Abstract

Fluorescence molecular tomography (FMT), as a promising imaging modality, can three-dimensionally locate the specific tumor position in small animals. However, it remains challenging for effective and robust reconstruction of fluorescent probe distribution in animals. In this paper, we present a novel method based on sparsity adaptive subspace pursuit (SASP) for FMT reconstruction. Some innovative strategies including subspace projection, the bottom-up sparsity adaptive approach, and backtracking technique are associated with the SASP method, which guarantees the accuracy, efficiency, and robustness for FMT reconstruction. Three numerical experiments based on a mouse-mimicking heterogeneous phantom have been performed to validate the feasibility of the SASP method. The results show that the proposed SASP method can achieve satisfactory source localization with a bias less than 1mm; the efficiency of the method is much faster than mainstream reconstruction methods; and this approach is robust even under quite ill-posed condition. Furthermore, we have applied this method to an in vivo mouse model, and the results demonstrate the feasibility of the practical FMT application with the SASP method.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]

2012 (2)

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods9(6), 615–620 (2012).
[CrossRef] [PubMed]

P. Wu, K. Liu, Q. Zhang, Z. Xue, Y. Li, N. Ning, X. Yang, X. Li, and J. Tian, “Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging,” J. Biomed. Opt.17(12), 126012 (2012).
[CrossRef] [PubMed]

2011 (2)

M. A. Whitney, J. L. Crisp, L. T. Nguyen, B. Friedman, L. A. Gross, P. Steinbach, R. Y. Tsien, and Q. T. Nguyen, “Fluorescent peptides highlight peripheral nerves during surgery in mice,” Nat. Biotechnol.29(4), 352–356 (2011).
[CrossRef] [PubMed]

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

2010 (7)

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity-promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng.57(10), 2564–2567 (2010).
[CrossRef] [PubMed]

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods7(8), 603–614 (2010).
[CrossRef] [PubMed]

H. Fan-Minogue, Z. Cao, R. Paulmurugan, C. T. Chan, T. F. Massoud, D. W. Felsher, and S. S. Gambhir, “Noninvasive molecular imaging of c-Myc activation in living mice,” Proc. Natl. Acad. Sci. U.S.A.107(36), 15892–15897 (2010).
[CrossRef] [PubMed]

C. H. Qin, S. P. Zhu, and J. Tian, “New Optical Molecular Imaging Systems,” Curr. Pharm. Biotechnol.11(6), 620–627 (2010).
[CrossRef] [PubMed]

D. Han, J. Tian, S. P. Zhu, J. C. Feng, C. H. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express18(8), 8630–8646 (2010).
[CrossRef] [PubMed]

X. Chen, X. Gao, D. Chen, X. Ma, X. Zhao, M. Shen, X. Li, X. Qu, J. Liang, J. Ripoll, and J. Tian, “3D reconstruction of light flux distribution on arbitrary surfaces from 2D multi-photographic images,” Opt. Express18(19), 19876–19893 (2010).
[CrossRef] [PubMed]

D. Han, X. Yang, K. Liu, C. Qin, B. Zhang, X. Ma, and J. Tian, “Efficient reconstruction method for L1 regularization in fluorescence molecular tomography,” Appl. Opt.49(36), 6930–6937 (2010).
[CrossRef] [PubMed]

2009 (4)

D. F. Wang, X. Liu, Y. P. Chen, and J. Bai, “A Novel Finite-Element-Based Algorithm for Fluorescence Molecular Tomography of Heterogeneous Media,” IEEE Trans. Inf. Technol. Biomed.13(5), 766–773 (2009).
[CrossRef] [PubMed]

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging2009, 960573 (2009).
[CrossRef] [PubMed]

N. Blow, “In vivo molecular imaging: the inside job,” Nat. Methods6(6), 465–469 (2009).
[CrossRef]

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev.51(1), 34–81 (2009).
[CrossRef]

2008 (3)

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

G. Yan, J. Tian, S. Zhu, Y. Dai, and C. Qin, “Fast cone-beam CT image reconstruction using GPU hardware,” J. XRay Sci. Technol.16, 225–234 (2008).

2007 (7)

P. Mohajerani, A. A. Eftekhar, J. D. 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]

J. H. Lee, A. Joshi, and E. M. Sevick-Muraca, “Fully adaptive finite element based tomography using tetrahedral dual-meshing for fluorescence enhanced optical imaging in tissue,” Opt. Express15(11), 6955–6975 (2007).
[CrossRef] [PubMed]

D. F. Wang, X. L. Song, and J. Bai, “Adaptive-mesh-based algorithm for fluorescence molecular tomography using an analytical solution,” Opt. Express15(15), 9722–9730 (2007).
[CrossRef] [PubMed]

N. Cao, A. Nehorai, and M. Jacobs, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express15(21), 13695–13708 (2007).
[CrossRef] [PubMed]

X. L. Song, D. F. Wang, N. G. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express15(26), 18300–18317 (2007).
[CrossRef] [PubMed]

Y. Lin, H. Gao, O. Nalcioglu, and G. Gulsen, “Fluorescence diffuse optical tomography with functional and anatomical a priori information: feasibility study,” Phys. Med. Biol.52(18), 5569–5585 (2007).
[CrossRef] [PubMed]

M. Elad, B. Matalon, and M. Zibulevsky, “Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization,” Appl. Comput. Harmon. Anal.23(3), 346–367 (2007).
[CrossRef]

2006 (4)

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

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
[CrossRef]

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys.220(1), 441–470 (2006).
[CrossRef]

F. Gao, H. Zhao, Y. Tanikawa, and Y. Yamada, “A linear, featured-data scheme for image reconstruction in time-domain fluorescence molecular tomography,” Opt. Express14(16), 7109–7124 (2006).
[CrossRef] [PubMed]

2005 (4)

W. X. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express13(18), 6756–6771 (2005).
[CrossRef] [PubMed]

A. X. Cong and G. Wang, “A finite-element-based reconstruction method for 3D fluorescence tomography,” Opt. Express13(24), 9847–9857 (2005).
[CrossRef] [PubMed]

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

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(1), 323–345 (2005).
[CrossRef]

2004 (2)

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]

Adibi, A.

Ale, A.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods9(6), 615–620 (2012).
[CrossRef] [PubMed]

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Arridge, S. R.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The Finite Element Method for the Propagation of Light in Scattering Media: Boundary and Source Conditions,” Med. Phys.22(11), 1779–1792 (1995).
[CrossRef] [PubMed]

Arts, H. J.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

Bai, J.

Bangerth, W.

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]

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express12(22), 5402–5417 (2004).
[CrossRef] [PubMed]

Bart, J.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

Blow, N.

N. Blow, “In vivo molecular imaging: the inside job,” Nat. Methods6(6), 465–469 (2009).
[CrossRef]

Boas, D. A.

Bouman, C. A.

Bruckstein, A. M.

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev.51(1), 34–81 (2009).
[CrossRef]

Cao, N.

Cao, Z.

H. Fan-Minogue, Z. Cao, R. Paulmurugan, C. T. Chan, T. F. Massoud, D. W. Felsher, and S. S. Gambhir, “Noninvasive molecular imaging of c-Myc activation in living mice,” Proc. Natl. Acad. Sci. U.S.A.107(36), 15892–15897 (2010).
[CrossRef] [PubMed]

Chan, C. T.

H. Fan-Minogue, Z. Cao, R. Paulmurugan, C. T. Chan, T. F. Massoud, D. W. Felsher, and S. S. Gambhir, “Noninvasive molecular imaging of c-Myc activation in living mice,” Proc. Natl. Acad. Sci. U.S.A.107(36), 15892–15897 (2010).
[CrossRef] [PubMed]

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Chen, D.

Chen, N. G.

Chen, X.

Chen, Y. P.

D. F. Wang, X. Liu, Y. P. Chen, and J. Bai, “A Novel Finite-Element-Based Algorithm for Fluorescence Molecular Tomography of Heterogeneous Media,” IEEE Trans. Inf. Technol. Biomed.13(5), 766–773 (2009).
[CrossRef] [PubMed]

Cohrs, C.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods9(6), 615–620 (2012).
[CrossRef] [PubMed]

Cong, A.

Cong, A. X.

Cong, W. X.

Crane, L. M.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

Crisp, J. L.

M. A. Whitney, J. L. Crisp, L. T. Nguyen, B. Friedman, L. A. Gross, P. Steinbach, R. Y. Tsien, and Q. T. Nguyen, “Fluorescent peptides highlight peripheral nerves during surgery in mice,” Nat. Biotechnol.29(4), 352–356 (2011).
[CrossRef] [PubMed]

Dai, Y.

G. Yan, J. Tian, S. Zhu, Y. Dai, and C. Qin, “Fast cone-beam CT image reconstruction using GPU hardware,” J. XRay Sci. Technol.16, 225–234 (2008).

de Angelis, M. H.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods9(6), 615–620 (2012).
[CrossRef] [PubMed]

de Jong, J. S.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

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]

Donoho, D. L.

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev.51(1), 34–81 (2009).
[CrossRef]

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
[CrossRef]

Eftekhar, A. A.

Elad, M.

A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev.51(1), 34–81 (2009).
[CrossRef]

M. Elad, B. Matalon, and M. Zibulevsky, “Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization,” Appl. Comput. Harmon. Anal.23(3), 346–367 (2007).
[CrossRef]

Ermolayev, V.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods9(6), 615–620 (2012).
[CrossRef] [PubMed]

Fan-Minogue, H.

H. Fan-Minogue, Z. Cao, R. Paulmurugan, C. T. Chan, T. F. Massoud, D. W. Felsher, and S. S. Gambhir, “Noninvasive molecular imaging of c-Myc activation in living mice,” Proc. Natl. Acad. Sci. U.S.A.107(36), 15892–15897 (2010).
[CrossRef] [PubMed]

Felsher, D. W.

H. Fan-Minogue, Z. Cao, R. Paulmurugan, C. T. Chan, T. F. Massoud, D. W. Felsher, and S. S. Gambhir, “Noninvasive molecular imaging of c-Myc activation in living mice,” Proc. Natl. Acad. Sci. U.S.A.107(36), 15892–15897 (2010).
[CrossRef] [PubMed]

Feng, J.

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity-promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng.57(10), 2564–2567 (2010).
[CrossRef] [PubMed]

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging2009, 960573 (2009).
[CrossRef] [PubMed]

Feng, J. C.

Friedman, B.

M. A. Whitney, J. L. Crisp, L. T. Nguyen, B. Friedman, L. A. Gross, P. Steinbach, R. Y. Tsien, and Q. T. Nguyen, “Fluorescent peptides highlight peripheral nerves during surgery in mice,” Nat. Biotechnol.29(4), 352–356 (2011).
[CrossRef] [PubMed]

Gambhir, S. S.

H. Fan-Minogue, Z. Cao, R. Paulmurugan, C. T. Chan, T. F. Massoud, D. W. Felsher, and S. S. Gambhir, “Noninvasive molecular imaging of c-Myc activation in living mice,” Proc. Natl. Acad. Sci. U.S.A.107(36), 15892–15897 (2010).
[CrossRef] [PubMed]

Gao, F.

Gao, H.

Y. Lin, H. Gao, O. Nalcioglu, and G. Gulsen, “Fluorescence diffuse optical tomography with functional and anatomical a priori information: feasibility study,” Phys. Med. Biol.52(18), 5569–5585 (2007).
[CrossRef] [PubMed]

Gao, X.

Gross, L. A.

M. A. Whitney, J. L. Crisp, L. T. Nguyen, B. Friedman, L. A. Gross, P. Steinbach, R. Y. Tsien, and Q. T. Nguyen, “Fluorescent peptides highlight peripheral nerves during surgery in mice,” Nat. Biotechnol.29(4), 352–356 (2011).
[CrossRef] [PubMed]

Gulsen, G.

Y. Lin, H. Gao, O. Nalcioglu, and G. Gulsen, “Fluorescence diffuse optical tomography with functional and anatomical a priori information: feasibility study,” Phys. Med. Biol.52(18), 5569–5585 (2007).
[CrossRef] [PubMed]

Han, D.

Harlaar, N. J.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

Herzog, E.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods9(6), 615–620 (2012).
[CrossRef] [PubMed]

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(1), 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(11), 1779–1792 (1995).
[CrossRef] [PubMed]

Hoffman, E. A.

Huang, J. D.

Jacobs, M.

Jiang, H. B.

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

Jiang, M.

Joshi, A.

Kelder, W.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

Klose, A. D.

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys.220(1), 441–470 (2006).
[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(1), 323–345 (2005).
[CrossRef]

Kumar, D.

Larsen, E. W.

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys.220(1), 441–470 (2006).
[CrossRef]

Lee, J. H.

Li, X.

P. Wu, K. Liu, Q. Zhang, Z. Xue, Y. Li, N. Ning, X. Yang, X. Li, and J. Tian, “Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging,” J. Biomed. Opt.17(12), 126012 (2012).
[CrossRef] [PubMed]

X. Chen, X. Gao, D. Chen, X. Ma, X. Zhao, M. Shen, X. Li, X. Qu, J. Liang, J. Ripoll, and J. Tian, “3D reconstruction of light flux distribution on arbitrary surfaces from 2D multi-photographic images,” Opt. Express18(19), 19876–19893 (2010).
[CrossRef] [PubMed]

Li, Y.

P. Wu, K. Liu, Q. Zhang, Z. Xue, Y. Li, N. Ning, X. Yang, X. Li, and J. Tian, “Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging,” J. Biomed. Opt.17(12), 126012 (2012).
[CrossRef] [PubMed]

Liang, J.

Lin, Y.

Y. Lin, H. Gao, O. Nalcioglu, and G. Gulsen, “Fluorescence diffuse optical tomography with functional and anatomical a priori information: feasibility study,” Phys. Med. Biol.52(18), 5569–5585 (2007).
[CrossRef] [PubMed]

Liu, K.

P. Wu, K. Liu, Q. Zhang, Z. Xue, Y. Li, N. Ning, X. Yang, X. Li, and J. Tian, “Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging,” J. Biomed. Opt.17(12), 126012 (2012).
[CrossRef] [PubMed]

D. Han, X. Yang, K. Liu, C. Qin, B. Zhang, X. Ma, and J. Tian, “Efficient reconstruction method for L1 regularization in fluorescence molecular tomography,” Appl. Opt.49(36), 6930–6937 (2010).
[CrossRef] [PubMed]

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity-promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng.57(10), 2564–2567 (2010).
[CrossRef] [PubMed]

Liu, X.

D. F. Wang, X. Liu, Y. P. Chen, and J. Bai, “A Novel Finite-Element-Based Algorithm for Fluorescence Molecular Tomography of Heterogeneous Media,” IEEE Trans. Inf. Technol. Biomed.13(5), 766–773 (2009).
[CrossRef] [PubMed]

Liu, Y.

Low, P. S.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

Ma, X.

Massoud, T. F.

H. Fan-Minogue, Z. Cao, R. Paulmurugan, C. T. Chan, T. F. Massoud, D. W. Felsher, and S. S. Gambhir, “Noninvasive molecular imaging of c-Myc activation in living mice,” Proc. Natl. Acad. Sci. U.S.A.107(36), 15892–15897 (2010).
[CrossRef] [PubMed]

Matalon, B.

M. Elad, B. Matalon, and M. Zibulevsky, “Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization,” Appl. Comput. Harmon. Anal.23(3), 346–367 (2007).
[CrossRef]

McCray, P. B.

McLennan, G.

Millane, R. P.

Milstein, A. B.

Mohajerani, P.

Nalcioglu, O.

Y. Lin, H. Gao, O. Nalcioglu, and G. Gulsen, “Fluorescence diffuse optical tomography with functional and anatomical a priori information: feasibility study,” Phys. Med. Biol.52(18), 5569–5585 (2007).
[CrossRef] [PubMed]

Nehorai, A.

Nguyen, L. T.

M. A. Whitney, J. L. Crisp, L. T. Nguyen, B. Friedman, L. A. Gross, P. Steinbach, R. Y. Tsien, and Q. T. Nguyen, “Fluorescent peptides highlight peripheral nerves during surgery in mice,” Nat. Biotechnol.29(4), 352–356 (2011).
[CrossRef] [PubMed]

Nguyen, Q. T.

M. A. Whitney, J. L. Crisp, L. T. Nguyen, B. Friedman, L. A. Gross, P. Steinbach, R. Y. Tsien, and Q. T. Nguyen, “Fluorescent peptides highlight peripheral nerves during surgery in mice,” Nat. Biotechnol.29(4), 352–356 (2011).
[CrossRef] [PubMed]

Ning, N.

P. Wu, K. Liu, Q. Zhang, Z. Xue, Y. Li, N. Ning, X. Yang, X. Li, and J. Tian, “Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging,” J. Biomed. Opt.17(12), 126012 (2012).
[CrossRef] [PubMed]

Ntziachristos, V.

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods9(6), 615–620 (2012).
[CrossRef] [PubMed]

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods7(8), 603–614 (2010).
[CrossRef] [PubMed]

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

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(1), 323–345 (2005).
[CrossRef]

Oh, S.

Paulmurugan, R.

H. Fan-Minogue, Z. Cao, R. Paulmurugan, C. T. Chan, T. F. Massoud, D. W. Felsher, and S. S. Gambhir, “Noninvasive molecular imaging of c-Myc activation in living mice,” Proc. Natl. Acad. Sci. U.S.A.107(36), 15892–15897 (2010).
[CrossRef] [PubMed]

Pleijhuis, R. G.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

Qin, C.

D. Han, X. Yang, K. Liu, C. Qin, B. Zhang, X. Ma, and J. Tian, “Efficient reconstruction method for L1 regularization in fluorescence molecular tomography,” Appl. Opt.49(36), 6930–6937 (2010).
[CrossRef] [PubMed]

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity-promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng.57(10), 2564–2567 (2010).
[CrossRef] [PubMed]

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging2009, 960573 (2009).
[CrossRef] [PubMed]

G. Yan, J. Tian, S. Zhu, Y. Dai, and C. Qin, “Fast cone-beam CT image reconstruction using GPU hardware,” J. XRay Sci. Technol.16, 225–234 (2008).

Qin, C. H.

Qu, X.

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Ripoll, J.

Sarantopoulos, A.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

Schweiger, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The Finite Element Method for the Propagation of Light in Scattering Media: Boundary and Source Conditions,” Med. Phys.22(11), 1779–1792 (1995).
[CrossRef] [PubMed]

Sevick-Muraca, E. M.

Shen, M.

Song, X. L.

Steinbach, P.

M. A. Whitney, J. L. Crisp, L. T. Nguyen, B. Friedman, L. A. Gross, P. Steinbach, R. Y. Tsien, and Q. T. Nguyen, “Fluorescent peptides highlight peripheral nerves during surgery in mice,” Nat. Biotechnol.29(4), 352–356 (2011).
[CrossRef] [PubMed]

Stott, J. J.

Tan, Y. Y.

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

Tanikawa, Y.

Themelis, G.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

Tian, J.

P. Wu, K. Liu, Q. Zhang, Z. Xue, Y. Li, N. Ning, X. Yang, X. Li, and J. Tian, “Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging,” J. Biomed. Opt.17(12), 126012 (2012).
[CrossRef] [PubMed]

D. Han, J. Tian, S. P. Zhu, J. C. Feng, C. H. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express18(8), 8630–8646 (2010).
[CrossRef] [PubMed]

C. H. Qin, S. P. Zhu, and J. Tian, “New Optical Molecular Imaging Systems,” Curr. Pharm. Biotechnol.11(6), 620–627 (2010).
[CrossRef] [PubMed]

X. Chen, X. Gao, D. Chen, X. Ma, X. Zhao, M. Shen, X. Li, X. Qu, J. Liang, J. Ripoll, and J. Tian, “3D reconstruction of light flux distribution on arbitrary surfaces from 2D multi-photographic images,” Opt. Express18(19), 19876–19893 (2010).
[CrossRef] [PubMed]

D. Han, X. Yang, K. Liu, C. Qin, B. Zhang, X. Ma, and J. Tian, “Efficient reconstruction method for L1 regularization in fluorescence molecular tomography,” Appl. Opt.49(36), 6930–6937 (2010).
[CrossRef] [PubMed]

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity-promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng.57(10), 2564–2567 (2010).
[CrossRef] [PubMed]

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging2009, 960573 (2009).
[CrossRef] [PubMed]

G. Yan, J. Tian, S. Zhu, Y. Dai, and C. Qin, “Fast cone-beam CT image reconstruction using GPU hardware,” J. XRay Sci. Technol.16, 225–234 (2008).

Tsien, R. Y.

M. A. Whitney, J. L. Crisp, L. T. Nguyen, B. Friedman, L. A. Gross, P. Steinbach, R. Y. Tsien, and Q. T. Nguyen, “Fluorescent peptides highlight peripheral nerves during surgery in mice,” Nat. Biotechnol.29(4), 352–356 (2011).
[CrossRef] [PubMed]

van Dam, G. M.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

van der Zee, A. G.

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

Wang, D. F.

Wang, G.

Wang, H.

Wang, L. V.

Webb, K. J.

Whitney, M. A.

M. A. Whitney, J. L. Crisp, L. T. Nguyen, B. Friedman, L. A. Gross, P. Steinbach, R. Y. Tsien, and Q. T. Nguyen, “Fluorescent peptides highlight peripheral nerves during surgery in mice,” Nat. Biotechnol.29(4), 352–356 (2011).
[CrossRef] [PubMed]

Wu, P.

P. Wu, K. Liu, Q. Zhang, Z. Xue, Y. Li, N. Ning, X. Yang, X. Li, and J. Tian, “Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging,” J. Biomed. Opt.17(12), 126012 (2012).
[CrossRef] [PubMed]

Xue, Z.

P. Wu, K. Liu, Q. Zhang, Z. Xue, Y. Li, N. Ning, X. Yang, X. Li, and J. Tian, “Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging,” J. Biomed. Opt.17(12), 126012 (2012).
[CrossRef] [PubMed]

Yamada, Y.

Yan, G.

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging2009, 960573 (2009).
[CrossRef] [PubMed]

G. Yan, J. Tian, S. Zhu, Y. Dai, and C. Qin, “Fast cone-beam CT image reconstruction using GPU hardware,” J. XRay Sci. Technol.16, 225–234 (2008).

Yang, X.

Zabner, J.

Zhang, B.

Zhang, Q.

P. Wu, K. Liu, Q. Zhang, Z. Xue, Y. Li, N. Ning, X. Yang, X. Li, and J. Tian, “Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging,” J. Biomed. Opt.17(12), 126012 (2012).
[CrossRef] [PubMed]

Zhao, H.

Zhao, X.

Zhu, S.

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging2009, 960573 (2009).
[CrossRef] [PubMed]

G. Yan, J. Tian, S. Zhu, Y. Dai, and C. Qin, “Fast cone-beam CT image reconstruction using GPU hardware,” J. XRay Sci. Technol.16, 225–234 (2008).

Zhu, S. P.

Zibulevsky, M.

M. Elad, B. Matalon, and M. Zibulevsky, “Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization,” Appl. Comput. Harmon. Anal.23(3), 346–367 (2007).
[CrossRef]

Annu. Rev. Biomed. Eng. (1)

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

Appl. Comput. Harmon. Anal. (1)

M. Elad, B. Matalon, and M. Zibulevsky, “Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization,” Appl. Comput. Harmon. Anal.23(3), 346–367 (2007).
[CrossRef]

Appl. Opt. (2)

Curr. Pharm. Biotechnol. (1)

C. H. Qin, S. P. Zhu, and J. Tian, “New Optical Molecular Imaging Systems,” Curr. Pharm. Biotechnol.11(6), 620–627 (2010).
[CrossRef] [PubMed]

IEEE Trans. Biomed. Eng. (1)

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity-promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng.57(10), 2564–2567 (2010).
[CrossRef] [PubMed]

IEEE Trans. Inf. Technol. Biomed. (1)

D. F. Wang, X. Liu, Y. P. Chen, and J. Bai, “A Novel Finite-Element-Based Algorithm for Fluorescence Molecular Tomography of Heterogeneous Media,” IEEE Trans. Inf. Technol. Biomed.13(5), 766–773 (2009).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory52(4), 1289–1306 (2006).
[CrossRef]

Int. J. Biomed. Imaging (1)

S. Zhu, J. Tian, G. Yan, C. Qin, and J. Feng, “Cone beam micro-CT system for small animal imaging and performance evaluation,” Int. J. Biomed. Imaging2009, 960573 (2009).
[CrossRef] [PubMed]

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. Biomed. Opt. (1)

P. Wu, K. Liu, Q. Zhang, Z. Xue, Y. Li, N. Ning, X. Yang, X. Li, and J. Tian, “Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging,” J. Biomed. Opt.17(12), 126012 (2012).
[CrossRef] [PubMed]

J. Comput. Phys. (2)

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(1), 323–345 (2005).
[CrossRef]

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys.220(1), 441–470 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. XRay Sci. Technol. (1)

G. Yan, J. Tian, S. Zhu, Y. Dai, and C. Qin, “Fast cone-beam CT image reconstruction using GPU hardware,” J. XRay Sci. Technol.16, 225–234 (2008).

Med. Phys. (2)

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

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]

Nat. Biotechnol. (1)

M. A. Whitney, J. L. Crisp, L. T. Nguyen, B. Friedman, L. A. Gross, P. Steinbach, R. Y. Tsien, and Q. T. Nguyen, “Fluorescent peptides highlight peripheral nerves during surgery in mice,” Nat. Biotechnol.29(4), 352–356 (2011).
[CrossRef] [PubMed]

Nat. Med. (1)

G. M. van Dam, G. Themelis, L. M. Crane, N. J. Harlaar, R. G. Pleijhuis, W. Kelder, A. Sarantopoulos, J. S. de Jong, H. J. Arts, A. G. van der Zee, J. Bart, P. S. Low, and V. Ntziachristos, “Intraoperative tumor-specific fluorescence imaging in ovarian cancer by folate receptor-α targeting: first in-human results,” Nat. Med.17(10), 1315–1319 (2011).
[CrossRef] [PubMed]

Nat. Methods (3)

A. Ale, V. Ermolayev, E. Herzog, C. Cohrs, M. H. de Angelis, and V. Ntziachristos, “FMT-XCT: in vivo animal studies with hybrid fluorescence molecular tomography-X-ray computed tomography,” Nat. Methods9(6), 615–620 (2012).
[CrossRef] [PubMed]

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods7(8), 603–614 (2010).
[CrossRef] [PubMed]

N. Blow, “In vivo molecular imaging: the inside job,” Nat. Methods6(6), 465–469 (2009).
[CrossRef]

Opt. Express (10)

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express12(22), 5402–5417 (2004).
[CrossRef] [PubMed]

W. X. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express13(18), 6756–6771 (2005).
[CrossRef] [PubMed]

A. X. Cong and G. Wang, “A finite-element-based reconstruction method for 3D fluorescence tomography,” Opt. Express13(24), 9847–9857 (2005).
[CrossRef] [PubMed]

F. Gao, H. Zhao, Y. Tanikawa, and Y. Yamada, “A linear, featured-data scheme for image reconstruction in time-domain fluorescence molecular tomography,” Opt. Express14(16), 7109–7124 (2006).
[CrossRef] [PubMed]

J. H. Lee, A. Joshi, and E. M. Sevick-Muraca, “Fully adaptive finite element based tomography using tetrahedral dual-meshing for fluorescence enhanced optical imaging in tissue,” Opt. Express15(11), 6955–6975 (2007).
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D. F. Wang, X. L. Song, and J. Bai, “Adaptive-mesh-based algorithm for fluorescence molecular tomography using an analytical solution,” Opt. Express15(15), 9722–9730 (2007).
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Figures (12)

Fig. 1
Fig. 1

A mouse-mimicking heterogeneous cylindrical phantom. Each kind of tissue material is labeled by a letter, B for Bone, L for lungs, H for heart, and M for muscle. (a) 3D view of the phantom. (b) Cross-section of the phantom in the z = 0 plane.

Fig. 2
Fig. 2

Three different phantom setups under the situation of single (a, d), double (b, e), and triple (c, f) sources respectively. The first row (a, b, c) shows the 3D views of the phantom setups and the second row (d, e, f) shows the corresponding slice images in the z = 0 plane. All of the fluorescent sources were set to be spherical and centered in the z = 0 plane. The diameters of these fluorescent sources were all set to be 2mm. Arrows in a-f indicate corresponding locations of the sources. S1, S2, and S3 respectively, denote the Source No of the first source, the second source and the third source in the tissue material of the lungs.

Fig. 3
Fig. 3

Fluorescent yield reconstruction results by the IS_L1 method (a, d), the StOMP method (b, e) and the proposed method (c, f) for a single spherical fluorescent source and 12 measurement data sets corrupted by 5% Gaussian noise. The first row (a, b, c) shows the 3D views of the reconstruction results and the second row (d, e, f) shows the corresponding slice images in the z = 0 plane. The red circles in the slice images denote the real locations of the fluorescent sources.

Fig. 4
Fig. 4

Fluorescent yield reconstruction results by the IS_L1 method (a, d), the StOMP method (b, e) and the proposed method (c, f) for the double spherical fluorescent sources and 12 measurement data sets corrupted by 5% Gaussian noise. The first row (a, b, c) shows the 3D views of the reconstruction results and the second row (d, e, f) shows the corresponding slice images in the z = 0 plane. The red circles in the slice images denote the real locations of the fluorescent sources.

Fig. 5
Fig. 5

Fluorescent yield reconstruction results by the IS_L1 method (a, d), the StOMP method (b, e) and the proposed method (c, f) for triple spherical fluorescent sources and 12 measurement data sets corrupted by 5% Gaussian noise. The first row (a, b, c) shows the 3D views of the reconstruction results and the second row shows the corresponding slice images in the z = 0 plane. The red circles in the slice images denote the real locations of the fluorescent sources.

Fig. 6
Fig. 6

The relationship curves as a function of iteration steps with a different number of sources. (a) The relationship curve between sparsity factor K and iteration n. (b) The relationship curve between residual r n and iteration n.

Fig. 7
Fig. 7

Reconstruction results from the IS_L1 method (a, d), the StOMP method (b, e) and the proposed method (c, f) for 3 spherical fluorescent sources and 4 measurement data sets corrupted by 5% Gaussian noise. These results are presented in the form of iso-surfaces for 30% of the maximum value (a, b, c) and slice images in the z = 0 plane (d, e, f). The red circles in the slice images denote the real positions of the fluorescent sources. The white arrows in a-c indicate the locations of the reconstructed sources.

Fig. 8
Fig. 8

The schematic illustration of the hybrid optical/micro-CT imaging system. It provides multi-view FMT and micro-CT.

Fig. 9
Fig. 9

Three slices of the micro-CT mouse data, where the yellow square marks the location of the luminescent bead; (a) the coronal view; (b) the sagittal view; (c) the transversal view.

Fig. 10
Fig. 10

The heterogeneous mouse model for the in vivo experiment. (a) The heterogeneous mouse body. (b) The heterogeneous mouse torso used for imaging reconstructions, including heart, lungs, liver, muscle, kidneys, and bone. (c) The surface view of the mouse torso with the front view measurement distribution mapped on it.

Fig. 11
Fig. 11

The iso-surface 3D views of the reconstruction results using the IS_L1 method, the StOMP method and the proposed method. (a) The reconstruction results by the IS_L1 method. (b) The reconstruction results by the StOMP method. (c) The reconstruction results by the proposed method.

Fig. 12
Fig. 12

The comparisons of the reconstruction results for in vivo mouse experiments. The cross-sections of the reconstruction results by different methods are compared to the corresponding micro-CT slices. The crosshairs of the red dashed lines denote the actual source center. (b), (c) and (f) are the lateral cross-sectional views of the reconstruction results at the z = 6.4 mm plane by the IS_L1 method (b), the StOMP method (d) and the proposed method (f) respectively. (a), (d) and (e) are the corresponding micro-CT slices respectively.

Tables (6)

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Table 1 Optical parameters of the heterogeneous phantom.

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Table 2 Quantitative analysis of the reconstruction accuracy from the results of the IS_L1 method, the StOMP method and the proposed method for 12 measurement data sets corrupted by 5% Gaussian noise.

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Table 3 The comparison of the reconstruction efficiency based on different methods. The size of the volumetric mesh equals the number of nodes multiplied by the number of tetrahedral elements.

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Table 4 Quantitative analysis of the reconstructed accuracy from the results of the IS_L1 method, the StOMP method and the proposed method for 4 measurement data sets corrupted by 5% Gaussian noise.

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Table 5 Optical properties of the mouse model.

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Table 6 Comparisons of the reconstruction results between different methods. Location Error denotes the distance between the center of the real source and the center of the reconstructed one.

Equations (16)

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{ [ D x (r) Φ x (r) ] μ ax (r) Φ x (r)=Θδ(r r l ) [ D m (r) Φ m (r) ] μ am (r) Φ m (r)= Φ x (r)η μ af (r) (rΩ) ,
2 D x,m (r) Φ x,m (r)/ n (r)+q Φ x,m (r)=0 (rΩ) ,
[ K x ]{ Φ x }={ S x },
[ K m ]{ Φ m }=[G]{X},
{ Φ m,l }=[ K m,l 1 ][ G l ]{X}=[ D l ]{X}.
{ Φ m,l meas }=[ A l ]{X}.
{Φ}=[A]{X}.
min X E(X)= 1 2 AXΦ 2 2 +λ X 1 ,
min X 1 subject to AX=Φ.
c n1 = A T r n1
J n = I n1 {  K indices corresponding to the largest magnitude entries in vector c n1 }.
Φ p, J n =proj(Φ, A J n )= A J n A J n + Φ,
x p = A J n + Φ.
I={ K indices with the largest magnitude entries of x p },
Φ p,I =proj(Φ, A I )= A I A I + Φ.
r=resid(Φ, A I )=Φproj(Φ, A I ).

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