Abstract

In fluorescence molecular tomography (FMT), diffuse-light measurements are obtained from a series of source–detector pairs placed on the boundary of the medium. The sensitivity of measurements deteriorates quickly with increased distance from the sources and detectors and therefore yields poor depth quantitative recovery. A depth compensation algorithm is presented in this paper to reconstruct fluorescent inclusions in deep tissues. Two weight matrixes are employed to level off sensitivity differences and enhance prominent elements of the solution. Results of numerical and phantom experiments demonstrate that both relative quantitation and spatial resolution of FMT are improved for inclusions at different depths.

© 2012 Optical Society of America

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2012 (1)

M. Li, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Reconstruction of fluorescence molecular tomography using a neighborhood regularization,” IEEE Trans. Biomed. Eng. 59, 1799–1803 (2012).
[CrossRef]

2011 (2)

2010 (5)

F. Liu, X. Liu, D. Wang, B. Zhang, and J. Bai, “A parallel excitation based fluorescence molecular tomography system for whole-body simultaneous imaging of small animals,” Ann. Biomed. Eng. 38, 3440–3448 (2010).
[CrossRef]

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7, 603–614 (2010).
[CrossRef]

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments, methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a combined tri-modality FT/DOT/XCT system,” Opt. Express 18, 7835–7850 (2010).
[CrossRef]

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. 15, 046005 (2010).
[CrossRef]

2009 (3)

2008 (2)

2007 (2)

2006 (2)

2005 (3)

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377–1386 (2005).
[CrossRef]

S. C. Davis, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Contrast-detail analysis characterizing diffuse optical fluorescence tomography image reconstruction,” J. Biomed. Opt. 10, 050501 (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]

2004 (3)

E. E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004).
[CrossRef]

J. Ripoll and V. Ntziachristos, “Imaging scattering media from a distance: theory and applications of noncontact optical tomography,” Mod. Phys. Lett. B 18, 1403–1431 (2004).
[CrossRef]

A. Godavarty, A. Thompson, R. Roy, M. Gurfinkel, M. Eppstein, C. Zhang, and E. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9, 488–496 (2004).
[CrossRef]

2003 (1)

V. Ntziachristos, C. Bremer, and R. Weissleder, “Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging,” Eur. Radiol. 13, 195–208 (2003).
[CrossRef]

2001 (1)

1999 (2)

1992 (1)

P. Hansen, “Analysis of discrete ill-posed problems by means of the L-curve,” SIAM Rev. 34, 561–580 (1992).
[CrossRef]

Andersson-Engels, S.

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, 3025–3035 (2009).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

S. R. Arridge, “Linear and non-linear methods in optical tomography,” in Biomedical Topical Meetings, Technical Digest (Optical Society of America, 2000), Vol. 38, pp. 495–497.

Axelsson, J.

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]

Bai, J.

M. Li, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Reconstruction of fluorescence molecular tomography using a neighborhood regularization,” IEEE Trans. Biomed. Eng. 59, 1799–1803 (2012).
[CrossRef]

B. Zhang, X. Cao, F. Liu, X. Liu, X. Wang, and J. Bai, “Early-photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation,” Appl. Opt. 50, 5397–5407 (2011).
[CrossRef]

F. Liu, X. Liu, D. Wang, B. Zhang, and J. Bai, “A parallel excitation based fluorescence molecular tomography system for whole-body simultaneous imaging of small animals,” Ann. Biomed. Eng. 38, 3440–3448 (2010).
[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, 766–773 (2009).
[CrossRef]

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

Barber, W. C.

Bremer, C.

V. Ntziachristos, C. Bremer, and R. Weissleder, “Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging,” Eur. Radiol. 13, 195–208 (2003).
[CrossRef]

Brooks, D.

Cao, X.

M. Li, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Reconstruction of fluorescence molecular tomography using a neighborhood regularization,” IEEE Trans. Biomed. Eng. 59, 1799–1803 (2012).
[CrossRef]

B. Zhang, X. Cao, F. Liu, X. Liu, X. Wang, and J. Bai, “Early-photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation,” Appl. Opt. 50, 5397–5407 (2011).
[CrossRef]

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]

Chen, N. G.

Chen, Y.

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, 766–773 (2009).
[CrossRef]

Cherry, S. R.

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

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]

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]

Davis, S. C.

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments, methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

D. S. Kepshire, S. C. Davis, H. Dehghani, K. D. Paulsen, and B. W. Pogue, “Subsurface diffuse optical tomography can localize absorber and fluorescent objects but recovered image sensitivity is nonlinear with depth,” Appl. Opt. 46, 1669–1678 (2007).
[CrossRef]

S. C. Davis, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Contrast-detail analysis characterizing diffuse optical fluorescence tomography image reconstruction,” J. Biomed. Opt. 10, 050501 (2005).
[CrossRef]

Dehghani, H.

Dhamne, S.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. 15, 046005 (2010).
[CrossRef]

Engl, H. W.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Springer Netherlands, 1996).

Eppstein, M.

A. Godavarty, A. Thompson, R. Roy, M. Gurfinkel, M. Eppstein, C. Zhang, and E. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9, 488–496 (2004).
[CrossRef]

Gao, F.

Godavarty, A.

A. Godavarty, A. Thompson, R. Roy, M. Gurfinkel, M. Eppstein, C. Zhang, and E. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9, 488–496 (2004).
[CrossRef]

Graves, E. E.

E. E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004).
[CrossRef]

Gulsen, G.

Guo, P.

Gurfinkel, M.

A. Godavarty, A. Thompson, R. Roy, M. Gurfinkel, M. Eppstein, C. Zhang, and E. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9, 488–496 (2004).
[CrossRef]

Hanke, M.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Springer Netherlands, 1996).

Hansen, P.

P. Hansen, “Analysis of discrete ill-posed problems by means of the L-curve,” SIAM Rev. 34, 561–580 (1992).
[CrossRef]

Hyde, D.

Iwanczyk, J. S.

Jiang, T. Z.

Kepshire, D. S.

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]

Leblond, F.

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments, methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

Li, M.

M. Li, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Reconstruction of fluorescence molecular tomography using a neighborhood regularization,” IEEE Trans. Biomed. Eng. 59, 1799–1803 (2012).
[CrossRef]

Lin, Y.

Lin, Z. J.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. 15, 046005 (2010).
[CrossRef]

Liu, F.

M. Li, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Reconstruction of fluorescence molecular tomography using a neighborhood regularization,” IEEE Trans. Biomed. Eng. 59, 1799–1803 (2012).
[CrossRef]

B. Zhang, X. Cao, F. Liu, X. Liu, X. Wang, and J. Bai, “Early-photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation,” Appl. Opt. 50, 5397–5407 (2011).
[CrossRef]

F. Liu, X. Liu, D. Wang, B. Zhang, and J. Bai, “A parallel excitation based fluorescence molecular tomography system for whole-body simultaneous imaging of small animals,” Ann. Biomed. Eng. 38, 3440–3448 (2010).
[CrossRef]

Liu, H.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. 15, 046005 (2010).
[CrossRef]

Liu, X.

B. Zhang, X. Cao, F. Liu, X. Liu, X. Wang, and J. Bai, “Early-photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation,” Appl. Opt. 50, 5397–5407 (2011).
[CrossRef]

F. Liu, X. Liu, D. Wang, B. Zhang, and J. Bai, “A parallel excitation based fluorescence molecular tomography system for whole-body simultaneous imaging of small animals,” Ann. Biomed. Eng. 38, 3440–3448 (2010).
[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, 766–773 (2009).
[CrossRef]

Luo, J.

M. Li, X. Cao, F. Liu, B. Zhang, J. Luo, and J. Bai, “Reconstruction of fluorescence molecular tomography using a neighborhood regularization,” IEEE Trans. Biomed. Eng. 59, 1799–1803 (2012).
[CrossRef]

Marjono, A.

McBride, T. O.

Miller, E.

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]

Nalcioglu, O.

Naser, M. A.

Neubauer, A.

H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems (Springer Netherlands, 1996).

Niu, H.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. 15, 046005 (2010).
[CrossRef]

Niu, H. J.

Ntziachristos, V.

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods 7, 603–614 (2010).
[CrossRef]

D. Hyde, R. Schulz, D. Brooks, E. Miller, and V. Ntziachristos, “Performance dependence of hybrid x-ray computed tomography/fluorescence molecular tomography on the optical forward problem,” J. Opt. Soc. Am. A 26, 919–923 (2009).
[CrossRef]

A. Soubret and V. Ntziachristos, “Fluorescence molecular tomography in the presence of background fluorescence,” Phys. Med. Biol. 51, 3983–4001 (2006).
[CrossRef]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377–1386 (2005).
[CrossRef]

J. Ripoll and V. Ntziachristos, “Imaging scattering media from a distance: theory and applications of noncontact optical tomography,” Mod. Phys. Lett. B 18, 1403–1431 (2004).
[CrossRef]

E. E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004).
[CrossRef]

V. Ntziachristos, C. Bremer, and R. Weissleder, “Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging,” Eur. Radiol. 13, 195–208 (2003).
[CrossRef]

V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. 26, 893–895 (2001).
[CrossRef]

Okawa, S.

Osterberg, U. L.

Patterson, M. S.

Paulsen, K. D.

Pogue, B. W.

Prewitt, J.

Ripoll, J.

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377–1386 (2005).
[CrossRef]

J. Ripoll and V. Ntziachristos, “Imaging scattering media from a distance: theory and applications of noncontact optical tomography,” Mod. Phys. Lett. B 18, 1403–1431 (2004).
[CrossRef]

Roeck, W.

Roy, R.

A. Godavarty, A. Thompson, R. Roy, M. Gurfinkel, M. Eppstein, C. Zhang, and E. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9, 488–496 (2004).
[CrossRef]

Schulz, R.

Schweiger, M.

Sevick-Muraca, E.

A. Godavarty, A. Thompson, R. Roy, M. Gurfinkel, M. Eppstein, C. Zhang, and E. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9, 488–496 (2004).
[CrossRef]

Smith, D. J.

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

Song, X. D.

Song, X. L.

Soubret, A.

A. Soubret and V. Ntziachristos, “Fluorescence molecular tomography in the presence of background fluorescence,” Phys. Med. Biol. 51, 3983–4001 (2006).
[CrossRef]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377–1386 (2005).
[CrossRef]

Svenmarker, P.

Thompson, A.

A. Godavarty, A. Thompson, R. Roy, M. Gurfinkel, M. Eppstein, C. Zhang, and E. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9, 488–496 (2004).
[CrossRef]

Tian, F.

H. Niu, Z. J. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. 15, 046005 (2010).
[CrossRef]

Valdes, P. A.

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments, methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

Wang, D.

F. Liu, X. Liu, D. Wang, B. Zhang, and J. Bai, “A parallel excitation based fluorescence molecular tomography system for whole-body simultaneous imaging of small animals,” Ann. Biomed. Eng. 38, 3440–3448 (2010).
[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, 766–773 (2009).
[CrossRef]

Wang, D. F.

Wang, H.

Wang, X.

Weissleder, R.

E. E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004).
[CrossRef]

V. Ntziachristos, C. Bremer, and R. Weissleder, “Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging,” Eur. Radiol. 13, 195–208 (2003).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

(a) 3D view of the cylindrical phantom with one fluorescent target. (b) Cross-sectional image at the height of z=2.0cm. The small circles marked S1–S18 represent excitation point sources. For each excitation position, measurement is taken on the opposite cylindrical surface within 150° FOV.

Fig. 2.
Fig. 2.

Reconstructed results of one fluorescent target at different depths using the ART without depth compensation. The off-center distance varies from 0 to 0.8 cm, with an increment of 0.2 cm. (a)–(e) 3D results. (f)–(j) Slice images at the height of z=2.0cm. The blue circles denote the real positions of the fluorescent targets. (k)–(o) Profiles along the yellow dotted lines in (f)–(j). The blue lines indicate the real distributions, while the red dotted curves indicate the reconstructed distributions.

Fig. 3.
Fig. 3.

Reconstructed results of one fluorescent target at different depths using the ART with depth compensation. The off-center distance varies from 0 to 0.8 cm, with an increment of 0.2 cm. (a)–(e) 3D results. (f)–(j) Slice images at the height of z=2.0cm. The blue circles denote the real positions of the fluorescent targets. (k)–(o) Profiles along the yellow dotted lines in (f)–(j). The blue lines indicate the real distributions, while the red dotted curves indicate the reconstructed distributions.

Fig. 4.
Fig. 4.

Reconstructed results of two fluorescent targets at different depths in cylindrical phantom. Results in the upper row are obtained using the ART without compensation, while those in the bottom row are obtained using the ART with compensation. The sagittal and transverse cross-sectional images along y=0.2cm and z=2.0cm planes are shown in the second and third columns. The blue circles show the real positions of fluorescent targets. Profiles along the yellow dotted lines are shown in (d) and (h). The blue lines indicate the real distributions, while the red dotted curves indicate the reconstructed distributions.

Fig. 5.
Fig. 5.

Arbitrarily shaped object for numerical simulation. (a) The forward model for generating surface measurements. The position of excitation lights are indicated by small blue circles. (b) Mesh of tetrahedral elements for the mouse chest region.

Fig. 6.
Fig. 6.

Reconstructed results of two fluorescent targets in the mouse-shaped model. Results in the left column are obtained using the ART without compensation, while those in the right column are obtained using the ART with compensation. (a) and (b) Coronal sectional images along y=1.1cm. (c) and (d) Transverse cross-sectional images along z=1.3cm. (e) and (f) Profiles along the blue lines in (a)–(d). The black lines indicate the real distributions, while the blue curves indicate the reconstructed distributions.

Fig. 7.
Fig. 7.

Schematic of the experimental setup. (a) Schematic of the homemade FMT imaging system. (b) Front view of the cylindrical phantom with two fluorescent targets. (c) Top view of the positions of the fluorescent targets.

Fig. 8.
Fig. 8.

Reconstructed results of the phantom experiment at z=4.0cm plane. (a) Reconstructed results obtained by the proposed method. (b) Reconstructed results obtained by the conventional ART with 100 iterations. (c) Reconstructed results obtained by the conventional ART with 1000 iterations. The data were normalized by the maximum reconstructed value in the phantom for purposes of comparison.

Tables (4)

Tables Icon

Table 1. Comparisons of Results with and without Depth Compensation for One Fluorophore at Different Depths

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Table 2. Comparisons of Results with and without Compensation for Two Targets in the Cylindrical Model

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Table 3. Comparisons of Results with and without Compensation for Two Targets in the Mouse-Shaped Model

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Table 4. Comparisons of Reconstructed Results with and without Compensation for Phantom Experiment

Equations (10)

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{De(r,λe)Φe(r,λe)μae(r,λe)Φe(r,λe)=Θsδ(rrsl)Dm(r,λm)Φm(r,λm)μam(r,λm)Φm(r,λm)=Φe(r,λe)η(λe)μaf(r,λe),
2De,m(r,λ)Φe,m(r)n⃗+qe,mΦe,m(r)=0(rΩ),
{KeΦe=PssSKmΦm=FX,
Φm=GmGxSX=(Km1Pss)(Ke1PssS)X.
{(Φm)1(Φm)2(Φm)L}=[A1A2AL]{x(1)x(2)x(N)}b=AX,
Xλ=argminx{AWdXb22+λ2WmX22},
{Y=WmXYλ=argminx{AWdWm1Yb22+λ2Y22,
Wd=diag(X˜p)=(x˜1p00x˜np),
{αj=1|max(Aj)min(Aj)|Wm=diag{αj*Aj1}=(α1*A1100αn*An1),j=1,2,,N
RQ_i=|I1maxI2max||I1max+I2max|/2,

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