Abstract

We propose a new method for reconstruction of emitting source distributions by use of a spatial filte and a successive updating process of the forward model for fluorescence/bioluminescenc diffuse optical tomography. The spatial filte transforms a set of the measurement data to a single source strength at a position of interest, and the forward model is updated by use of the estimated source strengths. This updating process ignores the dispensable source positions from reconstruction according to the reconstructed source distribution, and the spatial resolution of the reconstructed image is improved. The estimated sources are also used for the reduction of artifacts induced by noises based on the singular value decomposition. Some numerical experiments show the advantages of the proposed method by comparing the present results with those obtained by the conventional methods of the least squares method and Algebraic Reconstruction Technique. Finally the criteria for practical use of the method are quantitatively presented by the simulations for 2D and 3D geometries.

© 2010 OSA

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2008 (3)

2007 (3)

S. Okawa and S. Honda, “Dipole estimation with a combination of noise reduction and spatial filte,” International Congress Series 1300, 249–252 (2007).
[Crossref]

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]

Y. Lv, J. Yian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finit element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[Crossref] [PubMed]

2006 (5)

2005 (6)

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol. 50, 2503–2517 (2005).
[Crossref] [PubMed]

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (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]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[Crossref] [PubMed]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg,“Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429–2449 (2005).
[Crossref] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol. 50, 2451–2468 (2005).
[Crossref] [PubMed]

2004 (1)

2003 (1)

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media,” IEEE trans. Med. Imaging. 22(7), 824–836 (2003).
[Crossref] [PubMed]

2002 (2)

K. Vishwanath, B. Pogue, and M-A. Mycek, “Quantitative fluore cence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational method,” Phys. Med. Biol. 47, 3387–3405 (2002).
[Crossref] [PubMed]

V. Ntziachristos, C-H. Yung, C. Bremerand, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8 (7), 757–760 (2002).
[Crossref] [PubMed]

2001 (3)

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40(19), 3278–32887 (2001).
[Crossref]

S. Baillet, J. C. Mosher, and R. M. Leahy, “Electromagnetic brain mapping,” IEEE Signal Process Mag. 18, 14–30 (2001).
[Crossref]

M. J. Eppstein, D. E. Doughety, D. J. Hawrysz, and E. M. Sevick-Muraka, “Three-Dimensional Baysian Optical Image Reconstruction with Domain Decomposition,” IEEE trans. Med. Imaging 20(3), 147–163 (2001).
[Crossref] [PubMed]

2000 (1)

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments Toward Diagnostic Breast Cancer Imaging Using Near-Infrared Optical Measurements and Fluorescent Contrast Agents,” Neoplasia 2 (5), 388–417 (2000).
[Crossref]

1999 (2)

1997 (2)

D. Y. Paithankar, U. A. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, “Imaging of fluore cent yield and lifetime from multiply scattered light reemitted from random medium,” Appl. Opt. 36(10), 2260–2272 (1997).
[Crossref] [PubMed]

B. D. van Veen, W. van Drongelen, M. Yuchtman, and A. Suzuki, “Localization of brain electrical activity via linear constrained minimum variance spatial filte,” IEEE trans. Biomed. Eng. 44(9), 867–880 (1997).
[Crossref] [PubMed]

1996 (1)

1995 (1)

1994 (1)

1993 (1)

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the Finite-Element Method for the Forward and Inverse Model in Optical Tomography,” J. Math. Imaging Vis. 3, 263–283 (1993).
[Crossref]

1988 (1)

B. D. van Veen and K. M. Buckly, “Beamforming: A versatile approach to spatial filtering” IEEE ASSP Mag. 15, 4–23 (1988).
[Crossref]

1982 (1)

C. C. Paige and M. A. Saunders, “LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares,” ACM trans. on Math. Software 8(1), 43–71 (1982).
[Crossref]

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] [PubMed]

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol. 50, 2503–2517 (2005).
[Crossref] [PubMed]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40(19), 3278–32887 (2001).
[Crossref]

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

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the Finite-Element Method for the Forward and Inverse Model in Optical Tomography,” J. Math. Imaging Vis. 3, 263–283 (1993).
[Crossref]

Baillet, S.

S. Baillet, J. C. Mosher, and R. M. Leahy, “Electromagnetic brain mapping,” IEEE Signal Process Mag. 18, 14–30 (2001).
[Crossref]

Bakker, L.

L. Bakker, M. van der Mark, M van Beek, M. van der Voort, G. Hooft, T. Nielsen, T. Koehler, R. Ziegler, K. Licha, and M. Pessel, “Optical Fluorescence Imaging of Breast Cancer,” in Proceedings of Biomedical Optics Topical Meeting (OSA, Miami, Florida, 2006) SH56.

Boas, D. A.

Bouman, C. A.

Boverman, G.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

Bremerand, C.

V. Ntziachristos, C-H. Yung, C. Bremerand, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8 (7), 757–760 (2002).
[Crossref] [PubMed]

Brooks, D. H.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

Buckly, K. M.

B. D. van Veen and K. M. Buckly, “Beamforming: A versatile approach to spatial filtering” IEEE ASSP Mag. 15, 4–23 (1988).
[Crossref]

Chance, B.

Chaves, T.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

Chen, U. A.

Cong, A. X.

Cong, W.

Y. Lv, J. Yian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finit element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[Crossref] [PubMed]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. McLennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14(17), 7801–7809 (2006).
[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]

Dasari, R. R.

Dehghani, H.

Delpy, D. T.

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40(19), 3278–32887 (2001).
[Crossref]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the Finite-Element Method for the Forward and Inverse Model in Optical Tomography,” J. Math. Imaging Vis. 3, 263–283 (1993).
[Crossref]

Douek, M.

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol. 50, 2503–2517 (2005).
[Crossref] [PubMed]

Doughety, D. E.

M. J. Eppstein, D. E. Doughety, D. J. Hawrysz, and E. M. Sevick-Muraka, “Three-Dimensional Baysian Optical Image Reconstruction with Domain Decomposition,” IEEE trans. Med. Imaging 20(3), 147–163 (2001).
[Crossref] [PubMed]

Durairaj, K.

Eppstein, M. J.

M. J. Eppstein, D. E. Doughety, D. J. Hawrysz, and E. M. Sevick-Muraka, “Three-Dimensional Baysian Optical Image Reconstruction with Domain Decomposition,” IEEE trans. Med. Imaging 20(3), 147–163 (2001).
[Crossref] [PubMed]

Everdell, N.

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol. 50, 2503–2517 (2005).
[Crossref] [PubMed]

Feld, M. S.

Gao, F.

Gebauer, B.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg,“Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429–2449 (2005).
[Crossref] [PubMed]

Gibson, A.

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol. 50, 2503–2517 (2005).
[Crossref] [PubMed]

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] [PubMed]

Godavarty, A.

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media,” IEEE trans. Med. Imaging. 22(7), 824–836 (2003).
[Crossref] [PubMed]

Groetsch, C. W.

C. W. Groetsch, Inverse Problems in the Mathematical Sciences 1. Auflage (Friedr. Vieweg & Sohn Verlagsge-sellschaft mbH, Braunschweig/Wiesbaden, 1993).

C. W. Groetsch, Inverse problem (the Mathematical Association of America, Washington, 1999).

Grosenick, D.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg,“Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429–2449 (2005).
[Crossref] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol. 50, 2451–2468 (2005).
[Crossref] [PubMed]

D. Grosenick, H. Wabnitz, H. H. Rinneberg, T. Moesta, and P. M. Schlag, “Development of a time-domain optical mammography and fir t in vivo applications,” Appl. Opt. 38(13), 2927–2943 (1999).
[Crossref]

Hawrysz, D. J.

M. J. Eppstein, D. E. Doughety, D. J. Hawrysz, and E. M. Sevick-Muraka, “Three-Dimensional Baysian Optical Image Reconstruction with Domain Decomposition,” IEEE trans. Med. Imaging 20(3), 147–163 (2001).
[Crossref] [PubMed]

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments Toward Diagnostic Breast Cancer Imaging Using Near-Infrared Optical Measurements and Fluorescent Contrast Agents,” Neoplasia 2 (5), 388–417 (2000).
[Crossref]

He, H.

Hebdan, C.

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol. 50, 2503–2517 (2005).
[Crossref] [PubMed]

Hebden, J. C.

Henry, M.

Hillman, E. M. C.

Hoffman, E.

Holder, S.

S. Holder, Electrical Impedance Tomography: Methods, History and Applications (Institute of Physics Publishing, Bristol and Philadelphia, 2005).

Honda, S.

S. Okawa and S. Honda, “Dipole estimation with a combination of noise reduction and spatial filte,” International Congress Series 1300, 249–252 (2007).
[Crossref]

S. Okawa and S. Honda, “MEG Analysis with Spatial Filtered Reconstruction,” IEICE Trans. on Fundam. Electron. Commun. Comput. Sci. 89-A(5), 1428–1436 (2006).
[Crossref]

Hooft, G.

L. Bakker, M. van der Mark, M van Beek, M. van der Voort, G. Hooft, T. Nielsen, T. Koehler, R. Ziegler, K. Licha, and M. Pessel, “Optical Fluorescence Imaging of Breast Cancer,” in Proceedings of Biomedical Optics Topical Meeting (OSA, Miami, Florida, 2006) SH56.

Itzkan, I.

Koehler, T.

L. Bakker, M. van der Mark, M van Beek, M. van der Voort, G. Hooft, T. Nielsen, T. Koehler, R. Ziegler, K. Licha, and M. Pessel, “Optical Fluorescence Imaging of Breast Cancer,” in Proceedings of Biomedical Optics Topical Meeting (OSA, Miami, Florida, 2006) SH56.

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]

Leahy, R. M.

S. Baillet, J. C. Mosher, and R. M. Leahy, “Electromagnetic brain mapping,” IEEE Signal Process Mag. 18, 14–30 (2001).
[Crossref]

Li, A.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

Li, X. D.

Licha, K.

L. Bakker, M. van der Mark, M van Beek, M. van der Voort, G. Hooft, T. Nielsen, T. Koehler, R. Ziegler, K. Licha, and M. Pessel, “Optical Fluorescence Imaging of Breast Cancer,” in Proceedings of Biomedical Optics Topical Meeting (OSA, Miami, Florida, 2006) SH56.

Lv, Y.

Y. Lv, J. Yian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finit element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[Crossref] [PubMed]

Marjono, A.

McLennan, G.

Millane, R. P.

Miller, E. L.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

Milstein, A. B.

Moesta, K. T.

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol. 50, 2451–2468 (2005).
[Crossref] [PubMed]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg,“Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429–2449 (2005).
[Crossref] [PubMed]

Moesta, T.

Möller, M.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg,“Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429–2449 (2005).
[Crossref] [PubMed]

Mosher, J. C.

S. Baillet, J. C. Mosher, and R. M. Leahy, “Electromagnetic brain mapping,” IEEE Signal Process Mag. 18, 14–30 (2001).
[Crossref]

Mucke, J.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg,“Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429–2449 (2005).
[Crossref] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol. 50, 2451–2468 (2005).
[Crossref] [PubMed]

Mycek, M-A.

K. Vishwanath, B. Pogue, and M-A. Mycek, “Quantitative fluore cence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational method,” Phys. Med. Biol. 47, 3387–3405 (2002).
[Crossref] [PubMed]

Nielsen, T.

L. Bakker, M. van der Mark, M van Beek, M. van der Voort, G. Hooft, T. Nielsen, T. Koehler, R. Ziegler, K. Licha, and M. Pessel, “Optical Fluorescence Imaging of Breast Cancer,” in Proceedings of Biomedical Optics Topical Meeting (OSA, Miami, Florida, 2006) SH56.

Ntziachristos, V.

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]

V. Ntziachristos, C-H. Yung, C. Bremerand, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8 (7), 757–760 (2002).
[Crossref] [PubMed]

A. Soubret, J. Ripoll, D. Yessayan, and V. Ntziachristos, “Three-dimensional fluore cent tomography in presence of absorption: Study of the normalized Born approximation,” in 2004 Biomedical Optics Topical Meeting Technical Digest (OSA, Miami, Florida, 2004) WB6.

O’Leary, M. A.

Oh, S.

Okawa, S.

A. Marjono, A. Yano, S. Okawa, F. Gao, and Y. Yamada, “Total light approach of time-domain fluore cence diffuse optical tomography,” Opt. Express 16(19), 15268–15285 (2008).
[Crossref] [PubMed]

S. Okawa and S. Honda, “Dipole estimation with a combination of noise reduction and spatial filte,” International Congress Series 1300, 249–252 (2007).
[Crossref]

S. Okawa and S. Honda, “MEG Analysis with Spatial Filtered Reconstruction,” IEICE Trans. on Fundam. Electron. Commun. Comput. Sci. 89-A(5), 1428–1436 (2006).
[Crossref]

S. Okawa and Y. Yamada, “Source estimation with spatial filte for fluore cence diffuse optical tomography,” in Biomedical Optics Topical Meeting Technical Digest (OSA, Miami, Florida, 2008) BSuE41.

S. Okawa and Y. Yamada, “3D Light Source Reconstruction with Spatial Filter for Fluorescence/ Bioluminescence Diffuse Optical Tomography,ffi Diffuse Optical Imaging II, R. Cubeddu and A. H. Hielscher, eds., Proc. SPIE7369, 736916.

Paige, C. C.

C. C. Paige and M. A. Saunders, “LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares,” ACM trans. on Math. Software 8(1), 43–71 (1982).
[Crossref]

Paithankar, D. Y.

Patterson, M. S.

Perelman, L.

Pessel, M.

L. Bakker, M. van der Mark, M van Beek, M. van der Voort, G. Hooft, T. Nielsen, T. Koehler, R. Ziegler, K. Licha, and M. Pessel, “Optical Fluorescence Imaging of Breast Cancer,” in Proceedings of Biomedical Optics Topical Meeting (OSA, Miami, Florida, 2006) SH56.

Pogue, B.

K. Vishwanath, B. Pogue, and M-A. Mycek, “Quantitative fluore cence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational method,” Phys. Med. Biol. 47, 3387–3405 (2002).
[Crossref] [PubMed]

Pogue, B. W.

Qian, X.

Qin, C.

Y. Lv, J. Yian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finit element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[Crossref] [PubMed]

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]

Rinneberg, H.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg,“Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429–2449 (2005).
[Crossref] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol. 50, 2451–2468 (2005).
[Crossref] [PubMed]

Rinneberg, H. H.

Ripoll, J.

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]

A. Soubret, J. Ripoll, D. Yessayan, and V. Ntziachristos, “Three-dimensional fluore cent tomography in presence of absorption: Study of the normalized Born approximation,” in 2004 Biomedical Optics Topical Meeting Technical Digest (OSA, Miami, Florida, 2004) WB6.

Roy, R.

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media,” IEEE trans. Med. Imaging. 22(7), 824–836 (2003).
[Crossref] [PubMed]

Saunders, M. A.

C. C. Paige and M. A. Saunders, “LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares,” ACM trans. on Math. Software 8(1), 43–71 (1982).
[Crossref]

Schlag, P. M.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg,“Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429–2449 (2005).
[Crossref] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol. 50, 2451–2468 (2005).
[Crossref] [PubMed]

D. Grosenick, H. Wabnitz, H. H. Rinneberg, T. Moesta, and P. M. Schlag, “Development of a time-domain optical mammography and fir t in vivo applications,” Appl. Opt. 38(13), 2927–2943 (1999).
[Crossref]

Schweiger, M.

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40(19), 3278–32887 (2001).
[Crossref]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the Finite-Element Method for the Forward and Inverse Model in Optical Tomography,” J. Math. Imaging Vis. 3, 263–283 (1993).
[Crossref]

Scott, J. J.

Sevick-Muraca, E. M.

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media,” IEEE trans. Med. Imaging. 22(7), 824–836 (2003).
[Crossref] [PubMed]

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments Toward Diagnostic Breast Cancer Imaging Using Near-Infrared Optical Measurements and Fluorescent Contrast Agents,” Neoplasia 2 (5), 388–417 (2000).
[Crossref]

D. Y. Paithankar, U. A. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, “Imaging of fluore cent yield and lifetime from multiply scattered light reemitted from random medium,” Appl. Opt. 36(10), 2260–2272 (1997).
[Crossref] [PubMed]

Sevick-Muraka, E. M.

M. J. Eppstein, D. E. Doughety, D. J. Hawrysz, and E. M. Sevick-Muraka, “Three-Dimensional Baysian Optical Image Reconstruction with Domain Decomposition,” IEEE trans. Med. Imaging 20(3), 147–163 (2001).
[Crossref] [PubMed]

Shen, H.

Sinn, P.

Soubret, A.

A. Soubret, J. Ripoll, D. Yessayan, and V. Ntziachristos, “Three-dimensional fluore cent tomography in presence of absorption: Study of the normalized Born approximation,” in 2004 Biomedical Optics Topical Meeting Technical Digest (OSA, Miami, Florida, 2004) WB6.

Stroszczynski, C.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg,“Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429–2449 (2005).
[Crossref] [PubMed]

Suzuki, A.

B. D. van Veen, W. van Drongelen, M. Yuchtman, and A. Suzuki, “Localization of brain electrical activity via linear constrained minimum variance spatial filte,” IEEE trans. Biomed. Eng. 44(9), 867–880 (1997).
[Crossref] [PubMed]

Tanikawa, Y.

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 Beek, M

L. Bakker, M. van der Mark, M van Beek, M. van der Voort, G. Hooft, T. Nielsen, T. Koehler, R. Ziegler, K. Licha, and M. Pessel, “Optical Fluorescence Imaging of Breast Cancer,” in Proceedings of Biomedical Optics Topical Meeting (OSA, Miami, Florida, 2006) SH56.

van der Mark, M.

L. Bakker, M. van der Mark, M van Beek, M. van der Voort, G. Hooft, T. Nielsen, T. Koehler, R. Ziegler, K. Licha, and M. Pessel, “Optical Fluorescence Imaging of Breast Cancer,” in Proceedings of Biomedical Optics Topical Meeting (OSA, Miami, Florida, 2006) SH56.

van der Voort, M.

L. Bakker, M. van der Mark, M van Beek, M. van der Voort, G. Hooft, T. Nielsen, T. Koehler, R. Ziegler, K. Licha, and M. Pessel, “Optical Fluorescence Imaging of Breast Cancer,” in Proceedings of Biomedical Optics Topical Meeting (OSA, Miami, Florida, 2006) SH56.

van Drongelen, W.

B. D. van Veen, W. van Drongelen, M. Yuchtman, and A. Suzuki, “Localization of brain electrical activity via linear constrained minimum variance spatial filte,” IEEE trans. Biomed. Eng. 44(9), 867–880 (1997).
[Crossref] [PubMed]

van Veen, B. D.

B. D. van Veen, W. van Drongelen, M. Yuchtman, and A. Suzuki, “Localization of brain electrical activity via linear constrained minimum variance spatial filte,” IEEE trans. Biomed. Eng. 44(9), 867–880 (1997).
[Crossref] [PubMed]

B. D. van Veen and K. M. Buckly, “Beamforming: A versatile approach to spatial filtering” IEEE ASSP Mag. 15, 4–23 (1988).
[Crossref]

Veenstra, H.

Vishwanath, K.

K. Vishwanath, B. Pogue, and M-A. Mycek, “Quantitative fluore cence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational method,” Phys. Med. Biol. 47, 3387–3405 (2002).
[Crossref] [PubMed]

Vogel, C. R.

C. R. Vogel,Computational Methods for Inverse Problems (Frontiers in Applied Mathematics) (SIAM, Philadelphia, 2002).
[Crossref]

Wabnitz, H.

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol. 50, 2451–2468 (2005).
[Crossref] [PubMed]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg,“Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429–2449 (2005).
[Crossref] [PubMed]

D. Grosenick, H. Wabnitz, H. H. Rinneberg, T. Moesta, and P. M. Schlag, “Development of a time-domain optical mammography and fir t in vivo applications,” Appl. Opt. 38(13), 2927–2943 (1999).
[Crossref]

Wang, G.

Wang, L. V.

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]

Wang, Y.

Wassermann, B.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg,“Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429–2449 (2005).
[Crossref] [PubMed]

Webb, K. J.

Weissleder, R.

R. Weissleder, “Molecular Imaging in Cancer,” SCIENCE 321, 1168–1171 (2006).
[Crossref]

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]

V. Ntziachristos, C-H. Yung, C. Bremerand, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8 (7), 757–760 (2002).
[Crossref] [PubMed]

Wu, J.

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. Yian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finit element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[Crossref] [PubMed]

Yamada, Y.

A. Marjono, A. Yano, S. Okawa, F. Gao, and Y. Yamada, “Total light approach of time-domain fluore cence diffuse optical tomography,” Opt. Express 16(19), 15268–15285 (2008).
[Crossref] [PubMed]

F. Gao, H. Zhao, L. Zhang, Y. Tanikawa, A. Marjono, and Y. Yamada, “A self-normalized, full time-resolved method for fluore cence diffuse optical tomography,” Opt. Express 16(17), 13104–13121 (2008).
[Crossref] [PubMed]

F. Gao, H. Zhao, Y. Tanikawa, and Y. Yamada, “A linear, featured-data scheme for image reconstruction in time-domain fluore cence molecular tomography,” Opt. Express,  14(16), 7109–7124 (2006).
[Crossref] [PubMed]

S. Okawa and Y. Yamada, “3D Light Source Reconstruction with Spatial Filter for Fluorescence/ Bioluminescence Diffuse Optical Tomography,ffi Diffuse Optical Imaging II, R. Cubeddu and A. H. Hielscher, eds., Proc. SPIE7369, 736916.

S. Okawa and Y. Yamada, “Source estimation with spatial filte for fluore cence diffuse optical tomography,” in Biomedical Optics Topical Meeting Technical Digest (OSA, Miami, Florida, 2008) BSuE41.

Yang, W.

Y. Lv, J. Yian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finit element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[Crossref] [PubMed]

Yano, A.

Yates, T.

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol. 50, 2503–2517 (2005).
[Crossref] [PubMed]

Yessayan, D.

A. Soubret, J. Ripoll, D. Yessayan, and V. Ntziachristos, “Three-dimensional fluore cent tomography in presence of absorption: Study of the normalized Born approximation,” in 2004 Biomedical Optics Topical Meeting Technical Digest (OSA, Miami, Florida, 2004) WB6.

Yian, J.

Y. Lv, J. Yian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finit element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[Crossref] [PubMed]

Yodh, A. G.

Yuchtman, M.

B. D. van Veen, W. van Drongelen, M. Yuchtman, and A. Suzuki, “Localization of brain electrical activity via linear constrained minimum variance spatial filte,” IEEE trans. Biomed. Eng. 44(9), 867–880 (1997).
[Crossref] [PubMed]

Yung, C-H.

V. Ntziachristos, C-H. Yung, C. Bremerand, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8 (7), 757–760 (2002).
[Crossref] [PubMed]

Zhang, L.

Zhang, Q.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[Crossref] [PubMed]

Zhao, H

Zhao, H.

Ziegler, R.

L. Bakker, M. van der Mark, M van Beek, M. van der Voort, G. Hooft, T. Nielsen, T. Koehler, R. Ziegler, K. Licha, and M. Pessel, “Optical Fluorescence Imaging of Breast Cancer,” in Proceedings of Biomedical Optics Topical Meeting (OSA, Miami, Florida, 2006) SH56.

ACM trans. on Math. Software (1)

C. C. Paige and M. A. Saunders, “LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares,” ACM trans. on Math. Software 8(1), 43–71 (1982).
[Crossref]

Appl. Opt. (4)

IEEE ASSP Mag. (1)

B. D. van Veen and K. M. Buckly, “Beamforming: A versatile approach to spatial filtering” IEEE ASSP Mag. 15, 4–23 (1988).
[Crossref]

IEEE Signal Process Mag. (1)

S. Baillet, J. C. Mosher, and R. M. Leahy, “Electromagnetic brain mapping,” IEEE Signal Process Mag. 18, 14–30 (2001).
[Crossref]

IEEE trans. Biomed. Eng. (1)

B. D. van Veen, W. van Drongelen, M. Yuchtman, and A. Suzuki, “Localization of brain electrical activity via linear constrained minimum variance spatial filte,” IEEE trans. Biomed. Eng. 44(9), 867–880 (1997).
[Crossref] [PubMed]

IEEE trans. Med. Imaging (1)

M. J. Eppstein, D. E. Doughety, D. J. Hawrysz, and E. M. Sevick-Muraka, “Three-Dimensional Baysian Optical Image Reconstruction with Domain Decomposition,” IEEE trans. Med. Imaging 20(3), 147–163 (2001).
[Crossref] [PubMed]

IEEE trans. Med. Imaging. (1)

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media,” IEEE trans. Med. Imaging. 22(7), 824–836 (2003).
[Crossref] [PubMed]

IEICE Trans. on Fundam. Electron. Commun. Comput. Sci. (1)

S. Okawa and S. Honda, “MEG Analysis with Spatial Filtered Reconstruction,” IEICE Trans. on Fundam. Electron. Commun. Comput. Sci. 89-A(5), 1428–1436 (2006).
[Crossref]

International Congress Series (1)

S. Okawa and S. Honda, “Dipole estimation with a combination of noise reduction and spatial filte,” International Congress Series 1300, 249–252 (2007).
[Crossref]

Inverse Prob. (1)

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

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. Math. Imaging Vis. (1)

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the Finite-Element Method for the Forward and Inverse Model in Optical Tomography,” J. Math. Imaging Vis. 3, 263–283 (1993).
[Crossref]

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

Nat. Biotechnol. (1)

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]

Nat. Med. (1)

V. Ntziachristos, C-H. Yung, C. Bremerand, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8 (7), 757–760 (2002).
[Crossref] [PubMed]

Neoplasia (1)

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments Toward Diagnostic Breast Cancer Imaging Using Near-Infrared Optical Measurements and Fluorescent Contrast Agents,” Neoplasia 2 (5), 388–417 (2000).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Phys. Med. Biol. (7)

Y. Lv, J. Yian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finit 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] [PubMed]

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol. 50, 2503–2517 (2005).
[Crossref] [PubMed]

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
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Figures (15)

Fig. 1.
Fig. 1.

The reconstructed source distributions: (a)–(g) are in order of the number of the iteration. (h) is the true source distribution; i.e., true source at (x, y) =(20 mm, 0 mm) with the radius of 2.5 mm and the source strength of unity.

Fig. 2.
Fig. 2.

The residual error ratio as the function of the updating iterations.

Fig. 3.
Fig. 3.

The reconstructed source distributions by (a) the proposed method, (b) the minimum-norm solution, (c) and (d) LSQR, and (e) and (f) Algebraic Reconstruction Technique. The true distribution is shown in Fig. 1 (h).

Fig. 4.
Fig. 4.

The averages (top) and the standard deviations (bottom) of the reconstructed source strengths: (a-1) SDnoise = 0.01 and λSVD = 0.98, (a-2) SDnoise = 0.01 and λSVD = 1.0, (b) SDnoise = 0.001 and λSVD = 0.995, and (c) SDnoise = 0.1 and λSVD = 0.96.

Fig. 5.
Fig. 5.

The measured intensities of (solid line) the target signal light and of (dashed lines) the background emissions.

Fig. 6.
Fig. 6.

The reconstructed source distributions using the proposed noise reduction with (a-1) qBG = 0.0001 and λSVD = 0.995, (a-2) qBG = 0.0001 and λSVD = 0.97, (b-1) qBG = 0.001 and λSVD = 0.97, (b-2) qBG = 0.001 and λSVD = 0.80, and (c-1) qBG = 0.01 and λSVD = 0.97, (c-2) qBG = 0.01 and λSVD = 0.8.

Fig. 7.
Fig. 7.

The measured light intensities in the inhomogeneous medium (dashed curves) and in the homogeneous medium with µ s = 0.8 mm−1 (solid curve). µ s in the region of (3/4)πθ ≤ (5/4)π of the inhomogeneous medium is 0.72 mm−1, 0.4 mm−1 or 0.08 mm−1.

Fig. 8.
Fig. 8.

The source distributions reconstructed by use of incorrect homogeneous distribution of µ s . λSDV used in the noise reduction and the µ s in the particular region in the inhomogeneous medium are (a) λSVD = 0.995, µ s =0.72 mm−1, (b) λSVD = 0.98, µ s = 0.4 mm−1, (c-1) λSVD = 0.95, µ s =0.08 mm−1, and (c-2) λSVD = 0.99, µ s =0.08 mm−1. For (c-3), the correct distribution of µ s and λSVD = 0.99 are used. µ s =0.08 mm−1 in the particular region. And for (d), homogeneous µ s and λSVD = 0.995 are used. The particular region has µ s =8.0 mm−1.

Fig. 9.
Fig. 9.

The detected light intensities (dashed line) in the inhomogeneous medium and (solid) in the homogeneous medium with µa = 0.007 mm−1. The absorption coefficien in (3/4)πθ ≤ (5/4)π of the inhomogeneous medium varied.

Fig. 10.
Fig. 10.

The source distributions reconstructed by use of incorrect homogeneous distribution of µa . λSDV used in the noise reduction and the µ s in the particular region in the inhomogeneous medium are (a) λSVD = 0.99, µa =0.0035 mm−1, (b-1) λSVD = 0.97, µa =0.0007 mm−1, (b-2) λSVD = 0.99, µa =0.0007 mm−1. For (b-3), the correct distribution of µa and λSVD = 0.99 were used. µa =0.0007 mm−1 in the particular region. For (c), λSVD = 0.995 and the homogeneous µa are used. µa of the particular region is 0.07 mm−1.

Fig. 11.
Fig. 11.

The reconstructed (top) and true (bottom) distributions of the source strengths by the proposed method. The true centers of the two emitting source regions are at (a) (x, y) = (−10, 0) and (10, 0), (b) (x, y) = (−7.5, 0) and (7.5,0), (c) (x, y) = (−5, 0) and (5, 0), and (d) (x, y) = (−7.5, 20) and (7.5, 20).

Fig. 12.
Fig. 12.

(a) The distribution of µa of the circular medium, (b) the distribution of D = 1/(3µ s ), (c) the distribution of (µa + µaf ) where µaf is the absorption coefficien of ICG, (d) the calculated fluenc rate of the excitation light in the logarithmic scale, log10 Φ x , and (e) the fluorescenc light sources in the logarithmic scale, log10 q 0 = log10 ηµaf Φ x

Fig. 13.
Fig. 13.

The reconstructed images of the fluorescen source strengths with (a) λSVD =0.995 and six iterations, (b) λSVD = 0.9 and six iterations, (c) λSVD = 0.8 and six iterations, (d) λSVD = 0.80 and f ve iterations, and (e) λSVD = 0.8 and seven iterations.

Fig. 14.
Fig. 14.

The cross section in the plane of y = 0 mm of the cylindrical object consisting of annular regions which simulate various tissues of a mouse, i.e., (i) heart, (ii) lung, (iii) liver and (iv) fat. The illuminating and detecting positions are placed in the planes of z = 9, and 21 mm (dashed lines).

Fig. 15.
Fig. 15.

The cross sections of the reconstructed 3D source distributions (a) from the data without background emission, noise and mismatch in the optical properties, and no artifact reduction is carried out, (b) to (d) from the data with background emissions, noises and mismatches in the optical properties, λSVD = (b) 0.995, (c) 0.9, and (d) 0.8. The number of the updating iteration is seven.

Tables (1)

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Table 1. The optical properties of the tissues in the cylindrical object [mm−1].

Equations (15)

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{ · D ( r ) + μ a ( r ) } Φ ( r ) = q 0 ( r ) ,
n · D Φ = 1 2 A Φ on Ω ,
{ K ( D ) + C ( μ a ) + B } Φ = Q ,
Φ = G Q ,
m = L Q ,
Q ̂ = W T m ,
q ̂ k = w k T m = Σ i = 1 N w k T l i q i , ( k = 1 , 2 , , N ) ,
max w k ( w k T l k ) 2 , subject to w k T L 2 ( = Σ i = 1 N ( w k l i ) 2 ) = 1 .
w k = { l k T ( LL T ) 1 l k } 1 2 ( LL T ) 1 l k .
p i = q ̂ i Q ̂ ,
l i l i p i .
α = arg min α m α L Q ̂ 2 = m T L Q ̂ Q ̂ T L T L Q ̂ ,
Q ¯ = α · Q ̂ .
m = L Q + ε ,
m UHU T m ( = UHy ) ,

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