Abstract

In this paper, we present an incomplete variables truncated conjugate gradient (IVTCG) method for bioluminescence tomography (BLT). Considering the sparse characteristic of the light source and insufficient surface measurement in the BLT scenarios, we combine a sparseness-inducing ( 1 norm) regularization term with a quadratic error term in the IVTCG-based framework for solving the inverse problem. By limiting the number of variables updated at each iterative and combining a variable splitting strategy to find the search direction more efficiently, it obtains fast and stable source reconstruction, even without a priori information of the permissible source region and multispectral measurements. Numerical experiments on a mouse atlas validate the effectiveness of the method. In vivo mouse experimental results further indicate its potential for a practical BLT system.

© 2010 OSA

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2011

X. He, Y. Hou, D. Chen, Y. Jiang, M. Shen, J. Liu, Q. Zhang, and J. Tian, “Sparse regularization-based reconstruction for bioluminescence tomography using a multilevel adaptive finite element method,” Int. J. Biomed. Imaging 2011, 203537 (2011).
[CrossRef]

2010

H. Huang, X. Qu, J. Liang, X. He, X. Chen, D. Yang, and J. Tian, “A multi-phase level set framework for source reconstruction in bioluminescence tomography,” J. Comput. Phys. 229(13), 5246–5256 (2010).
[CrossRef]

M. A. Naser and M. S. Patterson, “Algorithms for bioluminescence tomography incorporating anatomical information and reconstruction of tissue optical properties,” J. Biomed. Opt. Express 1(2), 512–526 (2010).
[CrossRef]

X. He, J. Liang, X. Qu, H. Huang, Y. Hou, and J. Tian, “Truncated total least squares method with a practical truncation parameter choice scheme for bioluminescence tomography inverse problem,” Int. J. Biomed. Imaging 2010, 291874 (2010).
[CrossRef] [PubMed]

A. Cong, W. Cong, Y. Lu, P. Santago, A. Chatziioannou, and G. Wang, “Differential evolution approach for regularized bioluminescence tomography,” IEEE Trans. Biomed. Eng. 57(9), 2229–2238 (2010).
[CrossRef] [PubMed]

H. Gao and H. Zhao, “Multilevel bioluminescence tomography based on radiative transfer equation Part 1: l1 regularization,” Opt. Express 18(3), 1854–1871 (2010), http://www.opticsinfobase.org/oe/viewmedia.cfm?URI=oe-18-3-1854&seq=0 .
[CrossRef] [PubMed]

W. Cong and G. Wang, “Bioluminescence tomography based on the phase approximation model,” J. Opt. Soc. Am. A 27(2), 174–179 (2010).
[CrossRef]

K. Liu, J. Tian, Y. Lu, C. Qin, X. Yang, S. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18(4), 3732–3745 (2010), http://www.opticsinfobase.org/oe/viewmedia.cfm?URI=oe-18-4-3732&seq=0 .
[CrossRef] [PubMed]

J. Liu, Y. Wang, X. Qu, X. Li, X. Ma, R. Han, Z. Hu, X. Chen, D. Sun, R. Zhang, D. Chen, D. Chen, X. Chen, J. Liang, F. Cao, and J. Tian, “In vivo quantitative bioluminescence tomography using heterogeneous and homogeneous mouse models,” Opt. Express 18(12), 13102–13113 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-12-13102 .
[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. Express 18(19), 19876–19893 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=oe-18-19-19876 .
[CrossRef] [PubMed]

2009

2008

Q. Z. Zhang, L. Yin, Y. Y. Tan, Z. Yuan, and H. B. Jiang, “Quantitative bioluminescence tomography guided by diffuse optical tomography,” Opt. Express 16(3), 1481–1486 (2008), http://www.opticsinfobase.org/josab/viewmedia.cfm?id=149907&seq=0 .
[CrossRef] [PubMed]

J. Feng, K. Jia, G. Yan, S. Zhu, C. Qin, Y. Lv, and J. Tian, “An optimal permissible source region strategy for multispectral bioluminescence tomography,” Opt. Express 16(20), 15640–15654 (2008), http://www.opticsinfobase.org/oe/viewmedia.cfm?uri=oe-16-20-15640&seq=0 .
[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).

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

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35(11), 4863–4871 (2008).
[CrossRef] [PubMed]

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921–3942 (2008).
[CrossRef] [PubMed]

2007

M. Figueiredo, R. Nowak, and S. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems, IEEE J. Select,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[CrossRef]

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An Interior-Point Method for Large-Scale ℓ1-Regularized Least Squares,” IEEE J. Sel. Top. Signal Process. 1(4), 606–617 (2007).
[CrossRef]

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]

X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15(26), 18300–18317 (2007), http://www.opticsinfobase.org/VJBO/viewmedia.cfm?uri=oe-15-26-18300&seq=0 .
[CrossRef] [PubMed]

2006

2005

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(23), 5421–5441 (2005).
[CrossRef] [PubMed]

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

R. Fan, P. Chen, and C. Lin, “Working Set Selection Using Second Order Information for Training Support Vector Machines,” J. Mach. Learn. Res. 6, 1889–1918 (2005).

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]

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(18), 6756–6771 (2005), http://www.opticsinfobase.org/jdt/viewmedia.cfm?id=85344&seq=0 .
[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]

2003

H. Qi, L. Qi, and D. Sun, “Soving Karush-Kuhn-Tucker systems via trust region and the conjugate gradient methods,” SIAM J. Optim. 14(2), 439–463 (2003).
[CrossRef]

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9(1), 123–128 (2003).
[CrossRef] [PubMed]

2002

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

1999

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44(12), 2897–2906 (1999).
[CrossRef]

1995

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

Ahn, S.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921–3942 (2008).
[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.

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44(12), 2897–2906 (1999).
[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(11 Pt 1), 1779–1792 (1995).
[CrossRef] [PubMed]

Bachmann, M. H.

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

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(23), 5421–5441 (2005).
[CrossRef] [PubMed]

Bai, J.

Bouman, C. A.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921–3942 (2008).
[CrossRef] [PubMed]

Boyd, S.

S. J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An Interior-Point Method for Large-Scale ℓ1-Regularized Least Squares,” IEEE J. Sel. Top. Signal Process. 1(4), 606–617 (2007).
[CrossRef]

Cao, F.

Chan, T. F.

Chatziioannou, A.

A. Cong, W. Cong, Y. Lu, P. Santago, A. Chatziioannou, and G. Wang, “Differential evolution approach for regularized bioluminescence tomography,” IEEE Trans. Biomed. Eng. 57(9), 2229–2238 (2010).
[CrossRef] [PubMed]

Chatziioannou, A. F.

Y. Lu, X. Zhang, A. Douraghy, D. Stout, J. Tian, T. F. Chan, and A. F. Chatziioannou, “Source reconstruction for spectrally-resolved bioluminescence tomography with sparse a priori information,” Opt. Express 17(10), 8062–8080 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-10-8062 .
[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]

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]

Chaudhari, A. J.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53(14), 3921–3942 (2008).
[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(23), 5421–5441 (2005).
[CrossRef] [PubMed]

Chen, D.

Chen, N.

Chen, P.

R. Fan, P. Chen, and C. Lin, “Working Set Selection Using Second Order Information for Training Support Vector Machines,” J. Mach. Learn. Res. 6, 1889–1918 (2005).

Chen, X.

Cheng, J.

G. Wang, X. Qian, W. Cong, H. Shen, Y. Li, W. Han, K. Durairaj, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo, “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2(4), 453–457 (2006).
[CrossRef]

Cherry, S. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50(23), 5421–5441 (2005).
[CrossRef] [PubMed]

Cong, A.

Cong, W.

A. Cong, W. Cong, Y. Lu, P. Santago, A. Chatziioannou, and G. Wang, “Differential evolution approach for regularized bioluminescence tomography,” IEEE Trans. Biomed. Eng. 57(9), 2229–2238 (2010).
[CrossRef] [PubMed]

W. Cong and G. Wang, “Bioluminescence tomography based on the phase approximation model,” J. Opt. Soc. Am. A 27(2), 174–179 (2010).
[CrossRef]

G. Wang, H. Shen, W. Cong, S. Zhao, and G. W. Wei, “Temperature-modulated bioluminescence tomography,” Opt. Express 14(17), 7852–7871 (2006), http://www.opticsinfobase.org/oe/viewmedia.cfm?URI=oe-14-17-7852&seq=0 .
[CrossRef] [PubMed]

G. Wang, X. Qian, W. Cong, H. Shen, Y. Li, W. Han, K. Durairaj, M. Jiang, T. Zhou, J. Cheng, J. Tian, Y. Lv, H. Li, and J. Luo, “Recent development in bioluminescence tomography,” Curr. Med. Imaging Rev. 2(4), 453–457 (2006).
[CrossRef]

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, “A multilevel adaptive finite element algorithm for bioluminescence tomography,” Opt. Express 14(18), 8211–8223 (2006), http://www.opticsinfobase.org/jot/viewmedia.cfm?id=97939&seq=0 .
[CrossRef] [PubMed]

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Pogue, B. W.

H. Dehghani, S. C. Davis, and B. W. Pogue, “Spectrally resolved bioluminescence tomography using the reciprocity approach,” Med. Phys. 35(11), 4863–4871 (2008).
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J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
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Figures (7)

Fig. 1
Fig. 1

Reconstruction model in a single source case. (a) The torso of the mouse atlas model with a cylindrical source in the left kidney, (b) the mesh for reconstruction and the simulated photon distribution on the surface.

Fig. 2
Fig. 2

Reconstruction results at τ = 1e 3 . (a), (c) and (e) are respectively the isosurface views of the results by IVTCG, 1-s and GPSR, where the small red cylinder denotes the actual source; (b), (d) and (f) are the corresponding transverse views at z = 24.5mm where the small black circle denotes the actual source.

Fig. 3
Fig. 3

Error bar chart of power under different noise levels.

Fig. 4
Fig. 4

Reconstruction results in the double source case (a) The isosurface view (b) The corresponding coronal view at Y = 15.8mm. The small red cylinders in (a) and small black squares in (b) denote actual sources.

Fig. 5
Fig. 5

Multi-view superimposed images of photographs and luminescent images. (a)-(d) Anterior -posterior, right-lateral, posterior-anterior, and left-lateral views respectively.

Fig. 6
Fig. 6

In vivo model (a) The 3D view of the segmented micro-CT slices of the imaged mouse with a luminescent source implanted beneath the liver. (b) Surface view of the reconstruction mesh, with the detected photon distribution mapping on it.

Fig. 7
Fig. 7

The reconstruction result (a) the isosurface view of the reconstruction result. (b) the transverse view of the result and the comparison with the corresponding CT slices. The cross of the green lines denotes the actual source center and the cross of the red lines denotes the reconstructed center.

Tables (5)

Tables Icon

Table 1 Optical properties for the mouse organs

Tables Icon

Table 2 Reconstruction results in single source case with different parameters

Tables Icon

Table 3 Reconstruction results with optical parameter perturbation

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Table 4 Reconstruction results in the double-source case

Tables Icon

Table 5 Optical properties of the mouse model

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

( D ( r ) Φ ( r ) ) + μ a ( r ) Φ ( r ) = S ( r ) ( r Ω ) ,
Φ ( r ) + 2 A ( r ; n , n ) D ( r ) ( v ( r ) Φ ( r ) ) = 0 ( r Ω ) ,
Q ( r ) = D ( r ) ( v ( r ) Φ ( r ) ) = ( 2 A ( r ; n , n ) ) 1 Φ ( r ) ( r Ω ) .
M Φ = F S ,
Φ = M - 1 F S = A ¯ S .
A S = Φ m ,
min S 1 2 A S Φ m 2 2 + τ S 1 ,
min z c T z + 1 2 z T B z F ( z ) ,       s . t . z 0 ,
F ( z * ) = Ι υ * = υ * ,
υ * 0 , z * 0 , ( υ * ) T z * = 0 ,
F ( z * ) 0 , z * 0 , ( F ( z * ) ) T z * = 0 , F ( z * ) + z * > 0.
Γ k = { i | i { 1 , , 2 N } , [ ( z k ) i > 0 , ( F ( z k ) ) i 0 ] o r [ ( z k ) i = 0 , ( F ( z k ) ) i < 0 ] } ,
( z k ) i | ( F ( z * ) ) i | + i I * ,
( z k ) j | ( F ( z * ) ) j | 0 j I * .
I ^ k = { i { 1 , , 2 N } | ( z k ) i > 0 , ( z k ) i / ( F ( z k ) ) i > δ }
( z k ) i 1 | ( F ( z * ) ) i 1 | ( z k ) i 2 | ( F ( z * ) ) i 2 | δ .
I k = { i l I ^ k | l min { | I ^ k | , N s } } ,
J k = { j l J ^ k | l min { | J ^ k | , N max N s } } ,
min d I k k F ( z I k k + d I k k , z I ¯ k k + d I ¯ k k k ) ,       s . t . z I k k + d I k k 0 ,
min x b s u b T x + 1 2 x T B s u b x F s u b ( x ) ,       s . t . z I k k + x 0 ,

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