Abstract

As an emerging hybrid imaging modality, cone-beam X-ray luminescence computed tomography (CB-XLCT) has been proposed based on the development of X-ray excitable nanoparticles. Owing to the high degree of absorption and scattering of light through tissues, the CB-XLCT inverse problem is inherently ill-conditioned. Appropriate priors or regularizations are needed to facilitate reconstruction and to restrict the search space to a specific solution set. Typically, the goal of CB-XLCT reconstruction is to get the distributions of nanophosphors in the imaging object. Considering that the distributions of nanophosphors inside bodies preferentially accumulate in specific areas of interest, the reconstruction of XLCT images is usually sparse with some locally smoothed high-intensity regions. Therefore, a combination of the L1 and total variation regularization is designed to improve the imaging quality of CB-XLCT in this study. The L1 regularization is used for enforcing the sparsity of the reconstructed images and the total variation regularization is used for maintaining the local smoothness of the reconstructed image. The implementation of this method can be divided into two parts. First, the reconstruction image was reconstructed based on the fast iterative shrinkage-thresholding (FISTA) algorithm, then the reconstruction image was minimized by the gradient descent method. Numerical simulations and phantom experiments indicate that compared with the traditional ART, ADAPTIK and FISTA methods, the proposed method demonstrates its advantage in improving spatial resolution and reducing imaging time.

© 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] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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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).
[Crossref] [PubMed]

2017 (3)

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]

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]

R. Baikejiang, Y. Zhao, B. Z. Fite, K. W. Ferrara, and C. Li, “Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method,” J. Biomed. Opt. 22(5), 55001 (2017).
[Crossref] [PubMed]

2016 (1)

2014 (2)

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59(1), R1–R64 (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]

2013 (3)

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. Dong, S. Zhu, C. Qin, V. Kumar, J. V. Stein, S. Oehler, C. Savakis, J. Tian, and J. Ripoll, “Automated recovery of the center of rotation in optical projection tomography in the presence of scattering,” IEEE J. Biomed. Health Inform. 17(1), 198–204 (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 (3)

J. Feng, C. Qin, K. Jia, S. Zhu, X. Yang, and J. Tian, “Bioluminescence tomography imaging in vivo: recent advances,” IEEE J Sel Top Quant 18(4), 1394–1402 (2012).
[Crossref]

Y. Liu, J. Ma, Y. Fan, and Z. Liang, “Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction,” Phys. Med. Biol. 57(23), 7923–7956 (2012).
[Crossref] [PubMed]

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57(6), 1459–1476 (2012).
[Crossref] [PubMed]

2011 (3)

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]

M. Defrise, C. Vanhove, and X. Liu, “An algorithm for total variation regularization in high-dimensional linear problems,” Inverse Probl. 27(6), 065002 (2011).
[Crossref]

2010 (3)

H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization,” Opt. Express 18(3), 1854–1871 (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]

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]

2009 (2)

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]

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging 2009, 960573 (2009).
[Crossref] [PubMed]

2008 (2)

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

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]

2007 (1)

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

2006 (3)

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

E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. XRay Sci. Technol. 14, 119–139 (2006).

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, “A multilevel adaptive finite element algorithm for bioluminescence tomography,” Opt. Express 14(18), 8211–8223 (2006).
[Crossref] [PubMed]

2004 (1)

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
[Crossref]

1995 (2)

B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput. 24(2), 227–234 (1995).
[Crossref]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22(11 Pt 1), 1779–1792 (1995).
[Crossref] [PubMed]

1992 (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
[Crossref]

1989 (1)

T. Hebert and R. Leahy, “A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Med. Imaging 8(2), 194–202 (1989).
[Crossref] [PubMed]

Ahn, S.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57(6), 1459–1476 (2012).
[Crossref] [PubMed]

Arridge, S. R.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22(11 Pt 1), 1779–1792 (1995).
[Crossref] [PubMed]

Bai, 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]

Baikejiang, R.

R. Baikejiang, Y. Zhao, B. Z. Fite, K. W. Ferrara, and C. Li, “Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method,” J. Biomed. Opt. 22(5), 55001 (2017).
[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]

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]

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]

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]

Chen, D.

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]

Cherry, S. R.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57(6), 1459–1476 (2012).
[Crossref] [PubMed]

Cong, W.

Darne, C.

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59(1), R1–R64 (2014).
[Crossref] [PubMed]

Daubechies, I.

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
[Crossref]

De Mol, C.

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
[Crossref]

Defrise, M.

M. Defrise, C. Vanhove, and X. Liu, “An algorithm for total variation regularization in high-dimensional linear problems,” Inverse Probl. 27(6), 065002 (2011).
[Crossref]

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
[Crossref]

Delpy, D. T.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22(11 Pt 1), 1779–1792 (1995).
[Crossref] [PubMed]

Dong, D.

D. Dong, S. Zhu, C. Qin, V. Kumar, J. V. Stein, S. Oehler, C. Savakis, J. Tian, and J. Ripoll, “Automated recovery of the center of rotation in optical projection tomography in the presence of scattering,” IEEE J. Biomed. Health Inform. 17(1), 198–204 (2013).
[Crossref] [PubMed]

Donoho, D. L.

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

Dutta, J.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57(6), 1459–1476 (2012).
[Crossref] [PubMed]

Fan, Y.

Y. Liu, J. Ma, Y. Fan, and Z. Liang, “Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction,” Phys. Med. Biol. 57(23), 7923–7956 (2012).
[Crossref] [PubMed]

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
[Crossref]

Feng, J.

J. Feng, C. Qin, K. Jia, S. Zhu, X. Yang, and J. Tian, “Bioluminescence tomography imaging in vivo: recent advances,” IEEE J Sel Top Quant 18(4), 1394–1402 (2012).
[Crossref]

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging 2009, 960573 (2009).
[Crossref] [PubMed]

Ferrara, K. W.

R. Baikejiang, Y. Zhao, B. Z. Fite, K. W. Ferrara, and C. Li, “Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method,” J. Biomed. Opt. 22(5), 55001 (2017).
[Crossref] [PubMed]

Figueiredo, M. A.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

Fite, B. Z.

R. Baikejiang, Y. Zhao, B. Z. Fite, K. W. Ferrara, and C. Li, “Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method,” J. Biomed. Opt. 22(5), 55001 (2017).
[Crossref] [PubMed]

Gao, H.

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).
[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]

Hebert, T.

T. Hebert and R. Leahy, “A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Med. Imaging 8(2), 194–202 (1989).
[Crossref] [PubMed]

Hiraoka, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22(11 Pt 1), 1779–1792 (1995).
[Crossref] [PubMed]

Jia, K.

J. Feng, C. Qin, K. Jia, S. Zhu, X. Yang, and J. Tian, “Bioluminescence tomography imaging in vivo: recent advances,” IEEE J Sel Top Quant 18(4), 1394–1402 (2012).
[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, 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]

Kao, C.-M.

E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. XRay Sci. Technol. 14, 119–139 (2006).

Kumar, V.

D. Dong, S. Zhu, C. Qin, V. Kumar, J. V. Stein, S. Oehler, C. Savakis, J. Tian, and J. Ripoll, “Automated recovery of the center of rotation in optical projection tomography in the presence of scattering,” IEEE J. Biomed. Health Inform. 17(1), 198–204 (2013).
[Crossref] [PubMed]

Leahy, R.

T. Hebert and R. Leahy, “A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Med. Imaging 8(2), 194–202 (1989).
[Crossref] [PubMed]

Leahy, R. M.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57(6), 1459–1476 (2012).
[Crossref] [PubMed]

Li, C.

R. Baikejiang, Y. Zhao, B. Z. Fite, K. W. Ferrara, and C. Li, “Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method,” J. Biomed. Opt. 22(5), 55001 (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]

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57(6), 1459–1476 (2012).
[Crossref] [PubMed]

Li, H.

Liang, J.

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]

Liang, Z.

Y. Liu, J. Ma, Y. Fan, and Z. Liang, “Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction,” Phys. Med. Biol. 57(23), 7923–7956 (2012).
[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, 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]

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]

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).
[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]

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).
[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]

Liu, X.

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]

M. Defrise, C. Vanhove, and X. Liu, “An algorithm for total variation regularization in high-dimensional linear problems,” Inverse Probl. 27(6), 065002 (2011).
[Crossref]

Liu, Y.

Y. Liu, J. Ma, Y. Fan, and Z. Liang, “Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction,” Phys. Med. Biol. 57(23), 7923–7956 (2012).
[Crossref] [PubMed]

Lu, H.

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).
[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]

Lu, Y.

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59(1), R1–R64 (2014).
[Crossref] [PubMed]

Lun, M.

Luo, 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]

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, “A multilevel adaptive finite element algorithm for bioluminescence tomography,” Opt. Express 14(18), 8211–8223 (2006).
[Crossref] [PubMed]

Lv, Y.

Ma, J.

Y. Liu, J. Ma, Y. Fan, and Z. Liang, “Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction,” Phys. Med. Biol. 57(23), 7923–7956 (2012).
[Crossref] [PubMed]

Natarajan, B. K.

B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput. 24(2), 227–234 (1995).
[Crossref]

Nowak, R. D.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

Oehler, S.

D. Dong, S. Zhu, C. Qin, V. Kumar, J. V. Stein, S. Oehler, C. Savakis, J. Tian, and J. Ripoll, “Automated recovery of the center of rotation in optical projection tomography in the presence of scattering,” IEEE J. Biomed. Health Inform. 17(1), 198–204 (2013).
[Crossref] [PubMed]

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
[Crossref]

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]

Pan, X.

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, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. XRay Sci. Technol. 14, 119–139 (2006).

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]

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]

Pu, H.

Qin, C.

D. Dong, S. Zhu, C. Qin, V. Kumar, J. V. Stein, S. Oehler, C. Savakis, J. Tian, and J. Ripoll, “Automated recovery of the center of rotation in optical projection tomography in the presence of scattering,” IEEE J. Biomed. Health Inform. 17(1), 198–204 (2013).
[Crossref] [PubMed]

J. Feng, C. Qin, K. Jia, S. Zhu, X. Yang, and J. Tian, “Bioluminescence tomography imaging in vivo: recent advances,” IEEE J Sel Top Quant 18(4), 1394–1402 (2012).
[Crossref]

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging 2009, 960573 (2009).
[Crossref] [PubMed]

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]

Ripoll, J.

D. Dong, S. Zhu, C. Qin, V. Kumar, J. V. Stein, S. Oehler, C. Savakis, J. Tian, and J. Ripoll, “Automated recovery of the center of rotation in optical projection tomography in the presence of scattering,” IEEE J. Biomed. Health Inform. 17(1), 198–204 (2013).
[Crossref] [PubMed]

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).
[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]

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
[Crossref]

Savakis, C.

D. Dong, S. Zhu, C. Qin, V. Kumar, J. V. Stein, S. Oehler, C. Savakis, J. Tian, and J. Ripoll, “Automated recovery of the center of rotation in optical projection tomography in the presence of scattering,” IEEE J. Biomed. Health Inform. 17(1), 198–204 (2013).
[Crossref] [PubMed]

Schweiger, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22(11 Pt 1), 1779–1792 (1995).
[Crossref] [PubMed]

Sevick-Muraca, E. M.

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59(1), R1–R64 (2014).
[Crossref] [PubMed]

Sidky, E. Y.

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, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. XRay Sci. Technol. 14, 119–139 (2006).

Stein, J. V.

D. Dong, S. Zhu, C. Qin, V. Kumar, J. V. Stein, S. Oehler, C. Savakis, J. Tian, and J. Ripoll, “Automated recovery of the center of rotation in optical projection tomography in the presence of scattering,” IEEE J. Biomed. Health Inform. 17(1), 198–204 (2013).
[Crossref] [PubMed]

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]

Teboulle, M.

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]

Tian, J.

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. Dong, S. Zhu, C. Qin, V. Kumar, J. V. Stein, S. Oehler, C. Savakis, J. Tian, and J. Ripoll, “Automated recovery of the center of rotation in optical projection tomography in the presence of scattering,” IEEE J. Biomed. Health Inform. 17(1), 198–204 (2013).
[Crossref] [PubMed]

J. Feng, C. Qin, K. Jia, S. Zhu, X. Yang, and J. Tian, “Bioluminescence tomography imaging in vivo: recent advances,” IEEE J Sel Top Quant 18(4), 1394–1402 (2012).
[Crossref]

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging 2009, 960573 (2009).
[Crossref] [PubMed]

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, “A multilevel adaptive finite element algorithm for bioluminescence tomography,” Opt. Express 14(18), 8211–8223 (2006).
[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]

Vanhove, C.

M. Defrise, C. Vanhove, and X. Liu, “An algorithm for total variation regularization in high-dimensional linear problems,” Inverse Probl. 27(6), 065002 (2011).
[Crossref]

Wakin, M. B.

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

Wang, G.

Wang, H.

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]

Wright, S. J.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

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]

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]

Yan, G.

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging 2009, 960573 (2009).
[Crossref] [PubMed]

Yang, W.

Yang, X.

J. Feng, C. Qin, K. Jia, S. Zhu, X. Yang, and J. Tian, “Bioluminescence tomography imaging in vivo: recent advances,” IEEE J Sel Top Quant 18(4), 1394–1402 (2012).
[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]

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]

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]

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).
[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]

Zhao, H.

Zhao, Y.

R. Baikejiang, Y. Zhao, B. Z. Fite, K. W. Ferrara, and C. Li, “Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method,” J. Biomed. Opt. 22(5), 55001 (2017).
[Crossref] [PubMed]

Zhu, D.

Zhu, S.

D. Dong, S. Zhu, C. Qin, V. Kumar, J. V. Stein, S. Oehler, C. Savakis, J. Tian, and J. Ripoll, “Automated recovery of the center of rotation in optical projection tomography in the presence of scattering,” IEEE J. Biomed. Health Inform. 17(1), 198–204 (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. Feng, C. Qin, K. Jia, S. Zhu, X. Yang, and J. Tian, “Bioluminescence tomography imaging in vivo: recent advances,” IEEE J Sel Top Quant 18(4), 1394–1402 (2012).
[Crossref]

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging 2009, 960573 (2009).
[Crossref] [PubMed]

Biomed. Opt. Express (2)

Commun. Pure Appl. Math. (1)

I. Daubechies, M. Defrise, and C. De Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
[Crossref]

IEEE J Sel Top Quant (1)

J. Feng, C. Qin, K. Jia, S. Zhu, X. Yang, and J. Tian, “Bioluminescence tomography imaging in vivo: recent advances,” IEEE J Sel Top Quant 18(4), 1394–1402 (2012).
[Crossref]

IEEE J. Biomed. Health Inform. (1)

D. Dong, S. Zhu, C. Qin, V. Kumar, J. V. Stein, S. Oehler, C. Savakis, J. Tian, and J. Ripoll, “Automated recovery of the center of rotation in optical projection tomography in the presence of scattering,” IEEE J. Biomed. Health Inform. 17(1), 198–204 (2013).
[Crossref] [PubMed]

IEEE J. Sel. Top. Signal Process. (1)

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

IEEE Signal Process. Mag. (1)

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

IEEE Trans. Biomed. Eng. (1)

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]

IEEE Trans. Inf. Theory (1)

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

IEEE Trans. Med. Imaging (3)

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. 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]

T. Hebert and R. Leahy, “A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors,” IEEE Trans. Med. Imaging 8(2), 194–202 (1989).
[Crossref] [PubMed]

Int. J. Biomed. Imaging (1)

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging 2009, 960573 (2009).
[Crossref] [PubMed]

Inverse Probl. (1)

M. Defrise, C. Vanhove, and X. Liu, “An algorithm for total variation regularization in high-dimensional linear problems,” Inverse Probl. 27(6), 065002 (2011).
[Crossref]

J. Biomed. Opt. (2)

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).
[Crossref] [PubMed]

R. Baikejiang, Y. Zhao, B. Z. Fite, K. W. Ferrara, and C. Li, “Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method,” J. Biomed. Opt. 22(5), 55001 (2017).
[Crossref] [PubMed]

J. XRay Sci. Technol. (1)

E. Y. Sidky, C.-M. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. XRay Sci. Technol. 14, 119–139 (2006).

Med. Phys. (3)

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22(11 Pt 1), 1779–1792 (1995).
[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]

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]

Opt. Express (2)

Opt. Lett. (1)

Phys. Med. Biol. (6)

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59(1), R1–R64 (2014).
[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]

Y. Liu, J. Ma, Y. Fan, and Z. Liang, “Adaptive-weighted total variation minimization for sparse data toward low-dose x-ray computed tomography image reconstruction,” Phys. Med. Biol. 57(23), 7923–7956 (2012).
[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]

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57(6), 1459–1476 (2012).
[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]

Physica D (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60(1-4), 259–268 (1992).
[Crossref]

SIAM J. Comput. (1)

B. K. Natarajan, “Sparse approximate solutions to linear systems,” SIAM J. Comput. 24(2), 227–234 (1995).
[Crossref]

SIAM J. Imaging Sci. (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]

Other (3)

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[Crossref]

Y. Zhu, A. K. Jha, J. K. Dreyer, H. N. Le, J. U. Kang, P. E. Roland, D. F. Wong, and A. Rahmim, “A three-step reconstruction method for fluorescence molecular tomography based on compressive sensing,” SPIE Bios. Proc SPIE Int Soc Opt Eng, 1005911 (2017).

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Figures (8)

Fig. 1
Fig. 1 The flowchart of the proposed method.

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Fig. 2
Fig. 2 The cylinder phantom used in simulation studies. (a), (b), (c) A 3D view of the phantom, (d), (e), (f) the overhead view of the phantom. edge-to-edge distance between the two targets: (a),(d):3mm, (b),(e):2mm, (c),(f):1mm.

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Fig. 3
Fig. 3 The schematic diagram of the CB-XLCT system.

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Fig. 4
Fig. 4 The physical phantom used in imaging experiments. (a), (c) X-ray projections of the phantom corresponding to the two tubes with edge-to-edge distances of 5.5mm, 1.8mm. The region between two red lines is used for reconstruction in this study. (b), (d) CT slices of the phantom, corresponding to the transverse slices indicated by the blue lines in (a), (c).

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Fig. 5
Fig. 5 Tomographic images of the targets positioned at different distance were reconstructed from 24 projections. 1st row (from left to right): the true locations of the target edge to edge distances of 3mm, 2mm and 1mm respectively. 2nd row (from left to right): reconstructions with the ART algorithm for the two targets with edge to edge distances of 3 mm, 2mm and 1mm respectively. 3rd row (from left to right): reconstructions with the ADAPTIK algorithm for the two targets with edge to edge distances of 3 mm, 2mm and 1mm respectively. 4th row (from left to right): reconstructions with the FISTA algorithm for the two targets with edge to edge distances of 3 mm, 2mm and 1mm respectively 0.5th row (from left to right): reconstructions with the proposed L1-TV algorithm for the two targets with edge to edge distances of 3 mm, 2mm and 1mm respectively.

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Fig. 6
Fig. 6 Tomographic images of the targets positioned at different distance were reconstructed from 4 projections. 1st row (from left to right): the true locations of the target edge to edge distances of 3mm, 2mm and 1mm respectively. 2nd row (from left to right): reconstructions with the ART algorithm for the two targets with edge to edge distances of 3 mm, 2mm and 1mm respectively. 3rd row (from left to right): reconstructions with the ADAPTIK algorithm for the two targets with edge to edge distances of 3 mm, 2mm and 1mm respectively. 4th row (from left to right): reconstructions with the FISTA algorithm for the two targets with edge to edge distances of 3 mm, 2mm and 1mm respectively 0.5th row (from left to right): reconstructions with the proposed L1-TV algorithm for the two targets with edge to edge distances of 3 mm, 2mm and 1mm respectively.

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Fig. 7
Fig. 7 Tomographic images of the targets positioned at different distance were reconstructed from 24 projections for phantom experiments. 1st row (from left to right): the true locations of the target edge to edge distances of 5.5mm, 1.8mm respectively. 2nd row (from left to right): reconstructions with the ART algorithm and fusion of XLCT and XCT images for the two targets with edge to edge distances of 5.5mm, 1.8mm respectively. 3nd row (from left to right): reconstructions with the ADAPTIK algorithm and fusion of XLCT and XCT images for the two targets with edge to edge distances of 5.5mm, 1.8mm respectively. 4nd row (from left to right): reconstructions with the FISTA algorithm and fusion of XLCT and XCT images for the two targets with edge to edge distances of 5.5mm, 1.8mm respectively. 5nd row (from left to right): reconstructions with the proposed L1-TV algorithm and fusion of XLCT and XCT images for the two targets with edge to edge distances of 5.5mm, 1.8mm respectively.

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Fig. 8
Fig. 8 Tomographic images of the targets positioned at different distance were reconstructed from 4 projections for phantom experiments. 1st row (from left to right): the true locations of the target edge to edge distances of 5.5mm, 1.8mm respectively. 2nd row (from left to right): reconstructions with the ART algorithm and fusion of XLCT and XCT images for the two targets with edge to edge distances of 5.5mm, 1.8mm respectively. 3nd row (from left to right): reconstructions with the ADAPTIK algorithm and fusion of XLCT and XCT images for the two targets with edge to edge distances of 5.5mm, 1.8mm respectively. 4nd row (from left to right): reconstructions with the FISTA algorithm and fusion of XLCT and XCT images for the two targets with edge to edge distances of 5.5mm, 1.8mm respectively. 5nd row (from left to right): reconstructions with the proposed L1-TV algorithm and fusion of XLCT and XCT images for the two targets with edge to edge distances of 5.5mm, 1.8mm respectively.

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Tables (4)

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Table 1 Algorithm 1. FISTA-L1

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Table 1 Quantitative evaluation of numerical simulations with 4 projections

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Table 2 Quantitative evaluation of phantom experiments with 4 projections

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Table 3 The data acquisition and reconstruction time of phantom experiments with different projections

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Equations (17)

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S ( r ) = Γ X ( r ) n ( r )
− ∇ ⋅ [ D ( r ) ∇ Φ ( r ) ] + μ a ( r ) Φ ( r ) = S ( r ) ( r ∈ Ω )
Φ ( r ) + 2 κ D ( r ) [ ν ∇ Φ ( r ) ] = 0 ( r ∈ ∂ Ω )
A Φ = Γ F N
a i j = ∫ Ω [ D ( r ) ∇ ψ i ( r ) ∇ ψ j ( r ) + μ a ( r ) ψ i ( r ) ψ j ( r ) ] d r + 1 2 κ ∫ ∂ Ω ψ i ( r ) ψ j ( r ) d r
f i j = ∫ Ω X ( r ) ψ i ( r ) ψ j ( r ) d r ,
Φ = M N
Φ m e a s = W N
b = Φ m e a s + ς = W x + ς
x = arg min x ≥ 0 1 2 ‖ W x − b ‖ 2 2 + λ L 1 ‖ x ‖ 1 + λ T V | x | T V
min { F ( x ) ≡ f ( x ) + g ( x ) : x ∈ R n }
min x ( ‖ x ‖ T V ) s . t . 1 2 ‖ W x − b ‖ 2 2 + λ L 1 ‖ x ‖ 1 ≤ ε x ≥ 0
‖ x ‖ T V = ∑ i , j ( x i , j − x i , j − 1 ) 2 + ( x i , j − x i − 1 , j ) 2
∂ ‖ x ‖ T V ∂ x i , j ≈ 2 ( x i , j − x i , j − 1 ) + 2 ( x i , j − x i − 1 , j ) δ + ( x i , j − x i , j − 1 ) 2 + ( x i , j − x i − 1 , j ) 2 − 2 ( x i + 1 , j − x i , j ) δ + ( x i + 1 , j − x i , j ) 2 + ( x i + 1 , j − x i + 1 , j − 1 ) 2 − 2 ( x i , j + 1 − x i , j ) δ + ( x i , j + 1 − x i , j ) 2 + ( x i , j + 1 − x i − 1 , j + 1 ) 2
L E = ‖ L r - L t ‖ 2
D I C E = 2 | R O I r ∩ R O I t | | R O I r | + | R O I t |
C N R = | μ R O I − μ B C K | ( w R O I σ R O I 2 + w B C K σ B C K 2 ) 1 / 2

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