Abstract

Fluorescence molecular tomography (FMT) is a promising imaging technique that allows in vivo visualization of molecular-level events associated with disease progression and treatment response. Accurate and efficient 3D reconstruction algorithms will facilitate the wide-use of FMT in preclinical research. Here, we utilize L1/2-norm regularization for improving FMT reconstruction. To efficiently solve the nonconvex L1/2-norm penalized problem, we transform it into a weighted L1-norm minimization problem and employ a homotopy-based iterative reweighting algorithm to recover small fluorescent targets. Both simulations on heterogeneous mouse model and in vivo experiments demonstrated that the proposed L1/2-norm method outperformed the comparative L1-norm reconstruction methods in terms of location accuracy, spatial resolution and quantitation of fluorescent yield. Furthermore, simulation analysis showed the robustness of the proposed method, under different levels of measurement noise and number of excitation sources.

© 2015 Optical Society of America

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2014 (6)

K. Radrich, P. Mohajerani, J. Bussemer, M. Schwaiger, A. J. Beer, and V. Ntziachristos, “Limited-projection-angle hybrid fluorescence molecular tomography of multiple molecules,” J. Biomed. Opt. 19(4), 046016 (2014).
[Crossref] [PubMed]

L. Zhao, H. Yang, W. Cong, G. Wang, and X. Intes, “Lp regularization for early gate fluorescence molecular tomography,” Opt. Lett. 39(14), 4156–4159 (2014).
[Crossref] [PubMed]

X. Chen, D. Yang, Q. Zhang, and J. Liang, “L1/2 regularization based numerical method for effective reconstruction of bioluminescence tomography,” J. Appl. Phys. 115(18), 184702 (2014).
[Crossref]

D. Zhu and C. Li, “Nonconvex regularizations in fluorescence molecular tomography for sparsity enhancement,” Phys. Med. Biol. 59(12), 2901–2912 (2014).
[Crossref] [PubMed]

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of Regularization Methods in Fluorescence Molecular Tomography,” Photonics 1(2), 95–109 (2014).
[Crossref]

H. Guo, Y. Hou, X. He, J. Yu, J. Cheng, and X. Pu, “Adaptive hp finite element method for fluorescence molecular tomography with simplified spherical harmonics approximation,” J. Innov. Opt. Heal. Sci. 7(2), 1350057 (2014).
[Crossref]

2013 (6)

M. Asif and J. Romberg, “Fast and accurate algorithms for re-weighted L1-norm minimization,” IEEE Trans. Signal Process. 61(23), 5905–5916 (2013).
[Crossref]

Z. Xue, X. Ma, Q. Zhang, P. Wu, X. Yang, and J. Tian, “Adaptive regularized method based on homotopy for sparse fluorescence tomography,” Appl. Opt. 52(11), 2374–2384 (2013).
[Crossref] [PubMed]

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
[Crossref] [PubMed]

G. Zhan, X. Cao, B. Zhang, F. Liu, J. Luo, and J. Bai, “MAP estimation with structural priors for fluorescence molecular tomography,” Phys. Med. Biol. 58(2), 351–372 (2013).
[Crossref] [PubMed]

M. Solomon, R. E. Nothdruft, W. Akers, W. B. Edwards, K. Liang, B. Xu, G. P. Suddlow, H. Deghani, Y. C. Tai, A. T. Eggebrecht, S. Achilefu, and J. P. Culver, “Multimodal fluorescence-mediated tomography and SPECT/CT for small-animal imaging,” J. Nucl. Med. 54(4), 639–646 (2013).
[Crossref] [PubMed]

J. Chamorro-Servent, J. F. Abascal, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, M. Desco, and J. J. Vaquero, “Use of Split Bregman denoising for iterative reconstruction in fluorescence diffuse optical tomography,” J. Biomed. Opt. 18(7), 076016 (2013).
[Crossref] [PubMed]

2012 (6)

H. Yi, D. Chen, X. Qu, K. Peng, X. Chen, Y. Zhou, J. Tian, and J. Liang, “Multilevel, hybrid regularization method for reconstruction of fluorescent molecular tomography,” Appl. Opt. 51(7), 975–986 (2012).
[Crossref] [PubMed]

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

A. Behrooz, H. M. Zhou, A. A. Eftekhar, and A. Adibi, “Total variation regularization for 3D reconstruction in fluorescence tomography: experimental phantom studies,” Appl. Opt. 51(34), 8216–8227 (2012).
[PubMed]

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. Methods 9(6), 615–620 (2012).
[Crossref] [PubMed]

J. Zeng, J. Fang, and Z. Xu, “Sparse SAR imaging based on L1/2 regularization,” Sci. China. Inf. Sci. 55(8), 1755–1775 (2012).

Z. Xu, H. Guo, Y. Wang, and H. Zhang, “Representative of L1/2 Regularization among Lq (0<q<1) Regularizations: an Experimental Study Based on Phase Diagram,” Acta Automat. Sinica 38(7), 1225–1228 (2012).
[Crossref]

2011 (3)

2010 (6)

S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
[Crossref] [PubMed]

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15(4), 040503 (2010).
[Crossref] [PubMed]

M. Freiberger, C. Clason, and H. Scharfetter, “Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach,” Appl. Opt. 49(19), 3741–3747 (2010).
[Crossref] [PubMed]

H. Zhang, Y. Wang, X. Chang, and Z. Xu, “L1/2 regularization,” Sci. China Ser. E 40(3), 412–422 (2010).

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18(8), 8630–8646 (2010).
[Crossref] [PubMed]

J. C. Baritaux, K. Hassler, and M. Unser, “An efficient numerical method for general Lp regularization in fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29(4), 1075–1087 (2010).
[Crossref] [PubMed]

2009 (4)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

G. Gasso, A. Rakotomamonjy, and S. Canu, “Recovering sparse signals with a certain family of nonconvex penalties and DC programming,” IEEE Trans. Signal Process. 57(12), 4686–4698 (2009).
[Crossref]

D. Wang, X. Liu, Y. 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]

A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, “A matrix-free algorithm for multiple wavelength fluorescence tomography,” Opt. Express 17(5), 3025–3035 (2009).
[Crossref] [PubMed]

2007 (4)

X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15(26), 18300–18317 (2007).
[Crossref] [PubMed]

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
[Crossref] [PubMed]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
[Crossref] [PubMed]

R. Chartrand, “Exact reconstruction of sparse signals via nonconvex minimization,” IEEE Signal Process. Lett. 14(10), 707–710 (2007).
[Crossref]

2006 (1)

2005 (3)

A. Cong and G. Wang, “A finite-element-based reconstruction method for 3D fluorescence tomography,” Opt. Express 13(24), 9847–9857 (2005).
[Crossref] [PubMed]

X. Montet, V. Ntziachristos, J. Grimm, and R. Weissleder, “Tomographic fluorescence mapping of tumor targets,” Cancer Res. 65(14), 6330–6336 (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]

2004 (1)

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A. 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

2003 (1)

T. F. Massoud and S. S. Gambhir, “Molecular imaging in living subjects: seeing fundamental biological processes in a new light,” Genes Dev. 17(5), 545–580 (2003).
[Crossref] [PubMed]

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]

Abascal, J. F.

J. Chamorro-Servent, J. F. Abascal, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, M. Desco, and J. J. Vaquero, “Use of Split Bregman denoising for iterative reconstruction in fluorescence diffuse optical tomography,” J. Biomed. Opt. 18(7), 076016 (2013).
[Crossref] [PubMed]

Achilefu, S.

M. Solomon, R. E. Nothdruft, W. Akers, W. B. Edwards, K. Liang, B. Xu, G. P. Suddlow, H. Deghani, Y. C. Tai, A. T. Eggebrecht, S. Achilefu, and J. P. Culver, “Multimodal fluorescence-mediated tomography and SPECT/CT for small-animal imaging,” J. Nucl. Med. 54(4), 639–646 (2013).
[Crossref] [PubMed]

Adibi, A.

Aguirre, J.

J. Chamorro-Servent, J. F. Abascal, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, M. Desco, and J. J. Vaquero, “Use of Split Bregman denoising for iterative reconstruction in fluorescence diffuse optical tomography,” J. Biomed. Opt. 18(7), 076016 (2013).
[Crossref] [PubMed]

Ahn, S.

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

Akers, W.

M. Solomon, R. E. Nothdruft, W. Akers, W. B. Edwards, K. Liang, B. Xu, G. P. Suddlow, H. Deghani, Y. C. Tai, A. T. Eggebrecht, S. Achilefu, and J. P. Culver, “Multimodal fluorescence-mediated tomography and SPECT/CT for small-animal imaging,” J. Nucl. Med. 54(4), 639–646 (2013).
[Crossref] [PubMed]

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. Methods 9(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]

Andersson-Engels, S.

Arridge, S.

J. Chamorro-Servent, J. F. Abascal, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, M. Desco, and J. J. Vaquero, “Use of Split Bregman denoising for iterative reconstruction in fluorescence diffuse optical tomography,” J. Biomed. Opt. 18(7), 076016 (2013).
[Crossref] [PubMed]

Arridge, S. R.

A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, “A matrix-free algorithm for multiple wavelength fluorescence tomography,” Opt. Express 17(5), 3025–3035 (2009).
[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]

Asif, M.

M. Asif and J. Romberg, “Fast and accurate algorithms for re-weighted L1-norm minimization,” IEEE Trans. Signal Process. 61(23), 5905–5916 (2013).
[Crossref]

Axelsson, J.

Bai, J.

G. Zhan, X. Cao, B. Zhang, F. Liu, J. Luo, and J. Bai, “MAP estimation with structural priors for fluorescence molecular tomography,” Phys. Med. Biol. 58(2), 351–372 (2013).
[Crossref] [PubMed]

D. Wang, X. Liu, Y. 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]

X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15(26), 18300–18317 (2007).
[Crossref] [PubMed]

Baikejiang, R.

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of Regularization Methods in Fluorescence Molecular Tomography,” Photonics 1(2), 95–109 (2014).
[Crossref]

Barber, W. C.

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J. C. Baritaux, K. Hassler, and M. Unser, “An efficient numerical method for general Lp regularization in fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29(4), 1075–1087 (2010).
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J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
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G. Gasso, A. Rakotomamonjy, and S. Canu, “Recovering sparse signals with a certain family of nonconvex penalties and DC programming,” IEEE Trans. Signal Process. 57(12), 4686–4698 (2009).
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H. Yi, D. Chen, X. Qu, K. Peng, X. Chen, Y. Zhou, J. Tian, and J. Liang, “Multilevel, hybrid regularization method for reconstruction of fluorescent molecular tomography,” Appl. Opt. 51(7), 975–986 (2012).
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Chen, N.

Chen, X.

X. Chen, D. Yang, Q. Zhang, and J. Liang, “L1/2 regularization based numerical method for effective reconstruction of bioluminescence tomography,” J. Appl. Phys. 115(18), 184702 (2014).
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H. Yi, D. Chen, X. Qu, K. Peng, X. Chen, Y. Zhou, J. Tian, and J. Liang, “Multilevel, hybrid regularization method for reconstruction of fluorescent molecular tomography,” Appl. Opt. 51(7), 975–986 (2012).
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J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57(6), 1459–1476 (2012).
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Clason, C.

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. Methods 9(6), 615–620 (2012).
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S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
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Cong, W.

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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. Methods 9(6), 615–620 (2012).
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Dogdas, B.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
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S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
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Dutta, J.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57(6), 1459–1476 (2012).
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H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
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M. Solomon, R. E. Nothdruft, W. Akers, W. B. Edwards, K. Liang, B. Xu, G. P. Suddlow, H. Deghani, Y. C. Tai, A. T. Eggebrecht, S. Achilefu, and J. P. Culver, “Multimodal fluorescence-mediated tomography and SPECT/CT for small-animal imaging,” J. Nucl. Med. 54(4), 639–646 (2013).
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Eggebrecht, A. T.

M. Solomon, R. E. Nothdruft, W. Akers, W. B. Edwards, K. Liang, B. Xu, G. P. Suddlow, H. Deghani, Y. C. Tai, A. T. Eggebrecht, S. Achilefu, and J. P. Culver, “Multimodal fluorescence-mediated tomography and SPECT/CT for small-animal imaging,” J. Nucl. Med. 54(4), 639–646 (2013).
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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. Methods 9(6), 615–620 (2012).
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Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
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Gaspar, R.

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Gasso, G.

G. Gasso, A. Rakotomamonjy, and S. Canu, “Recovering sparse signals with a certain family of nonconvex penalties and DC programming,” IEEE Trans. Signal Process. 57(12), 4686–4698 (2009).
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Gleason, A.

S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
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Graves, E.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A. 101(33), 12294–12299 (2004).
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Guo, H.

H. Guo, Y. Hou, X. He, J. Yu, J. Cheng, and X. Pu, “Adaptive hp finite element method for fluorescence molecular tomography with simplified spherical harmonics approximation,” J. Innov. Opt. Heal. Sci. 7(2), 1350057 (2014).
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Hargreaves, R.

S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
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Hartman, G.

S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
[Crossref] [PubMed]

Hassler, K.

J. C. Baritaux, K. Hassler, and M. Unser, “An efficient numerical method for general Lp regularization in fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29(4), 1075–1087 (2010).
[Crossref] [PubMed]

He, X.

H. Guo, Y. Hou, X. He, J. Yu, J. Cheng, and X. Pu, “Adaptive hp finite element method for fluorescence molecular tomography with simplified spherical harmonics approximation,” J. Innov. Opt. Heal. Sci. 7(2), 1350057 (2014).
[Crossref]

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. Methods 9(6), 615–620 (2012).
[Crossref] [PubMed]

Hiraoka, M.

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

Ho, G.

S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
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Hoshi, Y.

Hou, Y.

H. Guo, Y. Hou, X. He, J. Yu, J. Cheng, and X. Pu, “Adaptive hp finite element method for fluorescence molecular tomography with simplified spherical harmonics approximation,” J. Innov. Opt. Heal. Sci. 7(2), 1350057 (2014).
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Intes, X.

Iwanczyk, J. S.

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15(4), 040503 (2010).
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Jensen, J.

S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
[Crossref] [PubMed]

Josephson, L.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A. 101(33), 12294–12299 (2004).
[Crossref] [PubMed]

Kossodo, S.

S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
[Crossref] [PubMed]

Leahy, R. M.

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

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007).
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Li, C.

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of Regularization Methods in Fluorescence Molecular Tomography,” Photonics 1(2), 95–109 (2014).
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D. Zhu and C. Li, “Nonconvex regularizations in fluorescence molecular tomography for sparsity enhancement,” Phys. Med. Biol. 59(12), 2901–2912 (2014).
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J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, “Joint L1 and total variation regularization for fluorescence molecular tomography,” Phys. Med. Biol. 57(6), 1459–1476 (2012).
[Crossref] [PubMed]

Li, W.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
[Crossref] [PubMed]

Liang, J.

X. Chen, D. Yang, Q. Zhang, and J. Liang, “L1/2 regularization based numerical method for effective reconstruction of bioluminescence tomography,” J. Appl. Phys. 115(18), 184702 (2014).
[Crossref]

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
[Crossref] [PubMed]

H. Yi, D. Chen, X. Qu, K. Peng, X. Chen, Y. Zhou, J. Tian, and J. Liang, “Multilevel, hybrid regularization method for reconstruction of fluorescent molecular tomography,” Appl. Opt. 51(7), 975–986 (2012).
[Crossref] [PubMed]

Liang, K.

M. Solomon, R. E. Nothdruft, W. Akers, W. B. Edwards, K. Liang, B. Xu, G. P. Suddlow, H. Deghani, Y. C. Tai, A. T. Eggebrecht, S. Achilefu, and J. P. Culver, “Multimodal fluorescence-mediated tomography and SPECT/CT for small-animal imaging,” J. Nucl. Med. 54(4), 639–646 (2013).
[Crossref] [PubMed]

Lin, S. A.

S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
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Lin, Y.

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15(4), 040503 (2010).
[Crossref] [PubMed]

Liu, F.

G. Zhan, X. Cao, B. Zhang, F. Liu, J. Luo, and J. Bai, “MAP estimation with structural priors for fluorescence molecular tomography,” Phys. Med. Biol. 58(2), 351–372 (2013).
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D. Wang, X. Liu, Y. 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).
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Luo, J.

G. Zhan, X. Cao, B. Zhang, F. Liu, J. Luo, and J. Bai, “MAP estimation with structural priors for fluorescence molecular tomography,” Phys. Med. Biol. 58(2), 351–372 (2013).
[Crossref] [PubMed]

Ma, X.

Massoud, T. F.

T. F. Massoud and S. S. Gambhir, “Molecular imaging in living subjects: seeing fundamental biological processes in a new light,” Genes Dev. 17(5), 545–580 (2003).
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Mohajerani, P.

K. Radrich, P. Mohajerani, J. Bussemer, M. Schwaiger, A. J. Beer, and V. Ntziachristos, “Limited-projection-angle hybrid fluorescence molecular tomography of multiple molecules,” J. Biomed. Opt. 19(4), 046016 (2014).
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Montet, X.

X. Montet, V. Ntziachristos, J. Grimm, and R. Weissleder, “Tomographic fluorescence mapping of tumor targets,” Cancer Res. 65(14), 6330–6336 (2005).
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Nalcioglu, O.

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15(4), 040503 (2010).
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Naser, M. A.

Nothdruft, R. E.

M. Solomon, R. E. Nothdruft, W. Akers, W. B. Edwards, K. Liang, B. Xu, G. P. Suddlow, H. Deghani, Y. C. Tai, A. T. Eggebrecht, S. Achilefu, and J. P. Culver, “Multimodal fluorescence-mediated tomography and SPECT/CT for small-animal imaging,” J. Nucl. Med. 54(4), 639–646 (2013).
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Ntziachristos, V.

K. Radrich, P. Mohajerani, J. Bussemer, M. Schwaiger, A. J. Beer, and V. Ntziachristos, “Limited-projection-angle hybrid fluorescence molecular tomography of multiple molecules,” J. Biomed. Opt. 19(4), 046016 (2014).
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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. Methods 9(6), 615–620 (2012).
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X. Montet, V. Ntziachristos, J. Grimm, and R. Weissleder, “Tomographic fluorescence mapping of tumor targets,” Cancer Res. 65(14), 6330–6336 (2005).
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V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A. 101(33), 12294–12299 (2004).
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Patterson, M. S.

Paulsen, K. D.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
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Peterson, J.

S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
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Peterson, J. D.

K. O. Vasquez, C. Casavant, and J. D. Peterson, “Quantitative whole body biodistribution of fluorescent-labeled agents by non-invasive tomographic imaging,” PLoS ONE 6(6), e20594 (2011).
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Pickarski, M.

S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
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Pogue, B. W.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
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Pu, X.

H. Guo, Y. Hou, X. He, J. Yu, J. Cheng, and X. Pu, “Adaptive hp finite element method for fluorescence molecular tomography with simplified spherical harmonics approximation,” J. Innov. Opt. Heal. Sci. 7(2), 1350057 (2014).
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Qin, C.

Qu, X.

Radrich, K.

K. Radrich, P. Mohajerani, J. Bussemer, M. Schwaiger, A. J. Beer, and V. Ntziachristos, “Limited-projection-angle hybrid fluorescence molecular tomography of multiple molecules,” J. Biomed. Opt. 19(4), 046016 (2014).
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S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
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G. Gasso, A. Rakotomamonjy, and S. Canu, “Recovering sparse signals with a certain family of nonconvex penalties and DC programming,” IEEE Trans. Signal Process. 57(12), 4686–4698 (2009).
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Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15(4), 040503 (2010).
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Schellenberger, E. A.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A. 101(33), 12294–12299 (2004).
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K. Radrich, P. Mohajerani, J. Bussemer, M. Schwaiger, A. J. Beer, and V. Ntziachristos, “Limited-projection-angle hybrid fluorescence molecular tomography of multiple molecules,” J. Biomed. Opt. 19(4), 046016 (2014).
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Srinivasan, S.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
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Tian, J.

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J. Chamorro-Servent, J. F. Abascal, J. Aguirre, S. Arridge, T. Correia, J. Ripoll, M. Desco, and J. J. Vaquero, “Use of Split Bregman denoising for iterative reconstruction in fluorescence diffuse optical tomography,” J. Biomed. Opt. 18(7), 076016 (2013).
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K. O. Vasquez, C. Casavant, and J. D. Peterson, “Quantitative whole body biodistribution of fluorescent-labeled agents by non-invasive tomographic imaging,” PLoS ONE 6(6), e20594 (2011).
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D. Wang, X. Liu, Y. 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).
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Z. Xu, H. Guo, Y. Wang, and H. Zhang, “Representative of L1/2 Regularization among Lq (0<q<1) Regularizations: an Experimental Study Based on Phase Diagram,” Acta Automat. Sinica 38(7), 1225–1228 (2012).
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H. Zhang, Y. Wang, X. Chang, and Z. Xu, “L1/2 regularization,” Sci. China Ser. E 40(3), 412–422 (2010).

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X. Montet, V. Ntziachristos, J. Grimm, and R. Weissleder, “Tomographic fluorescence mapping of tumor targets,” Cancer Res. 65(14), 6330–6336 (2005).
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V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A. 101(33), 12294–12299 (2004).
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J. Zeng, J. Fang, and Z. Xu, “Sparse SAR imaging based on L1/2 regularization,” Sci. China. Inf. Sci. 55(8), 1755–1775 (2012).

Z. Xu, H. Guo, Y. Wang, and H. Zhang, “Representative of L1/2 Regularization among Lq (0<q<1) Regularizations: an Experimental Study Based on Phase Diagram,” Acta Automat. Sinica 38(7), 1225–1228 (2012).
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H. Zhang, Y. Wang, X. Chang, and Z. Xu, “L1/2 regularization,” Sci. China Ser. E 40(3), 412–422 (2010).

Xue, Z.

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H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
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X. Chen, D. Yang, Q. Zhang, and J. Liang, “L1/2 regularization based numerical method for effective reconstruction of bioluminescence tomography,” J. Appl. Phys. 115(18), 184702 (2014).
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V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. U.S.A. 101(33), 12294–12299 (2004).
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H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
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D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of Regularization Methods in Fluorescence Molecular Tomography,” Photonics 1(2), 95–109 (2014).
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Zeng, J.

J. Zeng, J. Fang, and Z. Xu, “Sparse SAR imaging based on L1/2 regularization,” Sci. China. Inf. Sci. 55(8), 1755–1775 (2012).

Zhan, G.

G. Zhan, X. Cao, B. Zhang, F. Liu, J. Luo, and J. Bai, “MAP estimation with structural priors for fluorescence molecular tomography,” Phys. Med. Biol. 58(2), 351–372 (2013).
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Zhang, B.

G. Zhan, X. Cao, B. Zhang, F. Liu, J. Luo, and J. Bai, “MAP estimation with structural priors for fluorescence molecular tomography,” Phys. Med. Biol. 58(2), 351–372 (2013).
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D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18(8), 8630–8646 (2010).
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Zhang, H.

Z. Xu, H. Guo, Y. Wang, and H. Zhang, “Representative of L1/2 Regularization among Lq (0<q<1) Regularizations: an Experimental Study Based on Phase Diagram,” Acta Automat. Sinica 38(7), 1225–1228 (2012).
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H. Zhang, Y. Wang, X. Chang, and Z. Xu, “L1/2 regularization,” Sci. China Ser. E 40(3), 412–422 (2010).

Zhang, J.

S. Kossodo, M. Pickarski, S. A. Lin, A. Gleason, R. Gaspar, C. Buono, G. Ho, A. Blusztajn, G. Cuneo, J. Zhang, J. Jensen, R. Hargreaves, P. Coleman, G. Hartman, M. Rajopadhye, T. Duong, C. Sur, W. Yared, J. Peterson, and B. Bednar, “Dual in vivo quantification of integrin-targeted and protease-activated agents in cancer using fluorescence molecular tomography (FMT),” Mol. Imaging Biol. 12(5), 488–499 (2010).
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X. Chen, D. Yang, Q. Zhang, and J. Liang, “L1/2 regularization based numerical method for effective reconstruction of bioluminescence tomography,” J. Appl. Phys. 115(18), 184702 (2014).
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Zhao, L.

Zhao, Y.

D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of Regularization Methods in Fluorescence Molecular Tomography,” Photonics 1(2), 95–109 (2014).
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D. Zhu and C. Li, “Nonconvex regularizations in fluorescence molecular tomography for sparsity enhancement,” Phys. Med. Biol. 59(12), 2901–2912 (2014).
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D. Zhu, Y. Zhao, R. Baikejiang, Z. Yuan, and C. Li, “Comparison of Regularization Methods in Fluorescence Molecular Tomography,” Photonics 1(2), 95–109 (2014).
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Zhu, S.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
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D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18(8), 8630–8646 (2010).
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Acta Automat. Sinica (1)

Z. Xu, H. Guo, Y. Wang, and H. Zhang, “Representative of L1/2 Regularization among Lq (0<q<1) Regularizations: an Experimental Study Based on Phase Diagram,” Acta Automat. Sinica 38(7), 1225–1228 (2012).
[Crossref]

Appl. Opt. (4)

Biomed. Opt. Express (2)

Cancer Res. (1)

X. Montet, V. Ntziachristos, J. Grimm, and R. Weissleder, “Tomographic fluorescence mapping of tumor targets,” Cancer Res. 65(14), 6330–6336 (2005).
[Crossref] [PubMed]

Commun. Numer. Methods Eng. (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[Crossref] [PubMed]

Genes Dev. (1)

T. F. Massoud and S. S. Gambhir, “Molecular imaging in living subjects: seeing fundamental biological processes in a new light,” Genes Dev. 17(5), 545–580 (2003).
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IEEE Signal Process. Lett. (1)

R. Chartrand, “Exact reconstruction of sparse signals via nonconvex minimization,” IEEE Signal Process. Lett. 14(10), 707–710 (2007).
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IEEE Trans. Image Process. (1)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16(12), 2992–3004 (2007).
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IEEE Trans. Inf. Technol. Biomed. (1)

D. Wang, X. Liu, Y. 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. Med. Imaging (1)

J. C. Baritaux, K. Hassler, and M. Unser, “An efficient numerical method for general Lp regularization in fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29(4), 1075–1087 (2010).
[Crossref] [PubMed]

IEEE Trans. Signal Process. (2)

G. Gasso, A. Rakotomamonjy, and S. Canu, “Recovering sparse signals with a certain family of nonconvex penalties and DC programming,” IEEE Trans. Signal Process. 57(12), 4686–4698 (2009).
[Crossref]

M. Asif and J. Romberg, “Fast and accurate algorithms for re-weighted L1-norm minimization,” IEEE Trans. Signal Process. 61(23), 5905–5916 (2013).
[Crossref]

J. Appl. Phys. (1)

X. Chen, D. Yang, Q. Zhang, and J. Liang, “L1/2 regularization based numerical method for effective reconstruction of bioluminescence tomography,” J. Appl. Phys. 115(18), 184702 (2014).
[Crossref]

J. Biomed. Opt. (4)

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, “Reconstruction algorithms based on l1-norm and l2-norm for two imaging models of fluorescence molecular tomography: a comparative study,” J. Biomed. Opt. 18(5), 056013 (2013).
[Crossref] [PubMed]

K. Radrich, P. Mohajerani, J. Bussemer, M. Schwaiger, A. J. Beer, and V. Ntziachristos, “Limited-projection-angle hybrid fluorescence molecular tomography of multiple molecules,” J. Biomed. Opt. 19(4), 046016 (2014).
[Crossref] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

(a) Torso of the mouse atlas model with a cylindrical fluorescent targets in the liver, (b) Forward mesh and the simulated photon distribution on surface. (c) Point excitation sources on the plane of Z=16.4mm . The 18 black points denotes the point excitation sources. For each excitation source, fluorescence data is detected at the opposite side with a 120° FOV.

Fig. 2
Fig. 2

Reconstruction results in single-target case. (a) Cross-section views of the reconstructions by six comparative methods at the axial slice where the center of the real fluorescent target (denoted by the small black circle) is located; (b) 3D renderings of the results. The red cylinder is the real target while the green zone denotes the reconstructed target.

Fig. 3
Fig. 3

Illustration for simulation settings. (a) shows the tested target positions, where P1, P2 P3, and P4 correspond to Y = 8.4, 10.4, 12.4 and 14.4 mm, respectively. (b) shows different positions of excited nodes, where Z0 = 16.4mm, Z1 = 12.4mm, Z2 = 20.4mm and Z3 = 24.4mm.

Fig. 4
Fig. 4

Comparison results for reconstruction single-target at different depths, in terms of (a) location error, (b) fluorescent yield, and (c) full width at half maximum.

Fig. 5
Fig. 5

Comparison result for reconstruction a single-target with the excitation sources located at different planes, in terms of (a) location error, (b) fluorescent yield, and (c) full width at half maximum.

Fig. 6
Fig. 6

Illustrations of variations of error of RFY (a) and LE (b) obtained at different noise levels. Subfigure (a) and (b) correspond to absolute quantitative error of reconstructed fluorescent yield and location error, respectively.

Fig. 7
Fig. 7

Illustration of variations of R.FY (a) and LE (b) with different number of excitation nodes. Subfigures (a) and (b) correspond to absolute quantitative error of reconstructed fluorescent yield and location error, respectively.

Fig. 8
Fig. 8

Reconstruction results of two comparative methods for double targets with 4.5mm separation. Subfigure (a) shows the forward mesh and the photon distribution; (d) shows the digital mouse model with two targets with 4.5mm separation; (b) and (e) correspond to the results of IRW-L1/2, (c) and (f) present the results of Homotopy-L1; (b) and (c) correspond to the transverse view at the plane of z = 16.4mm, where the small black circle denotes the true source; (e) and (f) are the corresponding 3D view, where the red cylinder denotes the true target while the green zone is the reconstructed target.

Fig. 9
Fig. 9

Reconstruction results of two comparative methods for double fluorescent targets with 3mm separation. Subfigure (a) shows the forward mesh and the photon distribution; (d) shows the digital mouse model with two targets with 3mm separation; (b) and (e) correspond to the results of IRW-L1/2; (c) and (f) present the results of Homotopy-L1. (b) and (c) correspond to the transverse view at the plane of z = 16.4mm, where the small black circle denotes the actual source; (e) and (f) illustrate the 3D view of the reconstruction, where the red cylinder denotes the true target while the green zone is the reconstructed target.

Fig. 10
Fig. 10

Reconstructed results of in vivo experiment on BALB/C mouse with implanted fluorophore. (a) shows the forward mesh and the measurements mapped on surface, (e) shows the segmented torso with implanted fluorophore in a glass tube; (b) and (f) are the results of IRW-L1/2; (c) and (g) are the results of Homotopy-L1; (d) and (e) are the results of IVTCG. Subfigures (b), (c) and (d) correspond to the cross-section views, where the small black circle denotes the true source; (f), (g) and (h) are the corresponding 3D view, where the red cylinder is the true target while the green zone denotes the reconstructed one.

Fig. 11
Fig. 11

Transverse views of the result by IRW-L1/2 and the comparison with the corresponding CT slices. The area surrounded by the green lines denotes the true target determined by CT.

Tables (6)

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Table 1 Optical parameters for the mouse organs

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Table 2 Quantitative results in single-target experiment (Best results are in bold)

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Table 3 Quantitative results for reconstruction of two targets with 4.5mm separation

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Table 4 Quantitative results for reconstruction of two targets with 3mm separation

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Table 5 Optical parameters of the mouse organs at 670 and 710 nm

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Table 6 Quantitative results of in vivo experiment

Equations (13)

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{ ( D x (r) Φ x (r)) μ ax (r) Φ x (r)= Θ s δ(r r l ) ( D m (r) Φ m (r)) μ am (r) Φ m (r)= Φ x (r)η μ af (r) ,rΩ
AX=Φ
min X { 1 2 AXΦ 2 2 +λ X P P }
min X { 1 2 AXΦ 2 2 +λ i=1 n | x i | 1/2 }
min X { 1 2 AXΦ 2 2 +λ i=1 n (1/ | x i | )| x i |}
X t+1 =arg min X { 1 2 AXΦ 2 2 + i n w i | x i | }
min X { 1 2 AXΦ 2 2 + i n ((1ε) w t +ε w t+1 )| x i | }
a i T (A X * -Φ)=-((1-ε) w t +ε w t+1 ) z i for all iΓ
| a i T (A X * -Φ) |<(1-ε) w t +ε w t+1 , for all i Γ c
A Γ T (A X * Φ)+δ A Γ T AX=((1ε) W t +ε W t+1 )z+δ( W t W t+1 )z,
a i T (A X * Φ) pi +δ a i T Ax di (1ε) w t +ε w t+1 qi +δ ( w t + w t+1 ) si
X={ ( A Γ T A Γ ) 1 ( W t W t+1 )z on Γ 0 ...... otherwise. .
δ + = min i Γ c ( q i p i s i + d i , q i p i s i + d i ) + , δ =min ( X i * x i ) +

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