for in vivo applications, a truncated singular value decomposition (TSVD) based sparse view CB-XLCT reconstruction method is proposed in this study. With the weight matrix of the CB-XLCT system being converted to orthogonal by TSVD, the compressed sensing (CS) based L1-norm method could be applied for fast reconstruction from fewer projection views. Numerical simulations and phantom experiments demonstrate that by using the proposed method, two targets with different edge-to-edge distances (EEDs) could be resolved effectively. It indicates that the proposed method could improve the imaging quality of multi-targets significantly in terms of localization accuracy, target shape, image contrast, and spatial resolution, when compared with conventional methods.

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

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2018 (1)

T. Liu, J. Rong, P. Gao, W. Zhang, W. Liu, Y. Zhang, and H. Lu, “Cone-beam x-ray luminescence computed tomography based on x-ray absorption dosage,” J. Biomed. Opt. 23(2), 1–11 (2018).
[PubMed]

2017 (5)

G. Zhang, S. Tzoumas, K. Cheng, F. Liu, J. Liu, J. Luo, J. Bai, and L. Xing, “Generalized Adaptive Gaussian Markov Random Field for X-ray Luminescence Computed Tomography,” IEEE Trans. Biomed. Eng. 65, 2130–2133 (2017).
[PubMed]

G. Zhang, F. Liu, J. Liu, J. Luo, Y. Xie, J. Bai, and L. Xing, “Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method,” IEEE Trans. Med. Imaging 36(1), 225–235 (2017).
[Crossref] [PubMed]

W. Zhang, M. C. Lun, A. A.-T. Nguyen, and C. Li, “X-ray luminescence computed tomography using a focused x-ray beam,” J. Biomed. Opt. 22(11), 1–11 (2017).
[Crossref] [PubMed]

M. C. Lun, W. Zhang, and C. Li, “Sensitivity study of x-ray luminescence computed tomography,” Appl. Opt. 56(11), 3010–3019 (2017).
[Crossref] [PubMed]

P. Gao, H. Pu, J. Rong, W. Zhang, T. Liu, W. Liu, Y. Zhang, and H. Lu, “Resolving adjacent nanophosphors of different concentrations by excitation-based cone-beam X-ray luminescence tomography,” Biomed. Opt. Express 8(9), 3952–3965 (2017).
[Crossref] [PubMed]

2016 (2)

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

W. Zhang, D. Zhu, M. Lun, and C. Li, “Multiple pinhole collimator based X-ray luminescence computed tomography,” Biomed. Opt. Express 7(7), 2506–2523 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (6)

X. Liu, H. Wang, M. Xu, S. Nie, and H. Lu, “A wavelet-based single-view reconstruction approach for cone beam x-ray luminescence tomography imaging,” Biomed. Opt. Express 5(11), 3848–3858 (2014).
[Crossref] [PubMed]

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. Li, A. Martínez-Dávalos, and S. R. Cherry, “Numerical simulation of x-ray luminescence optical tomography for small-animal imaging,” J. Biomed. Opt. 19(4), 046002 (2014).
[Crossref] [PubMed]

H. Pu, G. Zhang, W. He, F. Liu, H. Guang, Y. Zhang, J. Bai, and J. Luo, “Resolving fluorophores by unmixing multispectral fluorescence tomography with independent component analysis,” Phys. Med. Biol. 59(17), 5025–5042 (2014).
[Crossref] [PubMed]

J. Shi, F. Liu, G. Zhang, J. Luo, and J. Bai, “Enhanced spatial resolution in fluorescence molecular tomography using restarted L1-regularized nonlinear conjugate gradient algorithm,” J. Biomed. Opt. 19(4), 046018 (2014).
[Crossref] [PubMed]

2013 (5)

X. Cao, B. Zhang, X. Wang, F. Liu, K. Liu, J. Luo, and J. Bai, “An adaptive Tikhonov regularization method for fluorescence molecular tomography,” Med. Biol. Eng. Comput. 51(8), 849–858 (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] [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]

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion,” J. Opt. Soc. Am. A 30(3), 437–447 (2013).
[Crossref] [PubMed]

X. Liu, Q. Liao, and H. Wang, “In vivo x-ray luminescence tomographic imaging with single-view data,” Opt. Lett. 38(22), 4530–4533 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (4)

X. Cao, B. Zhang, F. Liu, X. Wang, and J. Bai, “Reconstruction for limited-projection fluorescence molecular tomography based on projected restarted conjugate gradient normal residual,” Opt. Lett. 36(23), 4515–4517 (2011).
[Crossref] [PubMed]

X. Liu, F. Liu, Y. Zhang, and J. Bai, “Unmixing dynamic fluorescence diffuse optical tomography images with independent component analysis,” IEEE Trans. Med. Imaging 30(9), 1591–1604 (2011).
[Crossref] [PubMed]

C. M. Carpenter, G. Pratx, C. Sun, and L. Xing, “Limited-angle x-ray luminescence tomography: methodology and feasibility study,” Phys. Med. Biol. 56(12), 3487–3502 (2011).
[Crossref] [PubMed]

Z. Tian, X. Jia, K. Yuan, T. Pan, and S. B. Jiang, “Low-dose CT reconstruction via edge-preserving total variation regularization,” Phys. Med. Biol. 56(18), 5949–5967 (2011).
[Crossref] [PubMed]

2010 (3)

G. Pratx, C. M. Carpenter, C. Sun, and L. Xing, “X-ray luminescence computed tomography via selective excitation: a feasibility study,” IEEE Trans. Med. Imaging 29(12), 1992–1999 (2010).
[Crossref] [PubMed]

C. M. Carpenter, C. Sun, G. Pratx, R. Rao, and L. Xing, “Hybrid x-ray/optical luminescence imaging: characterization of experimental conditions,” Med. Phys. 37(8), 4011–4018 (2010).
[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]

2009 (1)

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

2008 (2)

J. Verhaeghe, D. Van de Ville, I. Khalidov, Y. D’Asseler, I. Lemahieu, and M. Unser, “Dynamic PET reconstruction using wavelet regularization with adapted basis functions,” IEEE Trans. Med. Imaging 27(7), 943–959 (2008).
[Crossref] [PubMed]

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

2006 (2)

2005 (1)

2001 (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18(6), 57–75 (2001).
[Crossref]

1984 (1)

Adibi, A.

Bai, J.

G. Zhang, S. Tzoumas, K. Cheng, F. Liu, J. Liu, J. Luo, J. Bai, and L. Xing, “Generalized Adaptive Gaussian Markov Random Field for X-ray Luminescence Computed Tomography,” IEEE Trans. Biomed. Eng. 65, 2130–2133 (2017).
[PubMed]

G. Zhang, F. Liu, J. Liu, J. Luo, Y. Xie, J. Bai, and L. Xing, “Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method,” IEEE Trans. Med. Imaging 36(1), 225–235 (2017).
[Crossref] [PubMed]

H. Pu, G. Zhang, W. He, F. Liu, H. Guang, Y. Zhang, J. Bai, and J. Luo, “Resolving fluorophores by unmixing multispectral fluorescence tomography with independent component analysis,” Phys. Med. Biol. 59(17), 5025–5042 (2014).
[Crossref] [PubMed]

J. Shi, F. Liu, G. Zhang, J. Luo, and J. Bai, “Enhanced spatial resolution in fluorescence molecular tomography using restarted L1-regularized nonlinear conjugate gradient algorithm,” J. Biomed. Opt. 19(4), 046018 (2014).
[Crossref] [PubMed]

X. Cao, B. Zhang, X. Wang, F. Liu, K. Liu, J. Luo, and J. Bai, “An adaptive Tikhonov regularization method for fluorescence molecular tomography,” Med. Biol. Eng. Comput. 51(8), 849–858 (2013).
[Crossref] [PubMed]

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion,” J. Opt. Soc. Am. A 30(3), 437–447 (2013).
[Crossref] [PubMed]

X. Cao, B. Zhang, F. Liu, X. Wang, and J. Bai, “Reconstruction for limited-projection fluorescence molecular tomography based on projected restarted conjugate gradient normal residual,” Opt. Lett. 36(23), 4515–4517 (2011).
[Crossref] [PubMed]

X. Liu, F. Liu, Y. Zhang, and J. Bai, “Unmixing dynamic fluorescence diffuse optical tomography images with independent component analysis,” IEEE Trans. Med. Imaging 30(9), 1591–1604 (2011).
[Crossref] [PubMed]

Beck, A.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

Behrooz, A.

Boas, D. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18(6), 57–75 (2001).
[Crossref]

Brooks, D. H.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18(6), 57–75 (2001).
[Crossref]

Candès, E. J.

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
[Crossref]

Cao, X.

Carpenter, C. M.

C. M. Carpenter, G. Pratx, C. Sun, and L. Xing, “Limited-angle x-ray luminescence tomography: methodology and feasibility study,” Phys. Med. Biol. 56(12), 3487–3502 (2011).
[Crossref] [PubMed]

C. M. Carpenter, C. Sun, G. Pratx, R. Rao, and L. Xing, “Hybrid x-ray/optical luminescence imaging: characterization of experimental conditions,” Med. Phys. 37(8), 4011–4018 (2010).
[Crossref] [PubMed]

G. Pratx, C. M. Carpenter, C. Sun, and L. Xing, “X-ray luminescence computed tomography via selective excitation: a feasibility study,” IEEE Trans. Med. Imaging 29(12), 1992–1999 (2010).
[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]

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]

Chen, D.

D. Chen, S. Zhu, X. Cao, F. Zhao, and J. Liang, “X-ray luminescence computed tomography imaging based on X-ray distribution model and adaptively split Bregman method,” Biomed. Opt. Express 6(7), 2649–2663 (2015).
[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]

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]

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] [PubMed]

Chen, 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]

Cheng, K.

G. Zhang, S. Tzoumas, K. Cheng, F. Liu, J. Liu, J. Luo, J. Bai, and L. Xing, “Generalized Adaptive Gaussian Markov Random Field for X-ray Luminescence Computed Tomography,” IEEE Trans. Biomed. Eng. 65, 2130–2133 (2017).
[PubMed]

Cherry, S. R.

C. Li, A. Martínez-Dávalos, and S. R. Cherry, “Numerical simulation of x-ray luminescence optical tomography for small-animal imaging,” J. Biomed. Opt. 19(4), 046002 (2014).
[Crossref] [PubMed]

Cong, A.

Cong, W.

D’Asseler, Y.

J. Verhaeghe, D. Van de Ville, I. Khalidov, Y. D’Asseler, I. Lemahieu, and M. Unser, “Dynamic PET reconstruction using wavelet regularization with adapted basis functions,” IEEE Trans. Med. Imaging 27(7), 943–959 (2008).
[Crossref] [PubMed]

Davis, L.

DiMarzio, C. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18(6), 57–75 (2001).
[Crossref]

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006).
[Crossref]

Durairaj, K.

Eftekhar, A. A.

Feldkamp, L.

Gao, P.

T. Liu, J. Rong, P. Gao, W. Zhang, W. Liu, Y. Zhang, and H. Lu, “Cone-beam x-ray luminescence computed tomography based on x-ray absorption dosage,” J. Biomed. Opt. 23(2), 1–11 (2018).
[PubMed]

P. Gao, H. Pu, J. Rong, W. Zhang, T. Liu, W. Liu, Y. Zhang, and H. Lu, “Resolving adjacent nanophosphors of different concentrations by excitation-based cone-beam X-ray luminescence tomography,” Biomed. Opt. Express 8(9), 3952–3965 (2017).
[Crossref] [PubMed]

Gaudette, R. J.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18(6), 57–75 (2001).
[Crossref]

Goy, A.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

Guang, H.

H. Pu, G. Zhang, W. He, F. Liu, H. Guang, Y. Zhang, J. Bai, and J. Luo, “Resolving fluorophores by unmixing multispectral fluorescence tomography with independent component analysis,” Phys. Med. Biol. 59(17), 5025–5042 (2014).
[Crossref] [PubMed]

He, W.

H. Pu, G. Zhang, W. He, F. Liu, H. Guang, Y. Zhang, J. Bai, and J. Luo, “Resolving fluorophores by unmixing multispectral fluorescence tomography with independent component analysis,” Phys. Med. Biol. 59(17), 5025–5042 (2014).
[Crossref] [PubMed]

Henry, M.

Hoffman, E.

Huang, L.

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]

Jia, X.

Z. Tian, X. Jia, K. Yuan, T. Pan, and S. B. Jiang, “Low-dose CT reconstruction via edge-preserving total variation regularization,” Phys. Med. Biol. 56(18), 5949–5967 (2011).
[Crossref] [PubMed]

Jiang, M.

Jiang, S. B.

Z. Tian, X. Jia, K. Yuan, T. Pan, and S. B. Jiang, “Low-dose CT reconstruction via edge-preserving total variation regularization,” Phys. Med. Biol. 56(18), 5949–5967 (2011).
[Crossref] [PubMed]

Kamilov, U. S.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

Khalidov, I.

J. Verhaeghe, D. Van de Ville, I. Khalidov, Y. D’Asseler, I. Lemahieu, and M. Unser, “Dynamic PET reconstruction using wavelet regularization with adapted basis functions,” IEEE Trans. Med. Imaging 27(7), 943–959 (2008).
[Crossref] [PubMed]

Kilmer, M.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18(6), 57–75 (2001).
[Crossref]

Kress, J.

Kumar, D.

Lemahieu, I.

J. Verhaeghe, D. Van de Ville, I. Khalidov, Y. D’Asseler, I. Lemahieu, and M. Unser, “Dynamic PET reconstruction using wavelet regularization with adapted basis functions,” IEEE Trans. Med. Imaging 27(7), 943–959 (2008).
[Crossref] [PubMed]

Li, C.

W. Zhang, M. C. Lun, A. A.-T. Nguyen, and C. Li, “X-ray luminescence computed tomography using a focused x-ray beam,” J. Biomed. Opt. 22(11), 1–11 (2017).
[Crossref] [PubMed]

M. C. Lun, W. Zhang, and C. Li, “Sensitivity study of x-ray luminescence computed tomography,” Appl. Opt. 56(11), 3010–3019 (2017).
[Crossref] [PubMed]

W. Zhang, D. Zhu, M. Lun, and C. Li, “Multiple pinhole collimator based X-ray luminescence computed tomography,” Biomed. Opt. Express 7(7), 2506–2523 (2016).
[Crossref] [PubMed]

C. Li, A. Martínez-Dávalos, and S. R. Cherry, “Numerical simulation of x-ray luminescence optical tomography for small-animal imaging,” J. Biomed. Opt. 19(4), 046002 (2014).
[Crossref] [PubMed]

Li, W.

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] [PubMed]

Liang, J.

D. Chen, S. Zhu, X. Cao, F. Zhao, and J. Liang, “X-ray luminescence computed tomography imaging based on X-ray distribution model and adaptively split Bregman method,” Biomed. Opt. Express 6(7), 2649–2663 (2015).
[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]

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] [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]

Liao, Q.

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]

X. Liu, Q. Liao, and H. Wang, “In vivo x-ray luminescence tomographic imaging with single-view data,” Opt. Lett. 38(22), 4530–4533 (2013).
[Crossref] [PubMed]

Liu, F.

G. Zhang, S. Tzoumas, K. Cheng, F. Liu, J. Liu, J. Luo, J. Bai, and L. Xing, “Generalized Adaptive Gaussian Markov Random Field for X-ray Luminescence Computed Tomography,” IEEE Trans. Biomed. Eng. 65, 2130–2133 (2017).
[PubMed]

G. Zhang, F. Liu, J. Liu, J. Luo, Y. Xie, J. Bai, and L. Xing, “Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method,” IEEE Trans. Med. Imaging 36(1), 225–235 (2017).
[Crossref] [PubMed]

H. Pu, G. Zhang, W. He, F. Liu, H. Guang, Y. Zhang, J. Bai, and J. Luo, “Resolving fluorophores by unmixing multispectral fluorescence tomography with independent component analysis,” Phys. Med. Biol. 59(17), 5025–5042 (2014).
[Crossref] [PubMed]

J. Shi, F. Liu, G. Zhang, J. Luo, and J. Bai, “Enhanced spatial resolution in fluorescence molecular tomography using restarted L1-regularized nonlinear conjugate gradient algorithm,” J. Biomed. Opt. 19(4), 046018 (2014).
[Crossref] [PubMed]

X. Cao, B. Zhang, X. Wang, F. Liu, K. Liu, J. Luo, and J. Bai, “An adaptive Tikhonov regularization method for fluorescence molecular tomography,” Med. Biol. Eng. Comput. 51(8), 849–858 (2013).
[Crossref] [PubMed]

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion,” J. Opt. Soc. Am. A 30(3), 437–447 (2013).
[Crossref] [PubMed]

X. Cao, B. Zhang, F. Liu, X. Wang, and J. Bai, “Reconstruction for limited-projection fluorescence molecular tomography based on projected restarted conjugate gradient normal residual,” Opt. Lett. 36(23), 4515–4517 (2011).
[Crossref] [PubMed]

X. Liu, F. Liu, Y. Zhang, and J. Bai, “Unmixing dynamic fluorescence diffuse optical tomography images with independent component analysis,” IEEE Trans. Med. Imaging 30(9), 1591–1604 (2011).
[Crossref] [PubMed]

Liu, J.

G. Zhang, F. Liu, J. Liu, J. Luo, Y. Xie, J. Bai, and L. Xing, “Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method,” IEEE Trans. Med. Imaging 36(1), 225–235 (2017).
[Crossref] [PubMed]

G. Zhang, S. Tzoumas, K. Cheng, F. Liu, J. Liu, J. Luo, J. Bai, and L. Xing, “Generalized Adaptive Gaussian Markov Random Field for X-ray Luminescence Computed Tomography,” IEEE Trans. Biomed. Eng. 65, 2130–2133 (2017).
[PubMed]

Liu, K.

X. Cao, B. Zhang, X. Wang, F. Liu, K. Liu, J. Luo, and J. Bai, “An adaptive Tikhonov regularization method for fluorescence molecular tomography,” Med. Biol. Eng. Comput. 51(8), 849–858 (2013).
[Crossref] [PubMed]

Liu, T.

T. Liu, J. Rong, P. Gao, W. Zhang, W. Liu, Y. Zhang, and H. Lu, “Cone-beam x-ray luminescence computed tomography based on x-ray absorption dosage,” J. Biomed. Opt. 23(2), 1–11 (2018).
[PubMed]

P. Gao, H. Pu, J. Rong, W. Zhang, T. Liu, W. Liu, Y. Zhang, and H. Lu, “Resolving adjacent nanophosphors of different concentrations by excitation-based cone-beam X-ray luminescence tomography,” Biomed. Opt. Express 8(9), 3952–3965 (2017).
[Crossref] [PubMed]

Liu, W.

T. Liu, J. Rong, P. Gao, W. Zhang, W. Liu, Y. Zhang, and H. Lu, “Cone-beam x-ray luminescence computed tomography based on x-ray absorption dosage,” J. Biomed. Opt. 23(2), 1–11 (2018).
[PubMed]

P. Gao, H. Pu, J. Rong, W. Zhang, T. Liu, W. Liu, Y. Zhang, and H. Lu, “Resolving adjacent nanophosphors of different concentrations by excitation-based cone-beam X-ray luminescence tomography,” Biomed. Opt. Express 8(9), 3952–3965 (2017).
[Crossref] [PubMed]

Liu, X.

X. Liu, H. Wang, M. Xu, S. Nie, and H. Lu, “A wavelet-based single-view reconstruction approach for cone beam x-ray luminescence tomography imaging,” Biomed. Opt. Express 5(11), 3848–3858 (2014).
[Crossref] [PubMed]

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]

X. Liu, Q. Liao, and H. Wang, “In vivo x-ray luminescence tomographic imaging with single-view data,” Opt. Lett. 38(22), 4530–4533 (2013).
[Crossref] [PubMed]

X. Liu, F. Liu, Y. Zhang, and J. Bai, “Unmixing dynamic fluorescence diffuse optical tomography images with independent component analysis,” IEEE Trans. Med. Imaging 30(9), 1591–1604 (2011).
[Crossref] [PubMed]

Liu, Y.

Lu, H.

Lun, M.

Lun, M. C.

M. C. Lun, W. Zhang, and C. Li, “Sensitivity study of x-ray luminescence computed tomography,” Appl. Opt. 56(11), 3010–3019 (2017).
[Crossref] [PubMed]

W. Zhang, M. C. Lun, A. A.-T. Nguyen, and C. Li, “X-ray luminescence computed tomography using a focused x-ray beam,” J. Biomed. Opt. 22(11), 1–11 (2017).
[Crossref] [PubMed]

Luo, J.

G. Zhang, S. Tzoumas, K. Cheng, F. Liu, J. Liu, J. Luo, J. Bai, and L. Xing, “Generalized Adaptive Gaussian Markov Random Field for X-ray Luminescence Computed Tomography,” IEEE Trans. Biomed. Eng. 65, 2130–2133 (2017).
[PubMed]

G. Zhang, F. Liu, J. Liu, J. Luo, Y. Xie, J. Bai, and L. Xing, “Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method,” IEEE Trans. Med. Imaging 36(1), 225–235 (2017).
[Crossref] [PubMed]

H. Pu, G. Zhang, W. He, F. Liu, H. Guang, Y. Zhang, J. Bai, and J. Luo, “Resolving fluorophores by unmixing multispectral fluorescence tomography with independent component analysis,” Phys. Med. Biol. 59(17), 5025–5042 (2014).
[Crossref] [PubMed]

J. Shi, F. Liu, G. Zhang, J. Luo, and J. Bai, “Enhanced spatial resolution in fluorescence molecular tomography using restarted L1-regularized nonlinear conjugate gradient algorithm,” J. Biomed. Opt. 19(4), 046018 (2014).
[Crossref] [PubMed]

X. Cao, B. Zhang, X. Wang, F. Liu, K. Liu, J. Luo, and J. Bai, “An adaptive Tikhonov regularization method for fluorescence molecular tomography,” Med. Biol. Eng. Comput. 51(8), 849–858 (2013).
[Crossref] [PubMed]

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion,” J. Opt. Soc. Am. A 30(3), 437–447 (2013).
[Crossref] [PubMed]

Martínez-Dávalos, A.

C. Li, A. Martínez-Dávalos, and S. R. Cherry, “Numerical simulation of x-ray luminescence optical tomography for small-animal imaging,” J. Biomed. Opt. 19(4), 046002 (2014).
[Crossref] [PubMed]

McCray, P.

McLennan, G.

Miller, E. L.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18(6), 57–75 (2001).
[Crossref]

Nguyen, A. A.-T.

W. Zhang, M. C. Lun, A. A.-T. Nguyen, and C. Li, “X-ray luminescence computed tomography using a focused x-ray beam,” J. Biomed. Opt. 22(11), 1–11 (2017).
[Crossref] [PubMed]

Nie, S.

Pan, T.

Z. Tian, X. Jia, K. Yuan, T. Pan, and S. B. Jiang, “Low-dose CT reconstruction via edge-preserving total variation regularization,” Phys. Med. Biol. 56(18), 5949–5967 (2011).
[Crossref] [PubMed]

Papadopoulos, I. N.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

Pratx, G.

C. M. Carpenter, G. Pratx, C. Sun, and L. Xing, “Limited-angle x-ray luminescence tomography: methodology and feasibility study,” Phys. Med. Biol. 56(12), 3487–3502 (2011).
[Crossref] [PubMed]

C. M. Carpenter, C. Sun, G. Pratx, R. Rao, and L. Xing, “Hybrid x-ray/optical luminescence imaging: characterization of experimental conditions,” Med. Phys. 37(8), 4011–4018 (2010).
[Crossref] [PubMed]

G. Pratx, C. M. Carpenter, C. Sun, and L. Xing, “X-ray luminescence computed tomography via selective excitation: a feasibility study,” IEEE Trans. Med. Imaging 29(12), 1992–1999 (2010).
[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]

Psaltis, D.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

Pu, H.

P. Gao, H. Pu, J. Rong, W. Zhang, T. Liu, W. Liu, Y. Zhang, and H. Lu, “Resolving adjacent nanophosphors of different concentrations by excitation-based cone-beam X-ray luminescence tomography,” Biomed. Opt. Express 8(9), 3952–3965 (2017).
[Crossref] [PubMed]

H. Pu, G. Zhang, W. He, F. Liu, H. Guang, Y. Zhang, J. Bai, and J. Luo, “Resolving fluorophores by unmixing multispectral fluorescence tomography with independent component analysis,” Phys. Med. Biol. 59(17), 5025–5042 (2014).
[Crossref] [PubMed]

Qian, X.

Rao, R.

C. M. Carpenter, C. Sun, G. Pratx, R. Rao, and L. Xing, “Hybrid x-ray/optical luminescence imaging: characterization of experimental conditions,” Med. Phys. 37(8), 4011–4018 (2010).
[Crossref] [PubMed]

Rao, R. P.

Rong, J.

T. Liu, J. Rong, P. Gao, W. Zhang, W. Liu, Y. Zhang, and H. Lu, “Cone-beam x-ray luminescence computed tomography based on x-ray absorption dosage,” J. Biomed. Opt. 23(2), 1–11 (2018).
[PubMed]

P. Gao, H. Pu, J. Rong, W. Zhang, T. Liu, W. Liu, Y. Zhang, and H. Lu, “Resolving adjacent nanophosphors of different concentrations by excitation-based cone-beam X-ray luminescence tomography,” Biomed. Opt. Express 8(9), 3952–3965 (2017).
[Crossref] [PubMed]

Shen, H.

Shi, J.

J. Shi, F. Liu, G. Zhang, J. Luo, and J. Bai, “Enhanced spatial resolution in fluorescence molecular tomography using restarted L1-regularized nonlinear conjugate gradient algorithm,” J. Biomed. Opt. 19(4), 046018 (2014).
[Crossref] [PubMed]

J. Shi, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Greedy reconstruction algorithm for fluorescence molecular tomography by means of truncated singular value decomposition conversion,” J. Opt. Soc. Am. A 30(3), 437–447 (2013).
[Crossref] [PubMed]

Shoreh, M. H.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

Sinn, P.

Sun, C.

C. M. Carpenter, G. Pratx, C. Sun, and L. Xing, “Limited-angle x-ray luminescence tomography: methodology and feasibility study,” Phys. Med. Biol. 56(12), 3487–3502 (2011).
[Crossref] [PubMed]

C. M. Carpenter, C. Sun, G. Pratx, R. Rao, and L. Xing, “Hybrid x-ray/optical luminescence imaging: characterization of experimental conditions,” Med. Phys. 37(8), 4011–4018 (2010).
[Crossref] [PubMed]

G. Pratx, C. M. Carpenter, C. Sun, and L. Xing, “X-ray luminescence computed tomography via selective excitation: a feasibility study,” IEEE Trans. Med. Imaging 29(12), 1992–1999 (2010).
[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).
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A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
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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).
[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]

Tian, Z.

Z. Tian, X. Jia, K. Yuan, T. Pan, and S. B. Jiang, “Low-dose CT reconstruction via edge-preserving total variation regularization,” Phys. Med. Biol. 56(18), 5949–5967 (2011).
[Crossref] [PubMed]

Tzoumas, S.

G. Zhang, S. Tzoumas, K. Cheng, F. Liu, J. Liu, J. Luo, J. Bai, and L. Xing, “Generalized Adaptive Gaussian Markov Random Field for X-ray Luminescence Computed Tomography,” IEEE Trans. Biomed. Eng. 65, 2130–2133 (2017).
[PubMed]

Unser, M.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
[Crossref]

J. Verhaeghe, D. Van de Ville, I. Khalidov, Y. D’Asseler, I. Lemahieu, and M. Unser, “Dynamic PET reconstruction using wavelet regularization with adapted basis functions,” IEEE Trans. Med. Imaging 27(7), 943–959 (2008).
[Crossref] [PubMed]

Van de Ville, D.

J. Verhaeghe, D. Van de Ville, I. Khalidov, Y. D’Asseler, I. Lemahieu, and M. Unser, “Dynamic PET reconstruction using wavelet regularization with adapted basis functions,” IEEE Trans. Med. Imaging 27(7), 943–959 (2008).
[Crossref] [PubMed]

Verhaeghe, J.

J. Verhaeghe, D. Van de Ville, I. Khalidov, Y. D’Asseler, I. Lemahieu, and M. Unser, “Dynamic PET reconstruction using wavelet regularization with adapted basis functions,” IEEE Trans. Med. Imaging 27(7), 943–959 (2008).
[Crossref] [PubMed]

Vonesch, C.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imag. 2(1), 59–70 (2016).
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E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008).
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Wang, H.

Wang, L.

Wang, X.

X. Cao, B. Zhang, X. Wang, F. Liu, K. Liu, J. Luo, and J. Bai, “An adaptive Tikhonov regularization method for fluorescence molecular tomography,” Med. Biol. Eng. Comput. 51(8), 849–858 (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] [PubMed]

X. Cao, B. Zhang, F. Liu, X. Wang, and J. Bai, “Reconstruction for limited-projection fluorescence molecular tomography based on projected restarted conjugate gradient normal residual,” Opt. Lett. 36(23), 4515–4517 (2011).
[Crossref] [PubMed]

Xie, Y.

G. Zhang, F. Liu, J. Liu, J. Luo, Y. Xie, J. Bai, and L. Xing, “Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method,” IEEE Trans. Med. Imaging 36(1), 225–235 (2017).
[Crossref] [PubMed]

Xing, L.

G. Zhang, F. Liu, J. Liu, J. Luo, Y. Xie, J. Bai, and L. Xing, “Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method,” IEEE Trans. Med. Imaging 36(1), 225–235 (2017).
[Crossref] [PubMed]

G. Zhang, S. Tzoumas, K. Cheng, F. Liu, J. Liu, J. Luo, J. Bai, and L. Xing, “Generalized Adaptive Gaussian Markov Random Field for X-ray Luminescence Computed Tomography,” IEEE Trans. Biomed. Eng. 65, 2130–2133 (2017).
[PubMed]

C. M. Carpenter, G. Pratx, C. Sun, and L. Xing, “Limited-angle x-ray luminescence tomography: methodology and feasibility study,” Phys. Med. Biol. 56(12), 3487–3502 (2011).
[Crossref] [PubMed]

G. Pratx, C. M. Carpenter, C. Sun, and L. Xing, “X-ray luminescence computed tomography via selective excitation: a feasibility study,” IEEE Trans. Med. Imaging 29(12), 1992–1999 (2010).
[Crossref] [PubMed]

C. M. Carpenter, C. Sun, G. Pratx, R. Rao, and L. Xing, “Hybrid x-ray/optical luminescence imaging: characterization of experimental conditions,” Med. Phys. 37(8), 4011–4018 (2010).
[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, M.

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] [PubMed]

Yuan, K.

Z. Tian, X. Jia, K. Yuan, T. Pan, and S. B. Jiang, “Low-dose CT reconstruction via edge-preserving total variation regularization,” Phys. Med. Biol. 56(18), 5949–5967 (2011).
[Crossref] [PubMed]

Zabner, J.

Zhang, B.

Zhang, G.

G. Zhang, F. Liu, J. Liu, J. Luo, Y. Xie, J. Bai, and L. Xing, “Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method,” IEEE Trans. Med. Imaging 36(1), 225–235 (2017).
[Crossref] [PubMed]

G. Zhang, S. Tzoumas, K. Cheng, F. Liu, J. Liu, J. Luo, J. Bai, and L. Xing, “Generalized Adaptive Gaussian Markov Random Field for X-ray Luminescence Computed Tomography,” IEEE Trans. Biomed. Eng. 65, 2130–2133 (2017).
[PubMed]

H. Pu, G. Zhang, W. He, F. Liu, H. Guang, Y. Zhang, J. Bai, and J. Luo, “Resolving fluorophores by unmixing multispectral fluorescence tomography with independent component analysis,” Phys. Med. Biol. 59(17), 5025–5042 (2014).
[Crossref] [PubMed]

J. Shi, F. Liu, G. Zhang, J. Luo, and J. Bai, “Enhanced spatial resolution in fluorescence molecular tomography using restarted L1-regularized nonlinear conjugate gradient algorithm,” J. Biomed. Opt. 19(4), 046018 (2014).
[Crossref] [PubMed]

Zhang, Q.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18(6), 57–75 (2001).
[Crossref]

Zhang, W.

Zhang, X.

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]

Zhang, Y.

T. Liu, J. Rong, P. Gao, W. Zhang, W. Liu, Y. Zhang, and H. Lu, “Cone-beam x-ray luminescence computed tomography based on x-ray absorption dosage,” J. Biomed. Opt. 23(2), 1–11 (2018).
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Figures (10)

Fig. 1
Fig. 1 Setup for simulation studies. (a)-(c) The view of XY plane of the three cases. (d)-(f) The view of XZ plane of the three cases. Two luminescent targets of Y2O3:Eu3+ are placed inside a cylinder phantom. The EED along X axis is 0.50 cm in case 1 (first column), 0.30 cm in case 2 (second column) and 0.10 cm in case 3 (third column).
Fig. 2
Fig. 2 Setup for experiment studies. (a)-(c) Representative X-ray projections of the phantoms with EED = 0.50 cm, 0.23 cm and 0.17 cm, respectively. Regions between the blue and green lines are used for the study. (d)-(f) XCT slice of the phantom, corresponding to the slice indicated by the red line in (a)-(c), respectively. The left and right tubes are named as tube 1 and tube 2. Scale bars in (a) and (d): 1 cm.
Fig. 3
Fig. 3 CB-XLCT reconstruction results of simulation with EED = 0.5 cm. The first to sixth column are results obtained with the ART, Adaptik, FISTA, wavelet regularization, TV regularization and proposed method. The first to third row are the results reconstructed with 24, 4 and 2 projections, respectively. The yellow circles depict the true locations of the two targets and the red circles depict the boundary of the phantom. All images are normalized to the maximal value.
Fig. 4
Fig. 4 CB-XLCT reconstruction results of simulation with EED = 0.30 cm. The first to fourth column are results obtained with the ART, Adaptik, FISTA and proposed method. The first to third rows are the results reconstructed with 24, 4 and 2 projections, respectively. The yellow circles depict the true locations of the two targets and the red circles depict the boundary of the phantom. All images are normalized to the maximal value.
Fig. 5
Fig. 5 CB-XLCT reconstruction results of simulation with EED = 0.10 cm. The first to fourth column are results obtained with the ART, Adaptik, FISTA and proposed method. The first to third rows are the results reconstructed with 24, 4 and 2 projections, respectively. The yellow circles depict the true locations of the two targets and the red circles depict the boundary of the phantom. All images are normalized to the maximal value.
Fig. 6
Fig. 6 3-D rendering of the simulation reconstruction results from 2 projections. Images in the first to the third row are results reconstructed with 2 projections of case 1 to case 3, respectively. The red objects represent the recovered targets.
Fig. 7
Fig. 7 CB-XLCT fusion results of phantom experiments with EED = 0.50 cm. The first to sixth column are results obtained with the ART, Adaptik, FISTA, wavelet regularization, TV regularization and proposed method. The first to third rows are the results reconstructed with 24, 8 and 4 projections, respectively. The slice is indicated by the red line in Fig. 2(a). The red circles depict the boundary of the phantom. All images are normalized to the maximal value.
Fig. 8
Fig. 8 CB-XLCT fusion results of phantom experiments with EED = 0.23 cm. The first to fourth column are results obtained with the ART, Adaptik, FISTA and proposed method. The first to third row are the results reconstructed with 24, 8 and 4 projections, respectively. The slice is the same as that indicated by the red line in Fig. 2(b). The red circles depict the boundary of the phantom. All images are normalized to the maximal value.
Fig. 9
Fig. 9 CB-XLCT fusion results of phantom experiments with EED = 0.17 cm. The first to fourth column are results obtained with the ART, Adaptik, FISTA and proposed method. The first to third row are the results reconstructed with 24, 8 and 4 projections, respectively. The slice is the same as that indicated by the red line in Fig. 2(c). The red circles depict the boundary of the phantom. All images are normalized to the maximal value.
Fig. 10
Fig. 10 3-D rendering of the simulation reconstruction results with 4 projections. Images in the first to the third row are results reconstructed with 4 projections of case 1 to case 3, respectively. The red objects represent the recovered targets.

Tables (6)

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Table 1 Quantitative analysis of simulation case 1 with 2 projections

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Table 2 Quantitative analysis of simulation case 2 with 2 projections

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Table 3 Quantitative analysis of simulation case 3 with 2 projections

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Table 4 Quantitative analysis of phantom experiment case 1 with 4 projections

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Table 5 Quantitative analysis of phantom experiment case 2 with 4 projections

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Table 6 Quantitative analysis of phantom experiment case 3 with 4 projections

Equations (22)

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A ( r ) = A ( r 0 ) exp { r 0 r μ t ( τ ) d τ }
S ( r ) = ε A ( r ) ρ ( r )
{ - [ D ( r ) Φ ( r ) ] + μ a ( r ) Φ ( r ) = S ( r ) ( r Ω ) Φ ( r ) + 2 α D ( r ) [ ν Φ ( r ) ] = 0 ( r Ω )
F ε A ρ = K Φ
{ F i j = Ω Φ ( r ) ψ i ψ j d r A i j = A i j ( r ) K i j = Ω ( D ψ i ψ j + μ a ψ i ψ j ) d r + 1 2 α Ω ψ i ψ j d r
W ρ = Φ meas
Q = W ρ Φ meas 2 + λ p ρ P
W m × n = U m × m Σ m × n V n × n T
Σ m × n = [ d i a g { δ i } 0 0 0 ]
U m × m Σ m × n V n × n T ρ n × 1 = Φ m × 1
U m × r Σ r × r V r × n T ρ n × 1 = Φ m × 1
V r × n T ρ n × 1 = Σ r × r 1 U m × r T Φ m × 1
Q = V r × n T ρ n × 1 Σ r × r 1 U m × r T Φ m × 1 2 + λ p ρ n × 1 P
x k = p L ( y k )
t k + 1 = 1 + 1 + 4 t k 2 2
y k + 1 = x k + ( t k 1 t k + 1 ) ( x k x k 1 )
LE = | | p r p t | | 2
DICE = 2 | R O I r R O I t | | R O I r | + | R O I t |
CNR = | μ R O I μ B K | ( w R O I σ R O I 2 + w B K σ B K 2 ) 1 / 2
SPI = ρ max l ρ valley l ρ max l ρ min l
min ρ V r × n T ρ n × 1 Σ r × r 1 U m × r T Φ m × 1 2 + λ wt ω n × 1 1
min ρ V r × n T ρ n × 1 Σ r × r 1 U m × r T Φ m × 1 2 + λ TV ρ n × 1 TV

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