Abstract

A Newton–Raphson inversion algorithm has been extended for simultaneous absorption and scattering reconstruction of fully three-dimensional (3D) diffuse optical tomographic imaging from time-resolved measurements. The proposed algorithm is derived from the efficient computation of the Jacobian matrix of the forward model and uses either the algebraic reconstruction technique or truncated singular-value decomposition as the linear inversion tool. Its validation was examined with numerically simulated data from 3-D finite-element discretization models of tissuelike phantoms, with several combinations of geometric and optical properties, as well as two commonly used source–detector configurations. Our results show that the fully 3-D image reconstruction of an object can be achieved with reasonable quality when volumetric light propagation in tissues is considered, and temporal information from the measurements can be effectively employed. Also, we investigated the conditions under which 3-D issues could be approximately addressed with two-dimensional reconstruction algorithms and further demonstrated that these conditions are seldom predictable or attainable in practice. Thus the application of 3-D algorithms to realistic situations is necessary.

© 2000 Optical Society of America

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  1. J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
    [CrossRef] [PubMed]
  2. S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
    [CrossRef] [PubMed]
  3. B. Chance, R. R. Alfano, eds., Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media, Proc. SPIE2389 (1995).
  4. A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
    [CrossRef] [PubMed]
  5. M. Tamura, “Multichannel near-infrared optical imaging of human brain activity,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 8–10.
  6. A. H. Grandjbakhche, R. J. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 176–185 (1994).
    [CrossRef]
  7. G. T. Herman, Image Reconstruction from Projections: the Fundamentals of Computerized Tomography (Academic, New York, 1980).
  8. I. Oda, H. Eda, Y. Tsunazawa, M. Takada, Y. Yamada, G. Nishimura, M. Tamura, “Optical tomography by the temporally extrapolated absorbance method,” Appl. Opt. 35, 169–175 (1996).
    [CrossRef] [PubMed]
  9. J. C. Hebden, K. S. Wong, “Time-resolved optical tomography,” Appl. Opt. 32, 372–380 (1993).
    [CrossRef] [PubMed]
  10. S. B. Colak, D. G. Papaioannou, G. W. ’t Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic imaging reconstruction from optical projection in light-diffusing media,” Appl. Opt. 36, 180–213 (1997).
  11. Y. Watanabe, T. Yuasa, T. Akatsuka, B. Devaraj, H. Inaba, “Enhancement of laser CT image contrast by correction of artifacts due to surface effects,” Opt. Express 3, 104–110 (1998), http://epubs.osa.org/opticsexpress .
  12. S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
    [CrossRef]
  13. M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vision 3, 263–283 (1993).
    [CrossRef]
  14. F. Gao, H. Zhao, H. Niu, “A study of numerical simulation of image reconstruction in optical computer tomography,” Bioimaging 5, 51–57 (1997).
    [CrossRef]
  15. F. Gao, H. Niu, H. Zhao, H. Zhang, “Application of optimal perturbation approach to the inverse problem in optical tomography,” Acta Opt. Sin. 19, 577–585 (1999) (in Chinese).
  16. R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van de Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87–120.
  17. R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of diffusing media by a progressive iterative backprojection method using time-domain data,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy ed., Proc. SPIE1767, 21–34 (1992).
  18. S. R. Arridge, M. Schweiger, “A gradient-based optimization scheme for optical tomography,” Opt. Express 2, 213–226 (1998), http://epubs.osa.org/opticsexpress .
    [CrossRef]
  19. M. Schweiger, S. R. Arridge, “Comparison of two- and three-dimensional reconstruction methods in optical tomography,” Appl. Opt. 37, 7419–7428 (1998).
    [CrossRef]
  20. J. J. Duderstadt, W. R. Matin, Transport Theory (Wiley, New York, 1979).
  21. S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
    [CrossRef] [PubMed]
  22. K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the application,” Phys. Rev. E 50, 3634–3640 (1994).
    [CrossRef]
  23. W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).
  24. M. Keijzer, W. M. Star, P. Storchi, “Optical diffusion in layered media,” Appl. Opt. 27, 1820–1824 (1988).
    [CrossRef] [PubMed]
  25. M. A. Viergever, A. Todd-Pokropek, eds., Mathematics and Computer Science in Medical Imaging, in NATO Advanced Science Institutes Series F: Computer and System Sciences (Springer-Verlag, Berlin, 1988), Vol. 39, pp. 127–141.
  26. F. Bevilacqua, D. Piquet, P. Marguet, J. D. Gross, B. J. Tromberg, C. Depeursigs, “In vivo local determination of tissue optical properties: applications to human brain,” Appl. Opt. 38, 4939–4950 (1999).
    [CrossRef]
  27. M. Schweiger, S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
    [CrossRef] [PubMed]
  28. H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
    [CrossRef]
  29. F. Gao, C. V. Zint, P. Poulet, “Experimental study on time-resolved optical tomography,” Acta Opt. Sin. (in press) (in Chinese).

1999 (4)

F. Gao, H. Niu, H. Zhao, H. Zhang, “Application of optimal perturbation approach to the inverse problem in optical tomography,” Acta Opt. Sin. 19, 577–585 (1999) (in Chinese).

F. Bevilacqua, D. Piquet, P. Marguet, J. D. Gross, B. J. Tromberg, C. Depeursigs, “In vivo local determination of tissue optical properties: applications to human brain,” Appl. Opt. 38, 4939–4950 (1999).
[CrossRef]

M. Schweiger, S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

1998 (3)

1997 (4)

S. B. Colak, D. G. Papaioannou, G. W. ’t Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic imaging reconstruction from optical projection in light-diffusing media,” Appl. Opt. 36, 180–213 (1997).

F. Gao, H. Zhao, H. Niu, “A study of numerical simulation of image reconstruction in optical computer tomography,” Bioimaging 5, 51–57 (1997).
[CrossRef]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

1996 (1)

1994 (1)

K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the application,” Phys. Rev. E 50, 3634–3640 (1994).
[CrossRef]

1993 (3)

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

J. C. Hebden, K. S. Wong, “Time-resolved optical tomography,” Appl. Opt. 32, 372–380 (1993).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vision 3, 263–283 (1993).
[CrossRef]

1988 (2)

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

M. Keijzer, W. M. Star, P. Storchi, “Optical diffusion in layered media,” Appl. Opt. 27, 1820–1824 (1988).
[CrossRef] [PubMed]

’t Hooft, G. W.

Akatsuka, T.

Aronson, R.

R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van de Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87–120.

Arridge, S. R.

M. Schweiger, S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “A gradient-based optimization scheme for optical tomography,” Opt. Express 2, 213–226 (1998), http://epubs.osa.org/opticsexpress .
[CrossRef]

M. Schweiger, S. R. Arridge, “Comparison of two- and three-dimensional reconstruction methods in optical tomography,” Appl. Opt. 37, 7419–7428 (1998).
[CrossRef]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vision 3, 263–283 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
[CrossRef]

Barbour, R. L.

R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van de Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87–120.

R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of diffusing media by a progressive iterative backprojection method using time-domain data,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy ed., Proc. SPIE1767, 21–34 (1992).

Bevilacqua, F.

Bonner, R. F.

A. H. Grandjbakhche, R. J. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 176–185 (1994).
[CrossRef]

Chang, J. H.

R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van de Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87–120.

Colak, S. B.

Cope, M.

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Delpy, D. T.

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vision 3, 263–283 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
[CrossRef]

Depeursigs, C.

Devaraj, B.

Duderstadt, J. J.

J. J. Duderstadt, W. R. Matin, Transport Theory (Wiley, New York, 1979).

Eda, H.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

I. Oda, H. Eda, Y. Tsunazawa, M. Takada, Y. Yamada, G. Nishimura, M. Tamura, “Optical tomography by the temporally extrapolated absorbance method,” Appl. Opt. 35, 169–175 (1996).
[CrossRef] [PubMed]

Edwards, A. D.

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Egan, W. G.

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).

Furutsu, K.

K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the application,” Phys. Rev. E 50, 3634–3640 (1994).
[CrossRef]

Gao, F.

F. Gao, H. Niu, H. Zhao, H. Zhang, “Application of optimal perturbation approach to the inverse problem in optical tomography,” Acta Opt. Sin. 19, 577–585 (1999) (in Chinese).

F. Gao, H. Zhao, H. Niu, “A study of numerical simulation of image reconstruction in optical computer tomography,” Bioimaging 5, 51–57 (1997).
[CrossRef]

F. Gao, C. V. Zint, P. Poulet, “Experimental study on time-resolved optical tomography,” Acta Opt. Sin. (in press) (in Chinese).

Graber, H. L.

R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van de Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87–120.

R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of diffusing media by a progressive iterative backprojection method using time-domain data,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy ed., Proc. SPIE1767, 21–34 (1992).

Grandjbakhche, A. H.

A. H. Grandjbakhche, R. J. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 176–185 (1994).
[CrossRef]

Gross, J. D.

Hebden, J. C.

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

J. C. Hebden, K. S. Wong, “Time-resolved optical tomography,” Appl. Opt. 32, 372–380 (1993).
[CrossRef] [PubMed]

Herman, G. T.

G. T. Herman, Image Reconstruction from Projections: the Fundamentals of Computerized Tomography (Academic, New York, 1980).

Hilgeman, T. W.

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Inaba, H.

Ito, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Keijzer, M.

Lubowsky, J.

R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of diffusing media by a progressive iterative backprojection method using time-domain data,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy ed., Proc. SPIE1767, 21–34 (1992).

Marguet, P.

Matin, W. R.

J. J. Duderstadt, W. R. Matin, Transport Theory (Wiley, New York, 1979).

Melissen, J. B. M.

Nishimura, G.

Niu, H.

F. Gao, H. Niu, H. Zhao, H. Zhang, “Application of optimal perturbation approach to the inverse problem in optical tomography,” Acta Opt. Sin. 19, 577–585 (1999) (in Chinese).

F. Gao, H. Zhao, H. Niu, “A study of numerical simulation of image reconstruction in optical computer tomography,” Bioimaging 5, 51–57 (1997).
[CrossRef]

Nossal, R. J.

A. H. Grandjbakhche, R. J. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 176–185 (1994).
[CrossRef]

Oda, I.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

I. Oda, H. Eda, Y. Tsunazawa, M. Takada, Y. Yamada, G. Nishimura, M. Tamura, “Optical tomography by the temporally extrapolated absorbance method,” Appl. Opt. 35, 169–175 (1996).
[CrossRef] [PubMed]

Oda, M.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Oikawa, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Paasschens, J. C. J.

Papaioannou, D. G.

Piquet, D.

Poulet, P.

F. Gao, C. V. Zint, P. Poulet, “Experimental study on time-resolved optical tomography,” Acta Opt. Sin. (in press) (in Chinese).

Reynolds, E. O.

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Richardson, C. E.

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Sassaroli, A.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Schomberg, H.

Schweiger, M.

M. Schweiger, S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “A gradient-based optimization scheme for optical tomography,” Opt. Express 2, 213–226 (1998), http://epubs.osa.org/opticsexpress .
[CrossRef]

M. Schweiger, S. R. Arridge, “Comparison of two- and three-dimensional reconstruction methods in optical tomography,” Appl. Opt. 37, 7419–7428 (1998).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vision 3, 263–283 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
[CrossRef]

Star, W. M.

Storchi, P.

Takada, M.

Tamura, M.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

I. Oda, H. Eda, Y. Tsunazawa, M. Takada, Y. Yamada, G. Nishimura, M. Tamura, “Optical tomography by the temporally extrapolated absorbance method,” Appl. Opt. 35, 169–175 (1996).
[CrossRef] [PubMed]

M. Tamura, “Multichannel near-infrared optical imaging of human brain activity,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 8–10.

Tromberg, B. J.

Tsuchiya, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Tsunazawa, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

I. Oda, H. Eda, Y. Tsunazawa, M. Takada, Y. Yamada, G. Nishimura, M. Tamura, “Optical tomography by the temporally extrapolated absorbance method,” Appl. Opt. 35, 169–175 (1996).
[CrossRef] [PubMed]

van Asten, N. A. A. J.

van der Mark, M. B.

Wada, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Wang, Y.

R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van de Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87–120.

Watanabe, Y.

Wong, K. S.

Wyatt, J. S.

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Yamada, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

I. Oda, H. Eda, Y. Tsunazawa, M. Takada, Y. Yamada, G. Nishimura, M. Tamura, “Optical tomography by the temporally extrapolated absorbance method,” Appl. Opt. 35, 169–175 (1996).
[CrossRef] [PubMed]

K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the application,” Phys. Rev. E 50, 3634–3640 (1994).
[CrossRef]

Yamashita, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Yuasa, T.

Zhang, H.

F. Gao, H. Niu, H. Zhao, H. Zhang, “Application of optimal perturbation approach to the inverse problem in optical tomography,” Acta Opt. Sin. 19, 577–585 (1999) (in Chinese).

Zhao, H.

F. Gao, H. Niu, H. Zhao, H. Zhang, “Application of optimal perturbation approach to the inverse problem in optical tomography,” Acta Opt. Sin. 19, 577–585 (1999) (in Chinese).

F. Gao, H. Zhao, H. Niu, “A study of numerical simulation of image reconstruction in optical computer tomography,” Bioimaging 5, 51–57 (1997).
[CrossRef]

Zint, C. V.

F. Gao, C. V. Zint, P. Poulet, “Experimental study on time-resolved optical tomography,” Acta Opt. Sin. (in press) (in Chinese).

Acta Opt. Sin. (1)

F. Gao, H. Niu, H. Zhao, H. Zhang, “Application of optimal perturbation approach to the inverse problem in optical tomography,” Acta Opt. Sin. 19, 577–585 (1999) (in Chinese).

Appl. Opt. (6)

Bioimaging (1)

F. Gao, H. Zhao, H. Niu, “A study of numerical simulation of image reconstruction in optical computer tomography,” Bioimaging 5, 51–57 (1997).
[CrossRef]

J. Math. Imag. Vision (1)

M. Schweiger, S. R. Arridge, D. T. Delpy, “Application of the finite element method for the forward and inverse models in optical tomography,” J. Math. Imag. Vision 3, 263–283 (1993).
[CrossRef]

Lancet (1)

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Med. Phys. (1)

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Med. Biol. (3)

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

Phys. Rev. E (1)

K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the application,” Phys. Rev. E 50, 3634–3640 (1994).
[CrossRef]

Rev. Sci. Instrum. (1)

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).
[CrossRef]

Other (11)

F. Gao, C. V. Zint, P. Poulet, “Experimental study on time-resolved optical tomography,” Acta Opt. Sin. (in press) (in Chinese).

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, New York, 1979).

M. A. Viergever, A. Todd-Pokropek, eds., Mathematics and Computer Science in Medical Imaging, in NATO Advanced Science Institutes Series F: Computer and System Sciences (Springer-Verlag, Berlin, 1988), Vol. 39, pp. 127–141.

B. Chance, R. R. Alfano, eds., Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media, Proc. SPIE2389 (1995).

J. J. Duderstadt, W. R. Matin, Transport Theory (Wiley, New York, 1979).

R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van de Zee, eds., Vol. IS11 of SPIE Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 87–120.

R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of diffusing media by a progressive iterative backprojection method using time-domain data,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy ed., Proc. SPIE1767, 21–34 (1992).

S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
[CrossRef]

M. Tamura, “Multichannel near-infrared optical imaging of human brain activity,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 8–10.

A. H. Grandjbakhche, R. J. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 176–185 (1994).
[CrossRef]

G. T. Herman, Image Reconstruction from Projections: the Fundamentals of Computerized Tomography (Academic, New York, 1980).

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Figures (9)

Fig. 1
Fig. 1

Geometric sketch of a cylindrical phantom: (a) top and (b) side view.

Fig. 2
Fig. 2

Target images of phantoms in Table 1: (a) phantom A, (b) phantom B, (c) phantom C. The columns from left to right correspond to the image planes of z = 8.333 mm, z = 4.167 mm, z = 0 mm, z = -4.167 mm, z = -8.333 mm.

Fig. 3
Fig. 3

Schemes for scanning modes: (a) FB and (b) PB.

Fig. 4
Fig. 4

FEM mesh structure of cylindrical phantom: (a) prism-shaped element, (b) 2-D mesh of an imaging plane.

Fig. 5
Fig. 5

Full 3-D reconstruction from data acquired with the FB mode, with both 〈t〉 and c 2, for (a) phantom A; (b) phantom B; and (c) phantom C; columns from left to right correspond to the image planes z = 8.333 mm, z = 4.167 mm, z = 0 mm, z = -4.167 mm, z = 8.333 mm.

Fig. 6
Fig. 6

Full 3-D reconstruction of phantom A (cf. Table 1), with different strategies: (a) PB/ART/〈t〉-c 2, (b) FB/t-SVD/〈t〉-c 2, (c) FB/ART/〈t〉.

Fig. 7
Fig. 7

Relative errors as a function of the number of iterations for reconstruction of phantom A with different strategies: (a) errors on measurements, (b) errors on images.

Fig. 8
Fig. 8

Model deviations regarding 〈t〉 (left-hand side) and c 2 (right-hand side) as functions of (a) optical and (b) geometric parameters.

Fig. 9
Fig. 9

Two-dimensional reconstruction of the middle layer of (a) phantom D and (b) phantom E (cf. Table 2), from 〈t〉 and c 2 computed from 3-D data, with the FB mode and 16 source–detector sites.

Tables (2)

Tables Icon

Table 1 Phantom Definition for 3-D Reconstructiona

Tables Icon

Table 2 Phantom Definition for 2-D Reconstruction from the 3-D Model

Equations (24)

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·κr-μarc-tΦr, rs, t=-δr-rs, t, cΦr, rs, t+2κr1+Rf1-Rfen·Φr, rs, trΩ=0,
·κr-μarcΨ0r, rs=-δr-rs, ·κr-μarcΨn r, rs=-nΨn-1r, rs, cΨnr, rs+2κr1+Rf1-Rfen·Ψnr, rsrΩ=0.
Tnξjs, ζs=c21-Rf1+RfΨnξjs, ζs.
Mean time of photon flight: t=0 tΓtdt/0 Γtdt,
 Variance to mean time: c2=0t-t2Γtdt/0 Γtdt=t2-t2.
Mν=Fνp+δp=Fνp+Jνpδp,
Jν=Fνξ11, ζ1/μFνξ11, ζ1/κFνξ21, ζ1/μFνξ21, ζ1/κFνξJS, ζS/μFνξJS, ζS/κ.
·κ+δκ-μa+δμacΨ0r, rs+δΨ0r, rs=-δr-rs, ·κ+δκ-μa+δμacΨnr, rs+δΨnr, rs=-nΨn-1r, rs+δΨn-1r, rs, cΨnr, rs+δΨnr, rs+2κ+δκ1+R1-Ren·Ψnr, rs+δΨnr, rsrΩ=0.
δΨnr, rs=-ΩΨ0r, rδμarcΨnr, rsdr-ΩrΨ0r, rδκrΨnr, rsdr+n ΩΨ0r, rδΨn-1r, rsdr,n0.
δTn=JaTnδa+JkTnδk,  n0,
Jγtξjs, ζs=JγT1ξjs, ζsT0ξjs, ζs-tξjs, ζsJγT0ξjs, ξsT0ξjs, ζs Jγc2ξjs, ζs=Jγt2ξjs, ζs-2tξjs, ζsJγtξjs, ζs, n=1, 2.
S=NfLf-2,  J=3Nf/2+1.
S=NθNpLp,  J=1.
D=3NRNR+1+1NL+1, E=6NR2NL.
img=i=1D |μatargetri-μareconsri|2i=1D |μatargetri|2+i=1D |μstargetri-μsreconsri|2i=1D |μstargetri|2,
data=1VSJνs=1Sj=1JMνξjs, ζs-Fνξjs, ζsMνξjs, ζs2,
minμ¯a, μ¯s χμ¯a, μ¯s=ν Mν-F¯νμ¯a, μ¯s2,
mν=1Nf/2+1i=1Nf/2+1m2Dνξi-m2Dνξi/m3Dνξi2,
JaT0ξjs, ζs=-Ω T0ξjs, rcΨ0r, ζsu1rdr-Ω T0ξjs, rcΨ0r, ζsu2rdr-Ω T0ξjs, rcΨ0r, ζsuDrdrT,
JkT0ξjs, ζs=-ΩrT0ξjs, rrΨ0r, ζsu1rdr-Ωr T0ξjs, rrΨ0r, ζsu2rdr-ΩrT0ξjs, rrΨ0r, ζsuDrdrT,
JaT1ξjs, ζs=-ΩT0ξjs, rΨ1r, ζs+T1ξjs, rΨ0r, ζscu1rdr-ΩT0ξjs, rΨ1r, ζs+T1ξjs, rΨ0r, ζscu2rdr-ΩT0ξjs, rΨ1r, ζs+T1ξjs, rΨ0r, ζscuDrdrT,
JkT1ξjs, ζs=-ΩrT0ξjs, rrΨ1r, ζs+rT1ξjs, rrΨ0r, ζsu1rdr-ΩrT0ξjs, rrΨ1r, ζs+rT1ξjs, rrΨ0r, ζsu2rdr-ΩrT0ξjs, rrΨ1r, ζs+rT1ξjs, rrΨ0r, ζsuDrdrT,
JaT2ξjs, ζs=-ΩT0ξjs, rΨ2r, ζs+2T1ξjs, rΨ1r, ζs+T2ξjs, rΨ0r, ζscu1rdr-ΩT0ξjs, rΨ2r, ζs+2T1ξjs, rΨ1r, ζs+T2ξjs, rΨ0r, ζscu2rdr-ΩT0ξjs, rΨ2r, ζs+2T1ξjs, rΨ1r, ζs+T2ξjs, rΨ0r, ζscuDrdrT,
JkT2ξjs, ζs=-ΩrT0ξjs, rrΨ2r, ζs+2rT1ξjs, rrΨ1r, ζs+rT2ξjs, rrΨ0r, ζsu1rdr-ΩrT0ξjs, rrΨ2r, ζs+2rT1ξjs, rrΨ1r, ζs+rT2ξjs, rrΨ0r, ζsu2rdr-ΩrT0ξjs, rrΨ2r, ζs+2rT1ξjs, rrΨ1r, ζs+rT2ξjs, rrΨ0r, ζsuDrdrT.

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