Abstract

Regularization methods have been broadly applied to bioluminescence tomography (BLT) to obtain stable solutions, including l2 and l1 regularizations. However, l2 regularization can oversmooth reconstructed images and l1 regularization may sparsify the source distribution, which degrades image quality. In this paper, the use of total variation (TV) regularization in BLT is investigated. Since a nonnegativity constraint can lead to improved image quality, the nonnegative constraint should be considered in BLT. However, TV regularization with a nonnegativity constraint is extremely difficult to solve due to its nondifferentiability and nonlinearity. The aim of this work is to validate the split Bregman method to minimize the TV regularization problem with a nonnegativity constraint for BLT. The performance of split Bregman-resolved TV (SBRTV) based BLT reconstruction algorithm was verified with numerical and in vivo experiments. Experimental results demonstrate that the SBRTV regularization can provide better regularization quality over l2 and l1 regularizations.

© 2012 Optical Society of America

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  1. 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]
  2. G. C. Kagadis, G. Loudos, K. Katsanos, S. G. Langer, and G. C. Nikiforidis, “In vivo small animal imaging: current status and future prospects,” Med. Phys. 37, 6421–6442 (2010).
    [CrossRef]
  3. 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).
  4. C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
    [CrossRef]
  5. D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
    [CrossRef]
  6. H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization,” Opt. Express 18, 1854–1871 (2010).
    [CrossRef]
  7. H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation Part 2: total variation and l1 data fidelity,” Opt. Express 18, 2894–2912 (2010).
    [CrossRef]
  8. 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]
  9. J. Feng, K. Jia, G. Yan, S. Zhu, Y. Lv, and J. Tian, “An optimal permissible source region strategy for multispectral bioluminescence tomography,” Opt. Express 16, 15640–15654 (2008).
    [CrossRef]
  10. Y. Lv, 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]
  11. 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, 8211–8223 (2006).
    [CrossRef]
  12. Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
    [CrossRef]
  13. A. D. Klose, B. J. Beattie, H. Dehghani, L. Vider, C. Le, V. Ponomarev, and R. Blasberg, “In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration,” Med. Phys. 37, 329–338 (2010).
    [CrossRef]
  14. K. Liu, J. Tian, C. Qin, X. Yang, S. Zhu, D. Han, and P. Wu, “Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models,” J. Biomed. Opt. 16, 046016 (2011).
  15. L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60, 259–268 (1992).
    [CrossRef]
  16. A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 89–97 (2004).
    [CrossRef]
  17. T. Chan and C. K. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370–375 (1998).
    [CrossRef]
  18. K. D. Paulsen and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt. 35, 3447–3458 (1996).
    [CrossRef]
  19. L. Yao and H. Jiang, “Enhancing finite element based photoacoustic tomography using total-variation minimization,” Appl. Opt. 50, 5031–5041 (2011).
    [CrossRef]
  20. L. Yao and H. Jiang, “Photoacoustic image reconstruction from few-detector and limited-angle data,” Biomed. Opt. Express 2, 2649–2654 (2011).
    [CrossRef]
  21. 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]
  22. A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
    [CrossRef]
  23. H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).
    [CrossRef]
  24. J. Feng, K. Jia, C. Qin, G. Yan, X. Zhang, J. Liu, and J. Tian, “3D bioluminescence tomography based on Bayesian approach,” Opt. Express 17, 16834–16848 (2009).
    [CrossRef]
  25. G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31, 2289–2299 (2004).
    [CrossRef]
  26. S. Osher, M. Burger, D. Glodfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation based image restoration,” Multiscale Model. Simul. 4, 460–489 (2005).
    [CrossRef]
  27. T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).
  28. T. Goldstein, X. Bresson, and S. Osher, “Geometric applications of the split Bregman method: segmentation and surface reconstruction,” J. Sci. Comput. 45, 272–293 (2010).
    [CrossRef]
  29. J. Cai, S. Osher, and Z. Shen, “Linearized Bregman iterations for compressed sensing,” Math. Comput. 78, 1515–1536(2009).
    [CrossRef]
  30. J. Cai, S. Osher, and Z. Shen, “Convergence of the linearized Bregman iteration for l1-norm minimization,” Math. Comput. 78, 2127–2136 (2009).
    [CrossRef]
  31. W. Yin, S. Osher, D. Goldfarb, and J. Darbon, “Bregman iterative algorithms for l1-minimization with applications to compressed sensing,” SIAM J. Imaging Sci. 1, 143–168 (2008).
  32. J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multi-spectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).
    [CrossRef]
  33. T. F. Coleman and Y. Li, “A reflective newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6, 1040–1058 (1996).
    [CrossRef]
  34. M. T. 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, 586–597 (2007).
    [CrossRef]
  35. J. Feng, K. Jia, C. Qin, S. Zhu, X. Yang, and J. Tian, “Sparse Bayesian reconstruction method for multispectral bioluminescence tomography,” Chin. Opt. Lett. 8, 1010–1014 (2010).
    [CrossRef]
  36. H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method,” Acad. Radiol. 11, 1029–1038 (2004).
  37. 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]

2011 (5)

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).

K. Liu, J. Tian, C. Qin, X. Yang, S. Zhu, D. Han, and P. Wu, “Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models,” J. Biomed. Opt. 16, 046016 (2011).

L. Yao and H. Jiang, “Enhancing finite element based photoacoustic tomography using total-variation minimization,” Appl. Opt. 50, 5031–5041 (2011).
[CrossRef]

L. Yao and H. Jiang, “Photoacoustic image reconstruction from few-detector and limited-angle data,” Biomed. Opt. Express 2, 2649–2654 (2011).
[CrossRef]

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multi-spectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).
[CrossRef]

2010 (7)

J. Feng, K. Jia, C. Qin, S. Zhu, X. Yang, and J. Tian, “Sparse Bayesian reconstruction method for multispectral bioluminescence tomography,” Chin. Opt. Lett. 8, 1010–1014 (2010).
[CrossRef]

T. Goldstein, X. Bresson, and S. Osher, “Geometric applications of the split Bregman method: segmentation and surface reconstruction,” J. Sci. Comput. 45, 272–293 (2010).
[CrossRef]

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

A. D. Klose, B. J. Beattie, H. Dehghani, L. Vider, C. Le, V. Ponomarev, and R. Blasberg, “In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration,” Med. Phys. 37, 329–338 (2010).
[CrossRef]

G. C. Kagadis, G. Loudos, K. Katsanos, S. G. Langer, and G. C. Nikiforidis, “In vivo small animal imaging: current status and future prospects,” Med. Phys. 37, 6421–6442 (2010).
[CrossRef]

H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization,” Opt. Express 18, 1854–1871 (2010).
[CrossRef]

H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation Part 2: total variation and l1 data fidelity,” Opt. Express 18, 2894–2912 (2010).
[CrossRef]

2009 (5)

J. Cai, S. Osher, and Z. Shen, “Linearized Bregman iterations for compressed sensing,” Math. Comput. 78, 1515–1536(2009).
[CrossRef]

J. Cai, S. Osher, and Z. Shen, “Convergence of the linearized Bregman iteration for l1-norm minimization,” Math. Comput. 78, 2127–2136 (2009).
[CrossRef]

D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
[CrossRef]

J. Feng, K. Jia, C. Qin, G. Yan, X. Zhang, J. Liu, and J. Tian, “3D bioluminescence tomography based on Bayesian approach,” Opt. Express 17, 16834–16848 (2009).
[CrossRef]

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).

2008 (5)

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

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

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

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]

2007 (2)

Y. Lv, 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]

M. T. 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, 586–597 (2007).
[CrossRef]

2006 (2)

2005 (3)

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

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

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]

2004 (3)

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

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 89–97 (2004).
[CrossRef]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method,” Acad. Radiol. 11, 1029–1038 (2004).

2002 (1)

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

1998 (1)

T. Chan and C. K. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370–375 (1998).
[CrossRef]

1996 (2)

K. D. Paulsen and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt. 35, 3447–3458 (1996).
[CrossRef]

T. F. Coleman and Y. Li, “A reflective newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6, 1040–1058 (1996).
[CrossRef]

1992 (1)

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

Bachmann, M. H.

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

Bading, J. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Beattie, B. J.

A. D. Klose, B. J. Beattie, H. Dehghani, L. Vider, C. Le, V. Ponomarev, and R. Blasberg, “In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration,” Med. Phys. 37, 329–338 (2010).
[CrossRef]

Blasberg, R.

A. D. Klose, B. J. Beattie, H. Dehghani, L. Vider, C. Le, V. Ponomarev, and R. Blasberg, “In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration,” Med. Phys. 37, 329–338 (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]

Bresson, X.

T. Goldstein, X. Bresson, and S. Osher, “Geometric applications of the split Bregman method: segmentation and surface reconstruction,” J. Sci. Comput. 45, 272–293 (2010).
[CrossRef]

Burger, M.

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

Cai, J.

J. Cai, S. Osher, and Z. Shen, “Convergence of the linearized Bregman iteration for l1-norm minimization,” Math. Comput. 78, 2127–2136 (2009).
[CrossRef]

J. Cai, S. Osher, and Z. Shen, “Linearized Bregman iterations for compressed sensing,” Math. Comput. 78, 1515–1536(2009).
[CrossRef]

Chambolle, A.

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 89–97 (2004).
[CrossRef]

Chan, T.

T. Chan and C. K. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370–375 (1998).
[CrossRef]

Chatziioannou, A. F.

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]

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]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Cherry, S. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Coleman, T. F.

T. F. Coleman and Y. Li, “A reflective newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6, 1040–1058 (1996).
[CrossRef]

Cong, W.

Y. Lv, 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. 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, 8211–8223 (2006).
[CrossRef]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method,” Acad. Radiol. 11, 1029–1038 (2004).

Contag, C. H.

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

Conti, P. S.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Darbon, J.

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

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]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[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.

A. D. Klose, B. J. Beattie, H. Dehghani, L. Vider, C. Le, V. Ponomarev, and R. Blasberg, “In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration,” Med. Phys. 37, 329–338 (2010).
[CrossRef]

D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
[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]

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]

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]

Fatemi, E.

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

Feng, J.

Figueiredo, M. T.

M. T. 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, 586–597 (2007).
[CrossRef]

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]

Gao, H.

Glodfarb, D.

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

Goldfarb, D.

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

Goldstein, T.

T. Goldstein, X. Bresson, and S. Osher, “Geometric applications of the split Bregman method: segmentation and surface reconstruction,” J. Sci. Comput. 45, 272–293 (2010).
[CrossRef]

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).

Gruber, J.

D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
[CrossRef]

Han, D.

K. Liu, J. Tian, C. Qin, X. Yang, S. Zhu, D. Han, and P. Wu, “Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models,” J. Biomed. Opt. 16, 046016 (2011).

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multi-spectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).
[CrossRef]

Hoffman, E. A.

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method,” Acad. Radiol. 11, 1029–1038 (2004).

Hutchins, M.

D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
[CrossRef]

Hypnarowski, J.

D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
[CrossRef]

Jia, K.

Jiang, H.

Jiang, M.

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

Jiang, S.

Kagadis, G. C.

G. C. Kagadis, G. Loudos, K. Katsanos, S. G. Langer, and G. C. Nikiforidis, “In vivo small animal imaging: current status and future prospects,” Med. Phys. 37, 6421–6442 (2010).
[CrossRef]

Katsanos, K.

G. C. Kagadis, G. Loudos, K. Katsanos, S. G. Langer, and G. C. Nikiforidis, “In vivo small animal imaging: current status and future prospects,” Med. Phys. 37, 6421–6442 (2010).
[CrossRef]

Kepshire, D.

D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
[CrossRef]

Khayat, M.

D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
[CrossRef]

Klose, A. D.

A. D. Klose, B. J. Beattie, H. Dehghani, L. Vider, C. Le, V. Ponomarev, and R. Blasberg, “In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration,” Med. Phys. 37, 329–338 (2010).
[CrossRef]

Langer, S. G.

G. C. Kagadis, G. Loudos, K. Katsanos, S. G. Langer, and G. C. Nikiforidis, “In vivo small animal imaging: current status and future prospects,” Med. Phys. 37, 6421–6442 (2010).
[CrossRef]

Le, C.

A. D. Klose, B. J. Beattie, H. Dehghani, L. Vider, C. Le, V. Ponomarev, and R. Blasberg, “In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration,” Med. Phys. 37, 329–338 (2010).
[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]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Leblond, F.

D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
[CrossRef]

Li, H.

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, 8211–8223 (2006).
[CrossRef]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method,” Acad. Radiol. 11, 1029–1038 (2004).

Li, Y.

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

T. F. Coleman and Y. Li, “A reflective newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6, 1040–1058 (1996).
[CrossRef]

Liu, J.

Liu, K.

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multi-spectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).
[CrossRef]

K. Liu, J. Tian, C. Qin, X. Yang, S. Zhu, D. Han, and P. Wu, “Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models,” J. Biomed. Opt. 16, 046016 (2011).

Loudos, G.

G. C. Kagadis, G. Loudos, K. Katsanos, S. G. Langer, and G. C. Nikiforidis, “In vivo small animal imaging: current status and future prospects,” Med. Phys. 37, 6421–6442 (2010).
[CrossRef]

Lu, Y.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

Luo, J.

Lv, Y.

Ma, X.

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).

Mincu, N.

D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
[CrossRef]

Moats, R. A.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Nikiforidis, G. C.

G. C. Kagadis, G. Loudos, K. Katsanos, S. G. Langer, and G. C. Nikiforidis, “In vivo small animal imaging: current status and future prospects,” Med. Phys. 37, 6421–6442 (2010).
[CrossRef]

Nowak, R. D.

M. T. 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, 586–597 (2007).
[CrossRef]

Osher, S.

T. Goldstein, X. Bresson, and S. Osher, “Geometric applications of the split Bregman method: segmentation and surface reconstruction,” J. Sci. Comput. 45, 272–293 (2010).
[CrossRef]

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).

J. Cai, S. Osher, and Z. Shen, “Convergence of the linearized Bregman iteration for l1-norm minimization,” Math. Comput. 78, 2127–2136 (2009).
[CrossRef]

J. Cai, S. Osher, and Z. Shen, “Linearized Bregman iterations for compressed sensing,” Math. Comput. 78, 1515–1536(2009).
[CrossRef]

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

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

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

Patterson, M. S.

Paulsen, K. D.

Pogue, B. W.

D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
[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]

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]

Ponomarev, V.

A. D. Klose, B. J. Beattie, H. Dehghani, L. Vider, C. Le, V. Ponomarev, and R. Blasberg, “In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration,” Med. Phys. 37, 329–338 (2010).
[CrossRef]

Qin, C.

K. Liu, J. Tian, C. Qin, X. Yang, S. Zhu, D. Han, and P. Wu, “Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models,” J. Biomed. Opt. 16, 046016 (2011).

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).

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multi-spectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).
[CrossRef]

J. Feng, K. Jia, C. Qin, S. Zhu, X. Yang, and J. Tian, “Sparse Bayesian reconstruction method for multispectral bioluminescence tomography,” Chin. Opt. Lett. 8, 1010–1014 (2010).
[CrossRef]

J. Feng, K. Jia, C. Qin, G. Yan, X. Zhang, J. Liu, and J. Tian, “3D bioluminescence tomography based on Bayesian approach,” Opt. Express 17, 16834–16848 (2009).
[CrossRef]

Y. Lv, 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]

Rannou, F. R.

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]

Rasmussen, J. C.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

Rudin, L.

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

Sevick-Muraca, E. M.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

Shen, H.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

Shen, Z.

J. Cai, S. Osher, and Z. Shen, “Linearized Bregman iterations for compressed sensing,” Math. Comput. 78, 1515–1536(2009).
[CrossRef]

J. Cai, S. Osher, and Z. Shen, “Convergence of the linearized Bregman iteration for l1-norm minimization,” Math. Comput. 78, 2127–2136 (2009).
[CrossRef]

Smith, D. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

Tian, J.

K. Liu, J. Tian, C. Qin, X. Yang, S. Zhu, D. Han, and P. Wu, “Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models,” J. Biomed. Opt. 16, 046016 (2011).

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).

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multi-spectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).
[CrossRef]

J. Feng, K. Jia, C. Qin, S. Zhu, X. Yang, and J. Tian, “Sparse Bayesian reconstruction method for multispectral bioluminescence tomography,” Chin. Opt. Lett. 8, 1010–1014 (2010).
[CrossRef]

J. Feng, K. Jia, C. Qin, G. Yan, X. Zhang, J. Liu, and J. Tian, “3D bioluminescence tomography based on Bayesian approach,” Opt. Express 17, 16834–16848 (2009).
[CrossRef]

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

Y. Lv, 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. 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, 8211–8223 (2006).
[CrossRef]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method,” Acad. Radiol. 11, 1029–1038 (2004).

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, 591–607 (2008).
[CrossRef]

Vider, L.

A. D. Klose, B. J. Beattie, H. Dehghani, L. Vider, C. Le, V. Ponomarev, and R. Blasberg, “In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration,” Med. Phys. 37, 329–338 (2010).
[CrossRef]

Wang, G.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

Y. Lv, 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. 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, 8211–8223 (2006).
[CrossRef]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method,” Acad. Radiol. 11, 1029–1038 (2004).

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

Wang, L. V.

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method,” Acad. Radiol. 11, 1029–1038 (2004).

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, 591–607 (2008).
[CrossRef]

Wong, C. K.

T. Chan and C. K. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370–375 (1998).
[CrossRef]

Wright, S. J.

M. T. 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, 586–597 (2007).
[CrossRef]

Wu, P.

K. Liu, J. Tian, C. Qin, X. Yang, S. Zhu, D. Han, and P. Wu, “Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models,” J. Biomed. Opt. 16, 046016 (2011).

Xu, J.

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

Xu, M.

Y. Lv, 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, 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).

Yan, G.

Yang, W.

Y. Lv, 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. 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, 8211–8223 (2006).
[CrossRef]

Yang, X.

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multi-spectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (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).

K. Liu, J. Tian, C. Qin, X. Yang, S. Zhu, D. Han, and P. Wu, “Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models,” J. Biomed. Opt. 16, 046016 (2011).

J. Feng, K. Jia, C. Qin, S. Zhu, X. Yang, and J. Tian, “Sparse Bayesian reconstruction method for multispectral bioluminescence tomography,” Chin. Opt. Lett. 8, 1010–1014 (2010).
[CrossRef]

Yao, L.

Yin, W.

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

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

Zhang, X.

Zhao, H.

Zhu, B.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

Zhu, F.

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method,” Acad. Radiol. 11, 1029–1038 (2004).

Zhu, S.

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multi-spectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (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).

K. Liu, J. Tian, C. Qin, X. Yang, S. Zhu, D. Han, and P. Wu, “Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models,” J. Biomed. Opt. 16, 046016 (2011).

J. Feng, K. Jia, C. Qin, S. Zhu, X. Yang, and J. Tian, “Sparse Bayesian reconstruction method for multispectral bioluminescence tomography,” Chin. Opt. Lett. 8, 1010–1014 (2010).
[CrossRef]

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

Acad. Radiol. (1)

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, “A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method,” Acad. Radiol. 11, 1029–1038 (2004).

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).

Annu. Rev. Biomed. Eng. (1)

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

Appl. Opt. (2)

Biomed. Opt. Express (1)

Chin. Opt. Lett. (1)

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

M. T. 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, 586–597 (2007).
[CrossRef]

IEEE Trans. Image Process. (1)

T. Chan and C. K. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370–375 (1998).
[CrossRef]

J. Biomed. Opt. (1)

K. Liu, J. Tian, C. Qin, X. Yang, S. Zhu, D. Han, and P. Wu, “Tomographic bioluminescence imaging reconstruction via a dynamically sparse regularized global method in mouse models,” J. Biomed. Opt. 16, 046016 (2011).

J. Math. Imaging Vision (1)

A. Chambolle, “An algorithm for total variation minimization and applications,” J. Math. Imaging Vision 20, 89–97 (2004).
[CrossRef]

J. Sci. Comput. (1)

T. Goldstein, X. Bresson, and S. Osher, “Geometric applications of the split Bregman method: segmentation and surface reconstruction,” J. Sci. Comput. 45, 272–293 (2010).
[CrossRef]

Math. Comput. (2)

J. Cai, S. Osher, and Z. Shen, “Linearized Bregman iterations for compressed sensing,” Math. Comput. 78, 1515–1536(2009).
[CrossRef]

J. Cai, S. Osher, and Z. Shen, “Convergence of the linearized Bregman iteration for l1-norm minimization,” Math. Comput. 78, 2127–2136 (2009).
[CrossRef]

Med. Phys. (5)

A. D. Klose, B. J. Beattie, H. Dehghani, L. Vider, C. Le, V. Ponomarev, and R. Blasberg, “In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration,” Med. Phys. 37, 329–338 (2010).
[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]

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

J. Feng, C. Qin, K. Jia, D. Han, K. Liu, S. Zhu, X. Yang, and J. Tian, “An adaptive regularization parameter choice strategy for multi-spectral bioluminescence tomography,” Med. Phys. 38, 5933–5944 (2011).
[CrossRef]

G. C. Kagadis, G. Loudos, K. Katsanos, S. G. Langer, and G. C. Nikiforidis, “In vivo small animal imaging: current status and future prospects,” Med. Phys. 37, 6421–6442 (2010).
[CrossRef]

Multiscale Model. Simul. (1)

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

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, 591–607 (2008).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Phys. Med. Biol. (5)

Y. Lv, 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, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53, 3921–3942 (2008).
[CrossRef]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef]

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]

Physica D (1)

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

Rev. Sci. Instrum. (1)

D. Kepshire, N. Mincu, M. Hutchins, J. Gruber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, 043701 (2009).
[CrossRef]

SIAM J. Imaging Sci. (2)

T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM J. Imaging Sci. 2, 323–343 (2009).

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

SIAM J. Optim. (1)

T. F. Coleman and Y. Li, “A reflective newton method for minimizing a quadratic function subject to bounds on some of the variables,” SIAM J. Optim. 6, 1040–1058 (1996).
[CrossRef]

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Figures (14)

Fig. 1.
Fig. 1.

Source configuration of the phantom. There are four sources with a diameter of 2 mm, whose boundary is delineated by the dashed lines. The source densities (unit: nano-Watts / mm 2 ) for sources 1, 2, 3, and 4 were 31, 34, 33, and 36 respectively.

Fig. 2.
Fig. 2.

(a), (b), and (c) are the reconstructed results with l 2 , l 1 , and SBRTV regularizations, respectively, in the case of a single source for noiseless data. The white circles denote the real sources.

Fig. 3.
Fig. 3.

Reconstructed images without a nonnegativity constraint. (a), (b), and (c) are the results with l 2 , l 1 , and SBRTV regularizations, respectively. The black circles denote the real sources.

Fig. 4.
Fig. 4.

Reconstructed images with different regularization methods in the case of the two sources for noiseless data. (a)  l 2 , (b)  l 1 , and (c) SBRTV regularizations. The white circles represent the actual sources.

Fig. 5.
Fig. 5.

Reconstructed images with different edge-to-edge distances. The edge-to-edge distance of the first row is 3 mm, and the second row is 2 mm. The first column shows the images reconstructed with l 2 regularizations, and the middle and right columns are the images using l 1 and SBRTV regularizations, respectively. The white circles represent the actual sources.

Fig. 6.
Fig. 6.

Comparison of different regularizations in case of three sources with noiseless data. (a), (b), and (c) are reconstruction results with l 2 , l 1 , and SBRTV regularizations, respectively. The white circles represent the actual sources.

Fig. 7.
Fig. 7.

Reconstructed images with 10% (the left column) and 30% (the right column) noisy data. The first and middle rows use l 2 and l 1 regularizations, while the last row shows the results with the SBRTV regularization. The white circles represent the actual sources.

Fig. 8.
Fig. 8.

Reconstructed images from different techniques with simulated data having 5% (the left column) and 10% (the right column) noise. The first and middle rows show the reconstruction results with l 2 and l 1 regularizations, while the last row shows the results with SBRTV regularization. The white circles represent the actual sources.

Fig. 9.
Fig. 9.

The left column is the configuration with detectors, and the small circles indicate the detector locations. The number of detectors for each wavelength from the top to bottom is 63, 41, and 30 respectively. The middle two columns and the last column are the results with l 2 , l 1 , and SBRTV regularizations with 3% Gaussian noise added to the simulated data. The white circles represent the actual sources.

Fig. 10.
Fig. 10.

3D reconstruction results for a cross-section of the 3D model at z = 12.5 mm . (a)–(c) are the corresponding results with l 2 , l 1 , and TV regularization methods, respectively, when the source locates at (22.8, 28.6, 12.5) mm. (d)–(f) are the corresponding results with l 2 , l 1 , and SBRTV regularization methods, respectively, when the source locates at (20.8, 30.96, 12.5) mm. The axes (left and bottom) illustrate the spatial scale in millimeters, and the black circles denote the actual sources.

Fig. 11.
Fig. 11.

Bioluminescent images overlaid on the corresponding white light images of the mouse. The top and the bottom rows are images of [650–700] nm and [700–750] nm, respectively.

Fig. 12.
Fig. 12.

(a) Transverse view of the mouse. (b) and (c) are the corresponding coronal view and sagittal view, respectively. Different colors correspond to different tissue types (royal blue, muscle; saddle brown, lungs; red, bones; lime green, liver; yellow green, heart).

Fig. 13.
Fig. 13.

In vivo reconstruction results. (a), (b), and (c) are l 2 , l 1 , and SBRTV regularizations, respectively. Only the slice through the actual source’s center is shown and the crossing white lines denote the actual source central position. The axes (left and bottom) illustrate the spatial scale in millimeters.

Fig. 14.
Fig. 14.

The value of objective function versus outer iteration number for SBRTV regularization.

Tables (7)

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Algorithm 1: The Split Bregman Method for TV Regularization

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Table 1. Optical Parameters for Different Bands [8]

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Table 2. Reconstruction Results using l 2 , l 1 , and SBRTV Regularization Methods in Case of Single Source

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Table 3. Reconstruction Results Using l 2 , l 1 , and SBRTV Regularization Methods in Case of Two Sources

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Table 4. Reconstruction Results Using l 2 , l 1 , and SBRTV Regularization Methods in Case of Three Sources with Noiseless Data

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Table 5. Optical Parameters for Different Bands. (Unit: mm 1 )

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Table 6. Quantitative Results for Different Regularization Methods

Equations (14)

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· ( D ( r , λ ) Φ ( r , λ ) ) + μ a ( r , λ ) Φ ( r , λ ) = S ( r , λ ) ( r Ω ) ,
Φ ( r , λ ) + 2 A ( r ; n , n ) D ( r , λ ) ( ν ( r , λ ) · Φ ( r , λ ) ) = 0 ( r Ω ) ,
A ( r ; n , n ) 1 + R ( r ) 1 R ( r ) ,
Q ( r , λ ) = D ( r ) ( ν · Φ ( r , λ ) ) = Φ ( r , λ ) 2 A ( r ; n , n ) ( r Ω ) .
F ( S ) = Φ meas .
S = arg min S 0 F ( S ) Φ meas 2 2 + α J ( S ) ,
J ( S ) = S TV = Ω | S | d r ,
S TV = | D S | .
min S 0 A S Φ meas 2 2 + λ · | u | s.t. D S = u .
min S 0 A S Φ meas 2 2 + λ · | u | + μ 2 D S u 2 2 ,
( S k + 1 , u k + 1 ) = min S 0 , u A S Φ meas 2 2 + λ · | u | + μ 2 · D S u b k 2 2 , b k + 1 = b k + u k + 1 D S k + 1 .
Step 1 : S k + 1 = min S 0 A S Φ meas 2 2 + μ 2 · D S u b k 2 2 , Step 2 : u k + 1 = min u λ · | u | + μ 2 · D S k + 1 u b k 2 2 , Step 3 : b k + 1 = b k + u k + 1 D S k + 1 .
u k + 1 = shrink ( D S k + 1 b k , λ μ ) ,
shrink ( r , ξ ) = r | r | * max ( | r | ξ , 0 ) .

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