Abstract

Bioluminescence tomography (BLT) can three-dimensionally and quantitatively resolve the molecular processes in small animals in vivo. In this paper, we propose a BLT reconstruction algorithm based on duality and variable splitting. By using duality and variable splitting to obtain a new equivalent constrained optimization problem and updating the primal variable as the Lagrangian multiplier in the dual augmented Lagrangian problem, the proposed method can obtain fast and stable source reconstruction even without the permissible source region and multispectral measurements. Numerical simulations on a mouse atlas and in vivo mouse experiments were conducted to validate the effectiveness and potential of the method.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (4)

D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” Proc. SPIE 7965, 79651C (2011).
[CrossRef]

S. Setzer, “Operator splittings, Bregman methods and frame shrinkage in image processing,” Int. J. Comput. Vis. 92, 265–280 (2011).
[CrossRef]

X. Ma, J. Tian, X. Yang, C. Qin, S. Zhu, and Z. Xue, “Research on liver tumor proliferation and angiogenesis based on multi-modality molecular imaging,” Acta Biophys. Sin. 27, 355–364 (2011).
[CrossRef]

X. Ma, J. Tian, C. Qin, X. Yang, B. Zhang, Z. Xue, X. Zhang, D. Han, D. Dong, and X. Liu, “Early detection of liver cancer based on bioluminescence tomography,” Appl. Opt. 50, 1389–1395 (2011).
[CrossRef]

2010 (12)

H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation. Part 1: L1 regularization,” Opt. Express 18, 1854–1871 (2010).
[CrossRef]

K. Liu, J. Tian, X. Yang, Y. Lu, C. Qin, S. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18, 3732–3745 (2010).
[CrossRef]

K. Liu, J. Tian, Y. Lu, C. Qin, X. Yang, S. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18, 3732–3745 (2010).
[CrossRef]

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, 6477–6491 (2010).
[CrossRef]

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[CrossRef]

M. Freiberger, C. Clason, and H. Scharfetter, “Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach,” Appl. Opt. 49, 3741–3747 (2010).
[CrossRef]

H. Gao, H. Zhao, W. Cong, and G. Wang, “Bioluminescence tomography with Gaussian prior,” Biomed. Opt. Express 1, 1259–1277 (2010).
[CrossRef]

X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18, 24825–24841 (2010).
[CrossRef]

C. Wu and X. Tai, “Augmented lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models,” SIAM J. Imaging Sci. 3, 300–339 (2010).
[CrossRef]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “Multiplicative noise removal using variable splitting and constrained optimization,” IEEE Trans. Image Process. 19, 1720–1730 (2010).
[CrossRef]

A. Cong, W. Cong, Y. Lu, P. Santago, A. Chatziioannou, and G. Wang, “Differential evolution approach for regularized bioluminescence tomography,” IEEE Trans. Biomed. Eng. 57, 2229–2238 (2010).
[CrossRef]

X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010).
[CrossRef]

2009 (5)

2008 (5)

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, 3921–3942 (2008).
[CrossRef]

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
[CrossRef]

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef]

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).
[CrossRef]

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, 15640–15654(2008).
[CrossRef]

2007 (4)

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12, 024007 (2007).
[CrossRef]

A. M. Loening, A. M. Wu, and S. S. Gambhir, “Red-shifted Renilla reniformis luciferase variants for imaging in living subjects,” Nat. Med. 4, 641–643 (2007).
[CrossRef]

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale L1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[CrossRef]

Y. Lu, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[CrossRef]

2006 (3)

2005 (3)

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50, 4225–4241 (2005).
[CrossRef]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the revolution of wholebody photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef]

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, 323–345 (2005).
[CrossRef]

2004 (1)

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31, 2289–2299 (2004).
[CrossRef]

1995 (1)

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, 1779–1792 (1995).
[CrossRef]

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, 3921–3942 (2008).
[CrossRef]

Alexandrakis, G.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study,” Phys. Med. Biol. 50, 4225–4241 (2005).
[CrossRef]

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, 1779–1792 (1995).
[CrossRef]

Bai, J.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef]

Bao, S.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef]

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “Multiplicative noise removal using variable splitting and constrained optimization,” IEEE Trans. Image Process. 19, 1720–1730 (2010).
[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, 3921–3942 (2008).
[CrossRef]

Boyd, S.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale L1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[CrossRef]

Chan, T. F.

Chatziioannou, A.

A. Cong, W. Cong, Y. Lu, P. Santago, A. Chatziioannou, and G. Wang, “Differential evolution approach for regularized bioluminescence tomography,” IEEE Trans. Biomed. Eng. 57, 2229–2238 (2010).
[CrossRef]

Chatziioannou, A. F.

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, 3921–3942 (2008).
[CrossRef]

Chen, D.

Clason, C.

Cong, A.

A. Cong, W. Cong, Y. Lu, P. Santago, A. Chatziioannou, and G. Wang, “Differential evolution approach for regularized bioluminescence tomography,” IEEE Trans. Biomed. Eng. 57, 2229–2238 (2010).
[CrossRef]

Cong, W.

A. Cong, W. Cong, Y. Lu, P. Santago, A. Chatziioannou, and G. Wang, “Differential evolution approach for regularized bioluminescence tomography,” IEEE Trans. Biomed. Eng. 57, 2229–2238 (2010).
[CrossRef]

H. Gao, H. Zhao, W. Cong, and G. Wang, “Bioluminescence tomography with Gaussian prior,” Biomed. Opt. Express 1, 1259–1277 (2010).
[CrossRef]

Y. Lu, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[CrossRef]

Y. Lu, 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, 8211–8223 (2006).
[CrossRef]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. O. Shen, P. Sinn, E. Hoffman, G. McLennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).
[CrossRef]

Coquoz, O.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12, 024007 (2007).
[CrossRef]

Darvas, F.

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, 3921–3942 (2008).
[CrossRef]

Davis, S. C.

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).
[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).
[CrossRef]

Dehghani, H.

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).
[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).
[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, 1779–1792 (1995).
[CrossRef]

Dinkelborg, L. M.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
[CrossRef]

Dong, D.

Douraghy, A.

Durairaj, K.

Feng, J.

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “Multiplicative noise removal using variable splitting and constrained optimization,” IEEE Trans. Image Process. 19, 1720–1730 (2010).
[CrossRef]

Freiberger, M.

Gambhir, S. S.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
[CrossRef]

A. M. Loening, A. M. Wu, and S. S. Gambhir, “Red-shifted Renilla reniformis luciferase variants for imaging in living subjects,” Nat. Med. 4, 641–643 (2007).
[CrossRef]

Gao, H.

Gorinevsky, D.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale L1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[CrossRef]

Han, D.

He, X.

X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010).
[CrossRef]

X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18, 24825–24841 (2010).
[CrossRef]

Henry, M.

Herschman, H.

Hielscher, A. H.

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, 323–345 (2005).
[CrossRef]

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, 1779–1792 (1995).
[CrossRef]

Hoffman, E.

Hou, Y.

X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010).
[CrossRef]

X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18, 24825–24841 (2010).
[CrossRef]

Huang, H.

X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010).
[CrossRef]

Jia, K.

Jiang, M.

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31, 2289–2299 (2004).
[CrossRef]

Jiang, S.

Kim, S.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale L1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[CrossRef]

Klose, A. D.

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, 323–345 (2005).
[CrossRef]

Koh, K.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale L1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[CrossRef]

Kuo, C.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12, 024007 (2007).
[CrossRef]

Leahy, R. M.

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, 3921–3942 (2008).
[CrossRef]

Li, H.

Li, X.

Li, Y.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
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X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010).
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X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18, 24825–24841 (2010).
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J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
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Liu, F.

Liu, J.

Liu, K.

Liu, X.

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A. M. Loening, A. M. Wu, and S. S. Gambhir, “Red-shifted Renilla reniformis luciferase variants for imaging in living subjects,” Nat. Med. 4, 641–643 (2007).
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Lu, Y.

A. Cong, W. Cong, Y. Lu, P. Santago, A. Chatziioannou, and G. Wang, “Differential evolution approach for regularized bioluminescence tomography,” IEEE Trans. Biomed. Eng. 57, 2229–2238 (2010).
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K. Liu, J. Tian, X. Yang, Y. Lu, C. Qin, S. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18, 3732–3745 (2010).
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K. Liu, J. Tian, Y. Lu, C. Qin, X. Yang, S. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18, 3732–3745 (2010).
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Y. Lu, X. Zhang, A. Douraghy, D. Stout, J. Tian, T. F. Chan, and A. F. Chatziioannou, “Source reconstruction for spectrally-resolved bioluminescence tomography with sparse a priori information,” Opt. Express 17, 8062–8080 (2009).
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Y. Lu, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
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Luo, J.

Lustig, M.

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale L1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
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X. Ma, J. Tian, X. Yang, C. Qin, S. Zhu, and Z. Xue, “Research on liver tumor proliferation and angiogenesis based on multi-modality molecular imaging,” Acta Biophys. Sin. 27, 355–364 (2011).
[CrossRef]

X. Ma, J. Tian, C. Qin, X. Yang, B. Zhang, Z. Xue, X. Zhang, D. Han, D. Dong, and X. Liu, “Early detection of liver cancer based on bioluminescence tomography,” Appl. Opt. 50, 1389–1395 (2011).
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D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” Proc. SPIE 7965, 79651C (2011).
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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, 6477–6491 (2010).
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McLennan, G.

Ntziachristos, V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the revolution of wholebody photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
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Paulsen, K. D.

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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, 6477–6491 (2010).
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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, 15640–15654(2008).
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X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010).
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X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18, 24825–24841 (2010).
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X. Ma, J. Tian, X. Yang, C. Qin, S. Zhu, and Z. Xue, “Research on liver tumor proliferation and angiogenesis based on multi-modality molecular imaging,” Acta Biophys. Sin. 27, 355–364 (2011).
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D. Han, J. Tian, C. Qin, B. Zhang, K. Liu, and X. Ma, “A fast reconstruction method for fluorescence molecular tomography based on improved iterated shrinkage,” Proc. SPIE 7965, 79651C (2011).
[CrossRef]

X. Ma, J. Tian, C. Qin, X. Yang, B. Zhang, Z. Xue, X. Zhang, D. Han, D. Dong, and X. Liu, “Early detection of liver cancer based on bioluminescence tomography,” Appl. Opt. 50, 1389–1395 (2011).
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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, 6477–6491 (2010).
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K. Liu, J. Tian, Y. Lu, C. Qin, X. Yang, S. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18, 3732–3745 (2010).
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X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010).
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X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18, 24825–24841 (2010).
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Y. Lu, X. Zhang, A. Douraghy, D. Stout, J. Tian, T. F. Chan, and A. F. Chatziioannou, “Source reconstruction for spectrally-resolved bioluminescence tomography with sparse a priori information,” Opt. Express 17, 8062–8080 (2009).
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C. Qin, J. Tian, X. Yang, J. Feng, K. Liu, J. Liu, G. Yan, S. Zhu, and M. Xu, “Adaptive improved element free Galerkin method for quasi- or multi-spectral bioluminescence tomography,” Opt. Express 17, 21925–21934 (2009).
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J. Feng, K. Jia, C. Qin, G. Yan, S. Zhu, X. Zhang, J. Liu, and J. Tian, “Three-dimensional bioluminescence tomography based on Bayesian approach,” Opt. Express 17, 16834–16848 (2009).
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J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef]

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, 15640–15654(2008).
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Y. Lu, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
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Y. Lu, 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, 8211–8223 (2006).
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R. Tomioka and M. Sugiyama, “Dual augmented Lagrangian method for efficient sparse reconstruction,” IEEE Signal Process. Lett. 16, 1067–1070 (2009).
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C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12, 024007 (2007).
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Y. Lu, 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, 8211–8223 (2006).
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[CrossRef]

Wang, X.

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the revolution of wholebody photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
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J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
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A. M. Loening, A. M. Wu, and S. S. Gambhir, “Red-shifted Renilla reniformis luciferase variants for imaging in living subjects,” Nat. Med. 4, 641–643 (2007).
[CrossRef]

Wu, C.

C. Wu and X. Tai, “Augmented lagrangian method, dual methods, and split Bregman iteration for ROF, vectorial TV, and high order models,” SIAM J. Imaging Sci. 3, 300–339 (2010).
[CrossRef]

Xu, H.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12, 024007 (2007).
[CrossRef]

Xu, M.

C. Qin, J. Tian, X. Yang, J. Feng, K. Liu, J. Liu, G. Yan, S. Zhu, and M. Xu, “Adaptive improved element free Galerkin method for quasi- or multi-spectral bioluminescence tomography,” Opt. Express 17, 21925–21934 (2009).
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Y. Lu, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[CrossRef]

Xue, Z.

X. Ma, J. Tian, C. Qin, X. Yang, B. Zhang, Z. Xue, X. Zhang, D. Han, D. Dong, and X. Liu, “Early detection of liver cancer based on bioluminescence tomography,” Appl. Opt. 50, 1389–1395 (2011).
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X. Ma, J. Tian, X. Yang, C. Qin, S. Zhu, and Z. Xue, “Research on liver tumor proliferation and angiogenesis based on multi-modality molecular imaging,” Acta Biophys. Sin. 27, 355–364 (2011).
[CrossRef]

Yan, G.

Yan, X.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef]

Yang, W.

Y. Lu, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
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Y. Lu, 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, 8211–8223 (2006).
[CrossRef]

Yang, X.

X. Ma, J. Tian, C. Qin, X. Yang, B. Zhang, Z. Xue, X. Zhang, D. Han, D. Dong, and X. Liu, “Early detection of liver cancer based on bioluminescence tomography,” Appl. Opt. 50, 1389–1395 (2011).
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X. Ma, J. Tian, X. Yang, C. Qin, S. Zhu, and Z. Xue, “Research on liver tumor proliferation and angiogenesis based on multi-modality molecular imaging,” Acta Biophys. Sin. 27, 355–364 (2011).
[CrossRef]

K. Liu, J. Tian, X. Yang, Y. Lu, C. Qin, S. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18, 3732–3745 (2010).
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D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[CrossRef]

K. Liu, J. Tian, Y. Lu, C. Qin, X. Yang, S. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18, 3732–3745 (2010).
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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, 6477–6491 (2010).
[CrossRef]

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, 6477–6491 (2010).
[CrossRef]

C. Qin, J. Tian, X. Yang, J. Feng, K. Liu, J. Liu, G. Yan, S. Zhu, and M. Xu, “Adaptive improved element free Galerkin method for quasi- or multi-spectral bioluminescence tomography,” Opt. Express 17, 21925–21934 (2009).
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J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef]

Yu, J.

Zhang, B.

Zhang, X.

Zhao, H.

Zhong, J.

Zhu, S.

X. Ma, J. Tian, X. Yang, C. Qin, S. Zhu, and Z. Xue, “Research on liver tumor proliferation and angiogenesis based on multi-modality molecular imaging,” Acta Biophys. Sin. 27, 355–364 (2011).
[CrossRef]

K. Liu, J. Tian, X. Yang, Y. Lu, C. Qin, S. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18, 3732–3745 (2010).
[CrossRef]

K. Liu, J. Tian, Y. Lu, C. Qin, X. Yang, S. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18, 3732–3745 (2010).
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D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[CrossRef]

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, 6477–6491 (2010).
[CrossRef]

C. Qin, J. Tian, X. Yang, J. Feng, K. Liu, J. Liu, G. Yan, S. Zhu, and M. Xu, “Adaptive improved element free Galerkin method for quasi- or multi-spectral bioluminescence tomography,” Opt. Express 17, 21925–21934 (2009).
[CrossRef]

J. Feng, K. Jia, C. Qin, G. Yan, S. Zhu, X. Zhang, J. Liu, and J. Tian, “Three-dimensional bioluminescence tomography based on Bayesian approach,” Opt. Express 17, 16834–16848 (2009).
[CrossRef]

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, 15640–15654(2008).
[CrossRef]

Acta Biophys. Sin. (1)

X. Ma, J. Tian, X. Yang, C. Qin, S. Zhu, and Z. Xue, “Research on liver tumor proliferation and angiogenesis based on multi-modality molecular imaging,” Acta Biophys. Sin. 27, 355–364 (2011).
[CrossRef]

Appl. Opt. (2)

Biomed. Opt. Express (1)

IEEE Eng. Med. Biol. Mag. (1)

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef]

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

S. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale L1-regularized least squares,” IEEE J. Sel. Top. Signal Process. 1, 606–617 (2007).
[CrossRef]

IEEE Signal Process. Lett. (1)

R. Tomioka and M. Sugiyama, “Dual augmented Lagrangian method for efficient sparse reconstruction,” IEEE Signal Process. Lett. 16, 1067–1070 (2009).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

A. Cong, W. Cong, Y. Lu, P. Santago, A. Chatziioannou, and G. Wang, “Differential evolution approach for regularized bioluminescence tomography,” IEEE Trans. Biomed. Eng. 57, 2229–2238 (2010).
[CrossRef]

IEEE Trans. Image Process. (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “Multiplicative noise removal using variable splitting and constrained optimization,” IEEE Trans. Image Process. 19, 1720–1730 (2010).
[CrossRef]

Int. J. Biomed. Imaging (1)

X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010).
[CrossRef]

Int. J. Comput. Vis. (1)

S. Setzer, “Operator splittings, Bregman methods and frame shrinkage in image processing,” Int. J. Comput. Vis. 92, 265–280 (2011).
[CrossRef]

J. Biomed. Opt. (1)

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12, 024007 (2007).
[CrossRef]

J. Comput. Phys. (1)

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, 323–345 (2005).
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Med. Phys. (3)

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Figures (8)

Fig. 1.
Fig. 1.

Reconstruction model with a single source. (a) Torso of the mouse atlas model with one source in the liver; (b) Simulated photon distribution on the surface.

Fig. 2.
Fig. 2.

Comparison of the reconstruction results. (a), (b), (c), and (d) are the reconstruction results with Newton-L2 (without PSR), Newton-L2 (with PSR), IS-L1, and the proposed method, respectively. The results are shown in the form of iso-surfaces for 40% of the maximum value (left column) and slice images in the z=47.29mm plane (right column). The small yellow sphere in the iso-surfaces view image and the circles in the slice images denote the real position of the bioluminescent source.

Fig. 3.
Fig. 3.

Reconstruction results with kth outer iteration.

Fig. 4.
Fig. 4.

Reconstruction results in the double-source case. The results are shown in the form of iso-surfaces for 40% of the maximum value (left column). Slice images in z=47.06mm and 47.29 mm planes (right column) were selected to show the results in more detail. The small yellow sphere in the iso-surfaces view image and the circles in the slice images denote the real position of the bioluminescent source.

Fig. 5.
Fig. 5.

Reconstruction results in the double-sources case. The results are shown in the form of iso-surfaces for 40% of the maximum value (left column). Slice images in z=47.06mm, 47.29 mm, and 47.45 mm planes (right column) were selected to show the results in more detail. The small yellow sphere in the iso-surfaces view image and the circles in the slice images denote the real position of the bioluminescent source.

Fig. 6.
Fig. 6.

Multiview superimposed images of photographs and luminescent images. (a), (b), (c), and (d) are 0°, 90°, 180°, and 270° views, respectively.

Fig. 7.
Fig. 7.

In vivo heterogeneous model. (a) Torso of the model. (b) Three-dimensional photon distribution on the surface resulting from two-dimensional bioluminescence photographs.

Fig. 8.
Fig. 8.

Reconstruction results: transverse view of the results and comparisons with the corresponding CT slices. The cross of the red lines denotes the actual source center.

Tables (8)

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Table 1. Optical Parameters of Each Organ in the Mouse Atlas [34]

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Table 2. Quantitative Comparisons of Reconstruction Results

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Table 3. Quantitative Information about Reconstruction Results with kth Outer Iteration

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Table 4. Quantitative Comparisons of Reconstruction Results with Different Gaussian Noise Levels

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Table 5. Quantitative Information about Reconstruction Results with kth Outer Iteration for Different Levels of Noise

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Table 6. Reconstruction Results in Double-source Case

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Table 7. Reconstruction Results in Multiple-source Case

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Table 8. Optical Parameters of Each Organ in the Heterogeneous Model [34,37]

Equations (16)

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·D(r)Φ(r)+μa(r)Φ(r)=S(r)(rΩ),
Φ(r)+2A(r;n,n)D(r)(v(r)·Φ(r))=0(rΩ),
Q(r)=D(r)(v(r)·Φ(r))=(2A(r;n,n))1Φ(r),(rΩ).
PΦ=FS,
AS=Φm,
minJ(w)=12AwΦm22+λw11,
minw1subject toAwΦm=0.
maxE(α,ν)=12αΦm2+12Φm2δλ(ν)subject toνATα=0,
L(α,ν,w,μ)=E(α,ν)wT(ATαν)μ2ATαν22,
wk+1=wk+μt(ATαtνt).
L(α,ν,w,μ)=12αΦm2+12Φm2j=1N(μ2(νj(wμ+ATα)j)2+δλ(νj)),
ν(α)=CLλ(wμ+ATα),
maxL(α,w,μ)=max12αΦm22μ2Shrinkλ(ATα+wμ)22,
wk+1=Shrinkλμk(wk+μkATαk),
Shrinkλ(w)=(max(|wj|λ,0)wj|wj|)j(j=1,,n).
P=diag(2L(α))=diag(ImμkA+A+T),

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