Abstract

Through the reconstruction of the fluorescent probe distributions, fluorescence molecular tomography (FMT) can three-dimensionally resolve the molecular processes in small animals in vivo. In this paper, we propose an FMT reconstruction algorithm based on the iterated shrinkage method. By incorporating a surrogate function, the original optimization problem can be decoupled, which enables us to use the general sparsity regularization. Due to the sparsity characteristic of the fluorescent sources, the performance of this method can be greatly enhanced, which leads to a fast reconstruction algorithm. Numerical simulations and physical experiments were conducted. Compared to Newton method with Tikhonov regularization, the iterated shrinkage based algorithm can obtain more accurate results, even with very limited measurement data.

© 2010 OSA

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  1. V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
    [CrossRef] [PubMed]
  2. R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
    [PubMed]
  3. J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
    [CrossRef] [PubMed]
  4. J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
    [CrossRef] [PubMed]
  5. C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4(1), 235–260 (2002).
    [CrossRef] [PubMed]
  6. V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8(1), 1–33 (2006).
    [CrossRef] [PubMed]
  7. X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15(26), 18300–18317 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=OE-15-26-18300 .
    [CrossRef] [PubMed]
  8. 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(10), 8062–8080 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8062 .
    [CrossRef] [PubMed]
  9. P. Mohajerani, A. A. Eftekhar, J. Huang, and A. Adibi, “Optimal sparse solution for fluorescent diffuse optical tomography: theory and phantom experimental results,” Appl. Opt. 46(10), 1679–1685 (2007).
    [CrossRef] [PubMed]
  10. D. Wang, X. Song, and J. Bai, “Adaptive-mesh-based algorithm for fluorescence molecular tomography using an analytical solution,” Opt. Express 15(15), 9722–9730 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-15-9722 .
    [CrossRef] [PubMed]
  11. W. Bangerth and A. Joshi, “Adaptive finite element methods for the solution of inverse problems in optical tomography,” Inverse Probl. 24(3), 034011 (2008).
    [CrossRef]
  12. N. Cao, A. Nehorai, and M. Jacobs, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express 15(21), 13695–13708 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-21-13695 .
    [CrossRef] [PubMed]
  13. I. F. Gorodnitsky and B. D. Rao, “Sparse signal reconstruction from limited data using focuss: a re-weighted minimum norm algorithm,” IEEE Trans. Signal Process. 45(3), 600–616 (1997).
    [CrossRef]
  14. E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
    [CrossRef]
  15. I. Daubechies, M. Defrise, and C. DeMol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
    [CrossRef]
  16. F. Gao, H. Zhao, L. Zhang, Y. Tanikawa, A. Marjono, and Y. Yamada, “A self-normalized, full time-resolved method for fluorescence diffuse optical tomography,” Opt. Express 16(17), 13104–13121 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-17-13104 .
    [CrossRef] [PubMed]
  17. Y. Tan and H. Jiang, “DOT guided fluorescence molecular tomography of arbitrarily shaped objects,” Med. Phys. 35(12), 5703–5707 (2008).
    [CrossRef]
  18. A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12(22), 5402–5417 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5402 .
    [CrossRef] [PubMed]
  19. J. Feng, K. Jia, G. Yan, S. Zhu, C. Qin, Y. Lv, and J. Tian, “An optimal permissible source region strategy for multispectral bioluminescence tomography,” Opt. Express 16(20), 15640–15654 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15640 .
    [CrossRef] [PubMed]
  20. C. Qin, J. Tian, X. Yang, K. Liu, G. Yan, J. Feng, Y. Lv, and M. Xu, “Galerkin-based meshless methods for photon transport in the biological tissue,” Opt. Express 16(25), 20317–20333 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20317 .
    [CrossRef] [PubMed]
  21. 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), 1779–1792 (1995).
    [CrossRef] [PubMed]
  22. R. Tibshirani, “Regression Shrinkage and Selection via the Lasso,” J. R. Stat. Soc., B 58, 267–288 (1996).
  23. M. Elad, B. Matalon, and M. Zibulevsky, “Image denoising with shrinkage and redundant representations,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, New York2, 1924–1931 (2006).
  24. H. Minc, Nonnegative matrices, (Wiley, New York, 1988).
  25. M. T. Chu and J. L. Watterson, “On a multivariate eigenvalue problem, Part I: Algebraic theory and a power method,” SIAM J. Sci. Comput. 14(5), 1089–1106 (1993).
    [CrossRef]
  26. A. X. Cong and G. Wang, “A finite-element-based reconstruction method for 3D fluorescence tomography,” Opt. Express 13(24), 9847–9857 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-24-9847 .
    [CrossRef] [PubMed]

2009 (1)

2008 (7)

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

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

W. Bangerth and A. Joshi, “Adaptive finite element methods for the solution of inverse problems in optical tomography,” Inverse Probl. 24(3), 034011 (2008).
[CrossRef]

F. Gao, H. Zhao, L. Zhang, Y. Tanikawa, A. Marjono, and Y. Yamada, “A self-normalized, full time-resolved method for fluorescence diffuse optical tomography,” Opt. Express 16(17), 13104–13121 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-17-13104 .
[CrossRef] [PubMed]

Y. Tan and H. Jiang, “DOT guided fluorescence molecular tomography of arbitrarily shaped objects,” Med. Phys. 35(12), 5703–5707 (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(20), 15640–15654 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15640 .
[CrossRef] [PubMed]

C. Qin, J. Tian, X. Yang, K. Liu, G. Yan, J. Feng, Y. Lv, and M. Xu, “Galerkin-based meshless methods for photon transport in the biological tissue,” Opt. Express 16(25), 20317–20333 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20317 .
[CrossRef] [PubMed]

2007 (4)

2006 (2)

V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8(1), 1–33 (2006).
[CrossRef] [PubMed]

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

2005 (2)

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[CrossRef] [PubMed]

A. X. Cong and G. Wang, “A finite-element-based reconstruction method for 3D fluorescence tomography,” Opt. Express 13(24), 9847–9857 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-24-9847 .
[CrossRef] [PubMed]

2004 (2)

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

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12(22), 5402–5417 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5402 .
[CrossRef] [PubMed]

2002 (1)

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4(1), 235–260 (2002).
[CrossRef] [PubMed]

2001 (1)

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

1997 (1)

I. F. Gorodnitsky and B. D. Rao, “Sparse signal reconstruction from limited data using focuss: a re-weighted minimum norm algorithm,” IEEE Trans. Signal Process. 45(3), 600–616 (1997).
[CrossRef]

1996 (1)

R. Tibshirani, “Regression Shrinkage and Selection via the Lasso,” J. R. Stat. Soc., B 58, 267–288 (1996).

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(11), 1779–1792 (1995).
[CrossRef] [PubMed]

1993 (1)

M. T. Chu and J. L. Watterson, “On a multivariate eigenvalue problem, Part I: Algebraic theory and a power method,” SIAM J. Sci. Comput. 14(5), 1089–1106 (1993).
[CrossRef]

Adibi, A.

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), 1779–1792 (1995).
[CrossRef] [PubMed]

Bachmann, M. H.

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4(1), 235–260 (2002).
[CrossRef] [PubMed]

Bai, J.

Bangerth, W.

Bao, S.

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

Candès, E. J.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

Cao, N.

Chan, T. F.

Chatziioannou, A. F.

Chen, N.

Chu, M. T.

M. T. Chu and J. L. Watterson, “On a multivariate eigenvalue problem, Part I: Algebraic theory and a power method,” SIAM J. Sci. Comput. 14(5), 1089–1106 (1993).
[CrossRef]

Cong, A. X.

Contag, C. H.

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4(1), 235–260 (2002).
[CrossRef] [PubMed]

Daubechies, I.

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

Defrise, M.

I. Daubechies, M. Defrise, and C. DeMol, “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), 1779–1792 (1995).
[CrossRef] [PubMed]

DeMol, C.

I. Daubechies, M. Defrise, and C. DeMol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Commun. Pure Appl. Math. 57(11), 1413–1457 (2004).
[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(7), 591–607 (2008).
[CrossRef] [PubMed]

Douraghy, A.

Eftekhar, A. A.

Feng, J.

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(7), 591–607 (2008).
[CrossRef] [PubMed]

Gao, F.

Gorodnitsky, I. F.

I. F. Gorodnitsky and B. D. Rao, “Sparse signal reconstruction from limited data using focuss: a re-weighted minimum norm algorithm,” IEEE Trans. Signal Process. 45(3), 600–616 (1997).
[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(11), 1779–1792 (1995).
[CrossRef] [PubMed]

Huang, J.

Jacobs, M.

Jia, K.

Jiang, H.

Y. Tan and H. Jiang, “DOT guided fluorescence molecular tomography of arbitrarily shaped objects,” Med. Phys. 35(12), 5703–5707 (2008).
[CrossRef]

Joshi, A.

Li, Y.

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

Liang, W.

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

Liu, K.

Lu, Y.

Lv, Y.

Mahmood, U.

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

Marjono, A.

Mohajerani, P.

Nehorai, A.

Ntziachristos, V.

V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8(1), 1–33 (2006).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[CrossRef] [PubMed]

Qin, C.

Rao, B. D.

I. F. Gorodnitsky and B. D. Rao, “Sparse signal reconstruction from limited data using focuss: a re-weighted minimum norm algorithm,” IEEE Trans. Signal Process. 45(3), 600–616 (1997).
[CrossRef]

Ripoll, J.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[CrossRef] [PubMed]

Romberg, J. K.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

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), 1779–1792 (1995).
[CrossRef] [PubMed]

Sevick-Muraca, E. M.

Song, X.

Stout, D.

Tan, Y.

Y. Tan and H. Jiang, “DOT guided fluorescence molecular tomography of arbitrarily shaped objects,” Med. Phys. 35(12), 5703–5707 (2008).
[CrossRef]

Tanikawa, Y.

Tao, T.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

Tian, J.

Tibshirani, R.

R. Tibshirani, “Regression Shrinkage and Selection via the Lasso,” J. R. Stat. Soc., B 58, 267–288 (1996).

van Bruggen, N.

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

Wang, D.

Wang, G.

Wang, H.

Wang, L. V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[CrossRef] [PubMed]

Watterson, J. L.

M. T. Chu and J. L. Watterson, “On a multivariate eigenvalue problem, Part I: Algebraic theory and a power method,” SIAM J. Sci. Comput. 14(5), 1089–1106 (1993).
[CrossRef]

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[CrossRef] [PubMed]

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

Willmann, J. K.

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

Xu, M.

Yamada, Y.

Yan, G.

Yan, X. P.

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

Yang, X.

Zhang, L.

Zhang, X.

Zhao, H.

Zhu, S.

Annu. Rev. Biomed. Eng. (2)

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4(1), 235–260 (2002).
[CrossRef] [PubMed]

V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8(1), 1–33 (2006).
[CrossRef] [PubMed]

Appl. Opt. (1)

Commun. Pure Appl. Math. (2)

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59(8), 1207–1223 (2006).
[CrossRef]

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

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

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

IEEE Trans. Signal Process. (1)

I. F. Gorodnitsky and B. D. Rao, “Sparse signal reconstruction from limited data using focuss: a re-weighted minimum norm algorithm,” IEEE Trans. Signal Process. 45(3), 600–616 (1997).
[CrossRef]

Inverse Probl. (1)

W. Bangerth and A. Joshi, “Adaptive finite element methods for the solution of inverse problems in optical tomography,” Inverse Probl. 24(3), 034011 (2008).
[CrossRef]

J. R. Stat. Soc., B (1)

R. Tibshirani, “Regression Shrinkage and Selection via the Lasso,” J. R. Stat. Soc., B 58, 267–288 (1996).

Med. Phys. (2)

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), 1779–1792 (1995).
[CrossRef] [PubMed]

Y. Tan and H. Jiang, “DOT guided fluorescence molecular tomography of arbitrarily shaped objects,” Med. Phys. 35(12), 5703–5707 (2008).
[CrossRef]

Nat. Biotechnol. (1)

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005).
[CrossRef] [PubMed]

Nat. Rev. Drug Discov. (1)

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

Opt. Express (9)

X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15(26), 18300–18317 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=OE-15-26-18300 .
[CrossRef] [PubMed]

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(10), 8062–8080 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8062 .
[CrossRef] [PubMed]

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12(22), 5402–5417 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5402 .
[CrossRef] [PubMed]

J. Feng, K. Jia, G. Yan, S. Zhu, C. Qin, Y. Lv, and J. Tian, “An optimal permissible source region strategy for multispectral bioluminescence tomography,” Opt. Express 16(20), 15640–15654 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15640 .
[CrossRef] [PubMed]

C. Qin, J. Tian, X. Yang, K. Liu, G. Yan, J. Feng, Y. Lv, and M. Xu, “Galerkin-based meshless methods for photon transport in the biological tissue,” Opt. Express 16(25), 20317–20333 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20317 .
[CrossRef] [PubMed]

N. Cao, A. Nehorai, and M. Jacobs, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express 15(21), 13695–13708 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-21-13695 .
[CrossRef] [PubMed]

D. Wang, X. Song, and J. Bai, “Adaptive-mesh-based algorithm for fluorescence molecular tomography using an analytical solution,” Opt. Express 15(15), 9722–9730 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-15-9722 .
[CrossRef] [PubMed]

F. Gao, H. Zhao, L. Zhang, Y. Tanikawa, A. Marjono, and Y. Yamada, “A self-normalized, full time-resolved method for fluorescence diffuse optical tomography,” Opt. Express 16(17), 13104–13121 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-17-13104 .
[CrossRef] [PubMed]

A. X. Cong and G. Wang, “A finite-element-based reconstruction method for 3D fluorescence tomography,” Opt. Express 13(24), 9847–9857 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-24-9847 .
[CrossRef] [PubMed]

Radiology (1)

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

SIAM J. Sci. Comput. (1)

M. T. Chu and J. L. Watterson, “On a multivariate eigenvalue problem, Part I: Algebraic theory and a power method,” SIAM J. Sci. Comput. 14(5), 1089–1106 (1993).
[CrossRef]

Other (2)

M. Elad, B. Matalon, and M. Zibulevsky, “Image denoising with shrinkage and redundant representations,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, New York2, 1924–1931 (2006).

H. Minc, Nonnegative matrices, (Wiley, New York, 1988).

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Fig. 1
Fig. 1

Mouse-mimicking heterogeneous phantom with four kinds of materials to represent muscle (M), lung (L), heart (H) and bone (B), respectively. (a) is the 3D view of the phantom. (b) is the slice image of the phantom in z = 0 plane. The black dots in (b) represent the excitation point source locations. For each excitation location, fluorescence is measured from the opposite cylindrical side with 160° field of view.

Fig. 2
Fig. 2

Three different phantom setups for single fluorescent source (left column), double fluorescent sources (middle column) and three fluorescent sources (right column), respectively. The first row is the 3D views of the phantoms, and the second row is the slice images in z = 0 plane. All the fluorescent sources are spherical and are centered in z = 0 plane. The diameters of these spherical fluorescent sources are all set to be 2mm.

Fig. 3
Fig. 3

Reconstruction results from the Newton method (first row) and the iterated shrinkage based method (second row) for 1 spherical fluorescent source and 15 measurement data sets. These results are presented in the form of slice images in z = 0 plane (left column) and iso-surfaces for 30% of the maximum value (right column). The small circles in the slice images denote the real positions of the fluorescent sources.

Fig. 4
Fig. 4

Reconstruction results from the Newton method (first row) and the iterated shrinkage based method (second row) for 2 spherical fluorescent sources and 15 measurement data sets. These results are presented in the form of slice images in z = 0 plane (left column) and iso-surfaces for 30% of the maximum value (right column). The small circles in the slice images denote the real positions of the fluorescent sources.

Fig. 5
Fig. 5

Reconstruction results from the Newton method (first row) and the iterated shrinkage based method (second row) for 3 spherical fluorescent sources and 15 measurement data sets. These results are presented in the form of slice images in z = 0 plane (left column) and iso-surfaces for 30% of the maximum value (right column). The small circles in the slice images denote the real positions of the fluorescent sources.

Fig. 6
Fig. 6

Reconstruction results from the Newton method (first row) and the iterated shrinkage based method (second row) for 1 spherical fluorescent source and 3 measurement data sets. These results are presented in the form of slice images in z = 0 plane (left column) and iso-surfaces for 30% of the maximum value (right column). The small circles in the slice images denote the real positions of the fluorescent sources.

Fig. 7
Fig. 7

Reconstruction results from the Newton method (first row) and the iterated shrinkage based method (second row) for 2 spherical fluorescent sources and 3 measurement data sets. These results are presented in the form of slice images in z = 0 plane (left column) and iso-surfaces for 30% of the maximum value (right column). The small circles in the slice images denote the real positions of the fluorescent sources.

Fig. 8
Fig. 8

Reconstruction results from the Newton method (first row) and the iterated shrinkage based method (second row) for 3 spherical fluorescent sources and 3 measurement data sets. These results are presented in the form of slice images in z = 0 plane (left column) and iso-surfaces for 30% of the maximum value (right column). The small circles in the slice images denote the real positions of the fluorescent sources.

Fig. 9
Fig. 9

The sketch of the experimental setup.

Fig. 10
Fig. 10

The homogeneous cubic phantom with 2 cylindrical fluorescent sources. (a) is the photograph of the phantom. (b) is the 3D view of the phantom and the sources. (c) is the slice image of the phantom in z = 0 plane. The black dots in (c) represent the excitation point source locations.

Fig. 11
Fig. 11

Reconstruction results of the cubic phantom from the Newton method (first row) and the iterated shrinkage based method (second row) using 4 measurement data sets. These results are presented in the form of slice images in z = 1mm plane (left column) and iso-surfaces for 30% of the maximum value (right column). The small circles in the slice images denote the real positions of the fluorescent sources.

Tables (5)

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Table 1 Reconstruction strategy 1

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Table 1 Optical parameters of the heterogeneous phantom [26]

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Table 2 Quantitative comparisons between the results from the Newton method with Tikhonov regularization (Newton-L2) and the iterated shrinkage based method with L1 regularization (IS-L1) for 15 measurement sets

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Table 3 Quantitative comparisons between the results from the Newton method with Tikhonov regularization (Newton-L2) and the iterated shrinkage based method with L1 regularization (IS-L1) for 3 measurement sets

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Table 4 Optical parameters of the cubic phantom

Equations (21)

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{ · ( D x ( r ) Φ x ( r ) ) μ a x ( r ) Φ x ( r ) = Θ δ ( r r l ) · ( D m ( r ) Φ m ( r ) ) μ a m ( r ) Φ m ( r ) = Φ x ( r ) η μ a f ( r ) ( r Ω )
Φ x , m ( r ) + 2 A D x , m ( r ) ( v ( r ) · Φ x , m ( r ) ) ( r Ω )
[ K x ] { Φ x } = { S x }
[ K m ] { Φ m } = [ F ] { X }
{ Φ m , l } = [ K m , l 1 ] [ F ] { X } = [ B l ] { X }
{ Φ m , l m e a s } = [ A l ] { X }
{ Φ } = [ A ] { X }
min X 0 E ( X ) = 1 2 A X Φ 2 2 + λ R ( X )
E ( X ) = 1 2 A X Φ 2 2 + λ X p p = 1 2 A X Φ 2 2 + λ i = 1 N x i p
A T A X A T Φ + λ p X p 1 = 0
S ( X ; X 0 ) = c 2 X X 0 2 2 1 2 A X A X 0 2 2
J ( X ; X 0 ) = 1 2 A X Φ 2 2 + λ X p p + c 2 X X 0 2 2 1 2 A X A X 0 2 2
J ( X ; X 0 ) = [ A T ( Φ A X 0 ) + c X 0 ] + λ p X p 1 + c X = 0
X D + λ p c X p 1 = 0
S h r i n k λ , c ( z ; p = 1 ) = { z λ c z > λ c 0 z λ c
X o p t = arg min X J ( X ; X 0 ) = [ S h r i n k λ , c ( d 1 ; p = 1 ) S h r i n k λ , c ( d 2 ; p = 1 ) S h r i n k λ , c ( d N ; p = 1 ) ]
A T A ( X X 0 ) = c ( X X 0 )
x k + 1 , i = S h r i n k λ , c ( d k , i ( X k ) ; p = 1 ) ( i = 1 , 2 , , N )
E ( X k + 1 ) J ( X k + 1 ; X k ) J ( X k ; X k ) = E ( X k )
D k = 1 c A T ( Φ A X k ) + X k
D k = 1 c A T Φ 1 c A T A X k + X k

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