Abstract

Through restoration of the light source information in small animals in vivo, optical molecular imaging, such as fluorescence molecular tomography (FMT) and bioluminescence tomography (BLT), can depict biological and physiological changes observed using molecular probes. A priori information plays an indispensable role in tomographic reconstruction. As a type of a priori information, the sparsity characteristic of the light source has not been sufficiently considered to date. In this paper, we introduce a compressed sensing method to develop a new tomographic algorithm for spectrally-resolved bioluminescence tomography. This method uses the nature of the source sparsity to improve the reconstruction quality with a regularization implementation. Based on verification of the inverse crime, the proposed algorithm is validated with Monte Carlo-based synthetic data and the popular Tikhonov regularization method. Testing with different noise levels and single/multiple source settings at different depths demonstrates the improved performance of this algorithm. Experimental reconstruction with a mouse-shaped phantom further shows the potential of the proposed algorithm.

© 2009 Optical Society of America

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2008 (1)

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

2007 (3)

Y. Lv, J. Tian,W. Cong, and G. Wang, "Experimental study on bioluminescence tomography with multimodality fusion," Int. J. Biomed. Img. 1,86741 (2007).

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

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

2006 (8)

W. Cong, K. Durairaj, L. V. Wang, and G. Wang, "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33,679-686 (2006).
[CrossRef] [PubMed]

E. J. Candès, J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pur. Appl. Math. 59,1207-1223 (2006).
[CrossRef]

E. J. Candès, "Compressive sampling," inProc. of the International Congress of Mathematicians, Madrid, Spain 3,1433-1452 (2006).

G. Wang, H. Shen, K. Durairaj, X. Qian, and W. Cong, "The first bioluminescence tomography system for simultaneous acquisition of multiview and multispectral data," Int. J. Biomed. Img.2006:Article ID 58601, (2006).

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

D. Donoho, "For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution," Commun. Pur. Appl. Math. 59,797-829 (2006).
[CrossRef]

G. Wang, H. Shen, W. Cong, S. Zhao, and G. Wei, "Temperature-modulated bioluminescence tomography," Opt. Express 14,7852-7871 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7852.
[CrossRef] [PubMed]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, "Spectrally resolved bioluminescence optical tomography," Opt. Lett. 31,365-367 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=ol-31-3-365.
[CrossRef] [PubMed]

2005 (7)

W. 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. Express 13,6756-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-18-6756.
[CrossRef] [PubMed]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [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. 202,323-345 (2005).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50,R1-R43 (2005).
[CrossRef]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weisslder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23,313-320 (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. 50,4225-4241 (2005).
[CrossRef] [PubMed]

C. Kuo, O. Coquoz, T. Troy, D. Zwarg, and B. Rice, "Bioluminescent tomography for in vivo localization and quantification of luminescent sources from a multiple-view imaging system," Mol. Img. 4,370 (2005).

2004 (3)

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

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

X. Gu, Q. Zhang, L. Larcom, and H. Jiang, "Three-dimensional bioluminescence tomography with model-based reconstruction," Opt. Express 12,3996-4000 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-17-3996.
[CrossRef] [PubMed]

2003 (2)

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

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. F. Meinel, "Development of the first bioluminescence CT scanner," Radiology 566,229 (2003).

2002 (3)

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

S. Bhaumik and S. S. Gambhir, "Optical imaging of renilla luciferase reporter gene expression in living mice," Proc. Natl. Acad. Sci. USA 99,377-382 (2002).
[CrossRef]

S. G. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process. 41,3397-3415 (2002).
[CrossRef]

2001 (1)

R. Weissleder and U. Mahmood, "Molecular imaing," Radiology 219,316-333 (2001).
[PubMed]

2000 (1)

1995 (1)

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22,1779- 1792 (1995).
[CrossRef] [PubMed]

1994 (1)

D. Donoho and I. Johnstone, "Ideal spatial adaption via wavelet shrinkage," Biometrika 81,425-455 (1994).
[CrossRef]

1993 (1)

1992 (1)

L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," J. Phys. D 60,259-268 (1992).
[CrossRef]

Alexandrakis, G.

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

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50,R1-R43 (2005).
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22,1779- 1792 (1995).
[CrossRef] [PubMed]

Bachmann, M. H.

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

Bading, J. R.

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

Bhaumik, S.

S. Bhaumik and S. S. Gambhir, "Optical imaging of renilla luciferase reporter gene expression in living mice," Proc. Natl. Acad. Sci. USA 99,377-382 (2002).
[CrossRef]

Candès, E. J.

E. J. Candès, J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pur. Appl. Math. 59,1207-1223 (2006).
[CrossRef]

E. J. Candès, "Compressive sampling," inProc. of the International Congress of Mathematicians, Madrid, Spain 3,1433-1452 (2006).

Chatziioannou, A. F.

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

Chaudhari, A. J.

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

Cherry, S. R.

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

Cong, A.

Cong, W.

Y. Lv, J. Tian,W. Cong, and G. Wang, "Experimental study on bioluminescence tomography with multimodality fusion," Int. J. Biomed. Img. 1,86741 (2007).

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

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

W. Cong, K. Durairaj, L. V. Wang, and G. Wang, "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33,679-686 (2006).
[CrossRef] [PubMed]

G. Wang, H. Shen, K. Durairaj, X. Qian, and W. Cong, "The first bioluminescence tomography system for simultaneous acquisition of multiview and multispectral data," Int. J. Biomed. Img.2006:Article ID 58601, (2006).

G. Wang, H. Shen, W. Cong, S. Zhao, and G. Wei, "Temperature-modulated bioluminescence tomography," Opt. Express 14,7852-7871 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7852.
[CrossRef] [PubMed]

W. 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. Express 13,6756-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-18-6756.
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

Contag, C. H.

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

Conti, P. S.

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

Coquoz, O.

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

C. Kuo, O. Coquoz, T. Troy, D. Zwarg, and B. Rice, "Bioluminescent tomography for in vivo localization and quantification of luminescent sources from a multiple-view imaging system," Mol. Img. 4,370 (2005).

Darvas, F.

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

Davis, S. C.

Dehghani, H.

Delpy, D. T.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22,1779- 1792 (1995).
[CrossRef] [PubMed]

Dinkelborg, L. M.

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

Donoho, D.

D. Donoho, "For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution," Commun. Pur. Appl. Math. 59,797-829 (2006).
[CrossRef]

D. Donoho and I. Johnstone, "Ideal spatial adaption via wavelet shrinkage," Biometrika 81,425-455 (1994).
[CrossRef]

Durairaj, K.

W. Cong, K. Durairaj, L. V. Wang, and G. Wang, "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33,679-686 (2006).
[CrossRef] [PubMed]

G. Wang, H. Shen, K. Durairaj, X. Qian, and W. Cong, "The first bioluminescence tomography system for simultaneous acquisition of multiview and multispectral data," Int. J. Biomed. Img.2006:Article ID 58601, (2006).

Fatemi, E.

L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," J. Phys. D 60,259-268 (1992).
[CrossRef]

Gambhir, S. S.

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

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

S. Bhaumik and S. S. Gambhir, "Optical imaging of renilla luciferase reporter gene expression in living mice," Proc. Natl. Acad. Sci. USA 99,377-382 (2002).
[CrossRef]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50,R1-R43 (2005).
[CrossRef]

Gu, X.

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50,R1-R43 (2005).
[CrossRef]

Hielscher, A. H.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on the radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202,323-345 (2005).
[CrossRef]

Hiraoka, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22,1779- 1792 (1995).
[CrossRef] [PubMed]

Hoffman, E. A.

W. 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. Express 13,6756-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-18-6756.
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. F. Meinel, "Development of the first bioluminescence CT scanner," Radiology 566,229 (2003).

Jiang, H.

Jiang, M.

Jiang, S.

Johnstone, I.

D. Donoho and I. Johnstone, "Ideal spatial adaption via wavelet shrinkage," Biometrika 81,425-455 (1994).
[CrossRef]

Klose, A. D.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on the radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202,323-345 (2005).
[CrossRef]

Kumar, D.

Kuo, C.

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

C. Kuo, O. Coquoz, T. Troy, D. Zwarg, and B. Rice, "Bioluminescent tomography for in vivo localization and quantification of luminescent sources from a multiple-view imaging system," Mol. Img. 4,370 (2005).

Larcom, L.

Leahy, R. M.

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

Li, H.

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

Li, Y.

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

Liu, Y.

Luo, J.

Lv, Y.

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

Y. Lv, J. Tian,W. Cong, and G. Wang, "Experimental study on bioluminescence tomography with multimodality fusion," Int. J. Biomed. Img. 1,86741 (2007).

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

Mahmood, U.

R. Weissleder and U. Mahmood, "Molecular imaing," Radiology 219,316-333 (2001).
[PubMed]

Mallat, S. G.

S. G. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process. 41,3397-3415 (2002).
[CrossRef]

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. 17,545-580 (2003).
[CrossRef] [PubMed]

McCray, P. B.

McLennan, G.

Meinel, J. F.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. F. Meinel, "Development of the first bioluminescence CT scanner," Radiology 566,229 (2003).

Moats, R. A.

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

Ntziachristos, V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weisslder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23,313-320 (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. 202,323-345 (2005).
[CrossRef]

Osher, S.

L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," J. Phys. D 60,259-268 (1992).
[CrossRef]

Patterson, M. S.

Paulsen, K. D.

Pogue, B. W.

Prahl, S. A.

Qian, X.

G. Wang, H. Shen, K. Durairaj, X. Qian, and W. Cong, "The first bioluminescence tomography system for simultaneous acquisition of multiview and multispectral data," Int. J. Biomed. Img.2006:Article ID 58601, (2006).

Qin, C.

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

Rannou, F. R.

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

Rice, B.

C. Kuo, O. Coquoz, T. Troy, D. Zwarg, and B. Rice, "Bioluminescent tomography for in vivo localization and quantification of luminescent sources from a multiple-view imaging system," Mol. Img. 4,370 (2005).

Rice, B. W.

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

Ripoll, J.

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

Romberg, J. K.

E. J. Candès, J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pur. Appl. Math. 59,1207-1223 (2006).
[CrossRef]

Roy, R.

Rudin, L.

L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," J. Phys. D 60,259-268 (1992).
[CrossRef]

Schweiger, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22,1779- 1792 (1995).
[CrossRef] [PubMed]

Sevick-Muraca, E. M.

Shen, H.

G. Wang, H. Shen, K. Durairaj, X. Qian, and W. Cong, "The first bioluminescence tomography system for simultaneous acquisition of multiview and multispectral data," Int. J. Biomed. Img.2006:Article ID 58601, (2006).

G. Wang, H. Shen, W. Cong, S. Zhao, and G. Wei, "Temperature-modulated bioluminescence tomography," Opt. Express 14,7852-7871 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7852.
[CrossRef] [PubMed]

Smith, D. J.

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

Suter, M.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. F. Meinel, "Development of the first bioluminescence CT scanner," Radiology 566,229 (2003).

Tao, T.

E. J. Candès, J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pur. Appl. Math. 59,1207-1223 (2006).
[CrossRef]

Tian, J.

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

Y. Lv, J. Tian,W. Cong, and G. Wang, "Experimental study on bioluminescence tomography with multimodality fusion," Int. J. Biomed. Img. 1,86741 (2007).

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

Troy, T.

C. Kuo, O. Coquoz, T. Troy, D. Zwarg, and B. Rice, "Bioluminescent tomography for in vivo localization and quantification of luminescent sources from a multiple-view imaging system," Mol. Img. 4,370 (2005).

Troy, T. L.

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

van Bruggen, N.

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

van Gemert, M. J. C.

Wang, G.

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

Y. Lv, J. Tian,W. Cong, and G. Wang, "Experimental study on bioluminescence tomography with multimodality fusion," Int. J. Biomed. Img. 1,86741 (2007).

G. Wang, H. Shen, W. Cong, S. Zhao, and G. Wei, "Temperature-modulated bioluminescence tomography," Opt. Express 14,7852-7871 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7852.
[CrossRef] [PubMed]

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

W. Cong, K. Durairaj, L. V. Wang, and G. Wang, "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33,679-686 (2006).
[CrossRef] [PubMed]

G. Wang, H. Shen, K. Durairaj, X. Qian, and W. Cong, "The first bioluminescence tomography system for simultaneous acquisition of multiview and multispectral data," Int. J. Biomed. Img.2006:Article ID 58601, (2006).

W. 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. Express 13,6756-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-18-6756.
[CrossRef] [PubMed]

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

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. F. Meinel, "Development of the first bioluminescence CT scanner," Radiology 566,229 (2003).

Wang, L. V.

W. Cong, K. Durairaj, L. V. Wang, and G. Wang, "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33,679-686 (2006).
[CrossRef] [PubMed]

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

W. 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. Express 13,6756-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-18-6756.
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. F. Meinel, "Development of the first bioluminescence CT scanner," Radiology 566,229 (2003).

Wei, G.

Weisslder, R.

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

Weissleder, R.

R. Weissleder and U. Mahmood, "Molecular imaing," Radiology 219,316-333 (2001).
[PubMed]

Welch, A. J.

Willmann, J. K.

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

Xu, H.

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

Xu, M.

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

Yang, W.

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

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

Zabner, J.

Zhang, Q.

Zhang, Z.

S. G. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process. 41,3397-3415 (2002).
[CrossRef]

Zhao, S.

Zhu, F.

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

Zwarg, D.

C. Kuo, O. Coquoz, T. Troy, D. Zwarg, and B. Rice, "Bioluminescent tomography for in vivo localization and quantification of luminescent sources from a multiple-view imaging system," Mol. Img. 4,370 (2005).

Acad. Radiol. (1)

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method," Acad. Radiol. 11,1029-1038 (2004).
[CrossRef] [PubMed]

Annu. Rev. Biomed. Eng. (1)

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

Appl. Opt. (1)

Biometrika (1)

D. Donoho and I. Johnstone, "Ideal spatial adaption via wavelet shrinkage," Biometrika 81,425-455 (1994).
[CrossRef]

Commun. Pur. Appl. Math. (2)

E. J. Candès, J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pur. Appl. Math. 59,1207-1223 (2006).
[CrossRef]

D. Donoho, "For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution," Commun. Pur. Appl. Math. 59,797-829 (2006).
[CrossRef]

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. 17,545-580 (2003).
[CrossRef] [PubMed]

IEEE Trans. Signal Process. (1)

S. G. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process. 41,3397-3415 (2002).
[CrossRef]

Int. J. Biomed. Img. (2)

G. Wang, H. Shen, K. Durairaj, X. Qian, and W. Cong, "The first bioluminescence tomography system for simultaneous acquisition of multiview and multispectral data," Int. J. Biomed. Img.2006:Article ID 58601, (2006).

Y. Lv, J. Tian,W. Cong, and G. Wang, "Experimental study on bioluminescence tomography with multimodality fusion," Int. J. Biomed. Img. 1,86741 (2007).

J. Biomed. Opt. (1)

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

J. Comput. Phys. (1)

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on the radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202,323-345 (2005).
[CrossRef]

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

J. Phys. D (1)

L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," J. Phys. D 60,259-268 (1992).
[CrossRef]

Med. Phys. (3)

W. Cong, K. Durairaj, L. V. Wang, and G. Wang, "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33,679-686 (2006).
[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. 22,1779- 1792 (1995).
[CrossRef] [PubMed]

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

Mol. Img. (1)

C. Kuo, O. Coquoz, T. Troy, D. Zwarg, and B. Rice, "Bioluminescent tomography for in vivo localization and quantification of luminescent sources from a multiple-view imaging system," Mol. Img. 4,370 (2005).

Nat. Biotechnol. (1)

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

Nat. Rev. Drug Discovery (1)

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

Opt. Express (4)

Opt. Lett. (1)

Phys. Med. Biol. (4)

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

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50,R1-R43 (2005).
[CrossRef]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [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. 50,4225-4241 (2005).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

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Michael Lustig, Sparse MRI, PhD thesis, Stanford University, 2008.

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Figures (11)

Fig. 1.
Fig. 1.

Verification to the inverse crime problem. The discretizations of the cubic domain in Figs. (a), (b) and (c) were used to generate the synthetic data using the finite element method (Figs. (a) and (b)) and Monte Carlo method (Fig. (c)). Figures (d), (e) and (f) are the reconstructed results respectively when the real source central position is at (0.0,0.0,0.0). The synthetic data on the top surface is used in reconstruction.

Fig. 2.
Fig. 2.

Quantitative comparison between HEX-, TET- and MC-based synthetic data at 650nm

Fig. 3.
Fig. 3.

BLT reconstructions when the real source central position is at (0.0,0.0,0.0) and 106 photons are tracked to generate the synthetic data at 600nm. Figures (a), (b) and (c) are the photons distribution at 600nm, 650nm and 700nm. Figures (d), (e) and (f) are the reconstructed results without regularization method and with l 2 and l 1 methods.

Fig. 4.
Fig. 4.

BLT reconstructions when the real source central position is at (0.0,0.0,0.0) and 104 photons are tracked to generate the synthetic data at 600nm. Figures (a), (b) and (c) are the photons distribution at 600nm, 650nm and 700nm. Figures (d), (e) and (f) are the reconstructed results without regularization method and with l 2 and l 1 methods.

Fig. 5.
Fig. 5.

Dual source BLT reconstructions when the real source central positions is at (-3.0,0.0,3.0) and (3.0,0.0,3.0). Figures (a), (b) and (c) are the corresponding reconstructed results without regularization and with l 2 and l 1 methods when 106 photons are tracked at 600nm. Figures (d), (e) and (f) are the counterparts corresponding to (a), (b) and (c) when 104 photons are tracked at 600nm.

Fig. 6.
Fig. 6.

Dual source BLT reconstructions when the real source central positions is at (-3.0,0.0,0.0) and (3.0,0.0,0.0). Figures (a), (b) and (c) are the corresponding reconstructed results without regularization and with l 2 and l 1 methods when 106 photons are tracked at 600nm. Figures (d), (e) and (f) are the counterparts corresponding to (a), (b) and (c) when 104 photons are tracked at 600nm.

Fig. 7.
Fig. 7.

Dual source BLT reconstructions with the heterogeneous media when the real source central positions is at (-3.0,0.0,0.0) and (3.0,0.0,0.0). Figures (a), (b) and (c) are the corresponding reconstructed results without regularization and with l 2 and l 1 methods when 106 photons are tracked at 600nm. Figures (d), (e) and (f) are the counterparts corresponding to (a), (b) and (c) when 104 photons are tracked at 600nm.

Fig. 8.
Fig. 8.

Triple source BLT reconstructions with the homogeneous media when the real source central positions is at (-2.0,2.0,4.0) , (0.0,0.0,0.0), and (3.0,-3.0,2.0). Figures (a), (b) and (c) are the corresponding reconstructed results without regularization and with l 2 and l 1 methods when 104 photons are tracked at 600nm.

Fig. 9.
Fig. 9.

Surface radiance images of the mouse-shaped phantom with embedded fiber optic source using GFP and DsRed emission filters.

Fig. 10.
Fig. 10.

Experimental BLT reconstructions with mouse-shaped phantom. Figure (a) are the volumetric mesh used in reconstruction. Figures (b), (d) and (d) show the reconstructed results without regularization and with l 2 and l 1 methods.

Tables (2)

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Table 1. Optical property at three wavelengths for cubic phantom in simulation verifications

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Table 2. Optical properties of Caliper mouse phantom at six wavelengths

Equations (24)

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·(D(r,λ)Φ(r,λ))+μa(r,λ)Φ(r,λ)=S(r,λ)(r∈Ω)
Φ(r,λ)+2A(r;n,n′)D(r,λ)(v(r)·Φ(r,λ))=0(rΩ)
A(r;n,n′)1+R(r)1R(r)
Q(r,λi)=D(r,λi)(v·Φ(r,λi))=Φ(r,λi)2A(r;n,n′)(rΩ)
Ω (D(r,λi)(Φ(r,λi))·(ψ(r))+μa(r,λi)Φ(r,λi)ψ(r)) d r
+Ω12An(r)Φ(r,λi)ψ(r)dr=ΩS(r,λi)ψ(r)dr
(K(λi)+C(λi)+B(λi))Φ(λi)=F(λi)S(λi)
Φb(λi)=(λi)S(λi)
Φb=𝓐S
Φb=[Φb(λ1)Φb(λi)Φb(λI)],=[γ1(λ1)γi(λi)γI(λI)]
minS12퓐SΦmeas2s.t.={0SSsup}
T퓐S=T Φmeas
minS12퓐SΦmeas2+δ2S2s.t.={0SSsup}.
Θ(S)=T(퓐SΦmeas)+δS.
minΘ(S)S:12퓐SΦmeas2+δ2S1s.t.={0SSsup}
Fε(ξ)={ξε2,ifξ>εξ22ε,ifξε.
[d](j)={d(j)ifS(j)(0,S(j)sup)min{d(j),0}ifS(j)=0max{d(j),0}ifS(j)=S(j)sup
[S](j)={S(j)ifS(j)[0,S(j)sup]0ifS(j)0S(j)supifS(j)>S(j)sup
Hk+1=VkTHkVk+ρkskTSk
Hk=(Vk1TVkmT)Hk0(VkmVk1)
+ρkm(Vk1TVkm+1T)SkmSkmT(Vkm+1Vk1)
+ρk2(Vk1)TSk2Sk1T (Vk1)
+ρk1Sk1Sk1T

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