Abstract

A method is presented for reconstruction of the optical absorption coefficient from transmission near-infrared data with a cw source. As it is distinct from other available schemes such as optimization or Newton’s iterative method, this method resolves the inverse problem by solving a boundary value problem for a Volterra-type integral-differential equation. It is demonstrated in numerical studies that this technique has a better than average stability with respect to the discrepancy between the initial guess and the actual unknown absorption coefficient. The method is particularly useful for reconstruction from a large data set obtained from a CCD camera. Several numerical reconstruction examples are presented.

© 2006 Optical Society of America

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  1. S. Gopinath, C. S. Robertson, R. G. Grossman, and B. Chance, "Near-infrared spectroscopic localization of intracranial hematomas," J. Neurosurg. 79, 43-47 (1993).
    [CrossRef] [PubMed]
  2. C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
    [CrossRef] [PubMed]
  3. G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
    [CrossRef] [PubMed]
  4. B. Chance, E. Anday, S. Nioka, S. Zhou, L. Hong, K. Worden, C. Li, T. Murray, Y. Ovetsky, D. Pidikiti, and R. Thomas, "A novel method for fast imaging of brain function, noninvasively, with light," Opt. Express 2, 411-423 (1998).
    [CrossRef] [PubMed]
  5. D. A. Boas, T. Gaudette, G. Strangman, X. Cheng, J. J. A. Marota, and J. B. Mandeville, "The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics," Neuroimage 13, 76-90 (2001).
    [CrossRef] [PubMed]
  6. A. G. Yodh and D. A. Boas, "Functional imaging with diffusing light," in Biomedical Photonics Handbook, T.Vo-Dinh, ed. (CRC, 2003).
    [CrossRef]
  7. S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally constrained reconstruction," Technol. Cancer Res. Treat. 4, 513-526 (2005).
    [PubMed]
  8. S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, "Improved quantification of small objects in near-infrared diffuse optical tomography," J. Biomed. Opt. 9, 1161-1171 (2004).
    [CrossRef] [PubMed]
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  11. A. Godavarty, A. B. Thompson, R. Roy, M. Gurfinkel, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraka, "Diagnostic of breast cancer using fluorescence-enhanced optical tomography: phantom studies," J. Biomed. Opt. 9, 488-496 (2004).
    [CrossRef] [PubMed]
  12. A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, and A. H. Hielscher, "Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia," J. Biomed. Opt. 9, 1046-1062 (2004).
    [CrossRef] [PubMed]
  13. T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, and K. D. Paulsen, "Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging," Opt. Lett. 26, 822-824 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
  16. E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, "Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation," Anal. Biochem. 195, 330-351 (1991).
    [CrossRef] [PubMed]
  17. A. H. Hielscher, A. D. Klose, and K. M. Hanson, "Gradient-based iterative reconstruction scheme for time-resolved optical tomography," IEEE Trans. Med. Imaging 18, 262-271 (1999).
    [CrossRef] [PubMed]
  18. J. C. Schotland, "Continuous-wave diffusion imaging," J. Opt. Soc. Am. A 14, 275-279 (1997).
    [CrossRef]
  19. M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, "Experimental images of heterogeneous turbid media by frequency-domain diffusion-photon tomography," Opt. Lett. 20, 426-428 (1995).
    [CrossRef] [PubMed]
  20. Y. A. Gryazin, M. V. Klibanov, and T. R. Lucas, "Numerical solution of a subsurface imaging inverse problem," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 664-683 (2001).
    [CrossRef]
  21. R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, "MRI-guided optical tomography: prospects and computation for a new imaging method," IEEE Comput. Sci. Eng. 2, 63-77 (1995).
    [CrossRef]
  22. G. S. Abdoulaev, K. Ren, and A. H. Hielscher, "Optical tomography as a PDE-constrained optimization problem," Inverse Probl. 21, 1507-1530 (2005).
    [CrossRef]
  23. Y. Pey, H. L. Graber, and R. L. Barbour, "Influence of systematic errors in reference states on image quality and on stability of derived information for DC optical imaging," Appl. Opt. 40, 5755-5769 (2001).
    [CrossRef]
  24. M. V. Klibanov and A. Timonov, Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (Brill Academic, 2004).

2005 (3)

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally constrained reconstruction," Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

C. Schmitz, D. Klemer, R. Hardin, M. Katz, Y. Pei, H. Graber, M. Levin, R. Levina, N. Franco, W. Solomon, and R. Barbour, "Design and implementation of dynamic near-infrared optical tomographic imaging instrumentation for simultaneous dual-breast measurements," Appl. Opt. 44, 2140-2153 (2005).
[CrossRef] [PubMed]

G. S. Abdoulaev, K. Ren, and A. H. Hielscher, "Optical tomography as a PDE-constrained optimization problem," Inverse Probl. 21, 1507-1530 (2005).
[CrossRef]

2004 (3)

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, "Improved quantification of small objects in near-infrared diffuse optical tomography," J. Biomed. Opt. 9, 1161-1171 (2004).
[CrossRef] [PubMed]

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

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, and A. H. Hielscher, "Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia," J. Biomed. Opt. 9, 1046-1062 (2004).
[CrossRef] [PubMed]

2003 (1)

2001 (5)

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

D. A. Boas, T. Gaudette, G. Strangman, X. Cheng, J. J. A. Marota, and J. B. Mandeville, "The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics," Neuroimage 13, 76-90 (2001).
[CrossRef] [PubMed]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, and K. D. Paulsen, "Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging," Opt. Lett. 26, 822-824 (2001).
[CrossRef]

Y. A. Gryazin, M. V. Klibanov, and T. R. Lucas, "Numerical solution of a subsurface imaging inverse problem," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 664-683 (2001).
[CrossRef]

Y. Pey, H. L. Graber, and R. L. Barbour, "Influence of systematic errors in reference states on image quality and on stability of derived information for DC optical imaging," Appl. Opt. 40, 5755-5769 (2001).
[CrossRef]

2000 (1)

G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
[CrossRef] [PubMed]

1999 (1)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, "Gradient-based iterative reconstruction scheme for time-resolved optical tomography," IEEE Trans. Med. Imaging 18, 262-271 (1999).
[CrossRef] [PubMed]

1998 (1)

1997 (2)

J. C. Schotland, "Continuous-wave diffusion imaging," J. Opt. Soc. Am. A 14, 275-279 (1997).
[CrossRef]

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

1995 (2)

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, "Experimental images of heterogeneous turbid media by frequency-domain diffusion-photon tomography," Opt. Lett. 20, 426-428 (1995).
[CrossRef] [PubMed]

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, "MRI-guided optical tomography: prospects and computation for a new imaging method," IEEE Comput. Sci. Eng. 2, 63-77 (1995).
[CrossRef]

1993 (1)

S. Gopinath, C. S. Robertson, R. G. Grossman, and B. Chance, "Near-infrared spectroscopic localization of intracranial hematomas," J. Neurosurg. 79, 43-47 (1993).
[CrossRef] [PubMed]

1991 (1)

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, "Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation," Anal. Biochem. 195, 330-351 (1991).
[CrossRef] [PubMed]

Abdoulaev, G. S.

G. S. Abdoulaev, K. Ren, and A. H. Hielscher, "Optical tomography as a PDE-constrained optimization problem," Inverse Probl. 21, 1507-1530 (2005).
[CrossRef]

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, and A. H. Hielscher, "Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia," J. Biomed. Opt. 9, 1046-1062 (2004).
[CrossRef] [PubMed]

Alfano, R. R.

G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
[CrossRef] [PubMed]

Anday, E.

Aronson, R.

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, "MRI-guided optical tomography: prospects and computation for a new imaging method," IEEE Comput. Sci. Eng. 2, 63-77 (1995).
[CrossRef]

Arridge, S. R.

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

Barbour, R.

Barbour, R. L.

Y. Pey, H. L. Graber, and R. L. Barbour, "Influence of systematic errors in reference states on image quality and on stability of derived information for DC optical imaging," Appl. Opt. 40, 5755-5769 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, "MRI-guided optical tomography: prospects and computation for a new imaging method," IEEE Comput. Sci. Eng. 2, 63-77 (1995).
[CrossRef]

Barbour, S. L. S.

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, "MRI-guided optical tomography: prospects and computation for a new imaging method," IEEE Comput. Sci. Eng. 2, 63-77 (1995).
[CrossRef]

Beyer, D.

G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
[CrossRef] [PubMed]

Bluestone, A. Y.

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, and A. H. Hielscher, "Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia," J. Biomed. Opt. 9, 1046-1062 (2004).
[CrossRef] [PubMed]

Boas, D. A.

D. A. Boas, T. Gaudette, G. Strangman, X. Cheng, J. J. A. Marota, and J. B. Mandeville, "The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics," Neuroimage 13, 76-90 (2001).
[CrossRef] [PubMed]

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, "Experimental images of heterogeneous turbid media by frequency-domain diffusion-photon tomography," Opt. Lett. 20, 426-428 (1995).
[CrossRef] [PubMed]

A. G. Yodh and D. A. Boas, "Functional imaging with diffusing light," in Biomedical Photonics Handbook, T.Vo-Dinh, ed. (CRC, 2003).
[CrossRef]

Brooksby, B.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally constrained reconstruction," Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

Chance, B.

B. Chance, E. Anday, S. Nioka, S. Zhou, L. Hong, K. Worden, C. Li, T. Murray, Y. Ovetsky, D. Pidikiti, and R. Thomas, "A novel method for fast imaging of brain function, noninvasively, with light," Opt. Express 2, 411-423 (1998).
[CrossRef] [PubMed]

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, "Experimental images of heterogeneous turbid media by frequency-domain diffusion-photon tomography," Opt. Lett. 20, 426-428 (1995).
[CrossRef] [PubMed]

S. Gopinath, C. S. Robertson, R. G. Grossman, and B. Chance, "Near-infrared spectroscopic localization of intracranial hematomas," J. Neurosurg. 79, 43-47 (1993).
[CrossRef] [PubMed]

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, "Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation," Anal. Biochem. 195, 330-351 (1991).
[CrossRef] [PubMed]

B. Chance, "High sensitivity and specificity in human breast cancer detection with near-infrared imaging," in Biomedical Topical Meetings, Postconference Digest, Vol. 71, OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 450-455.

Chang, J. W.

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, "MRI-guided optical tomography: prospects and computation for a new imaging method," IEEE Comput. Sci. Eng. 2, 63-77 (1995).
[CrossRef]

Cheng, X.

D. A. Boas, T. Gaudette, G. Strangman, X. Cheng, J. J. A. Marota, and J. B. Mandeville, "The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics," Neuroimage 13, 76-90 (2001).
[CrossRef] [PubMed]

Cheung, C.

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

Culver, J. P.

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

Dehghani, H.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally constrained reconstruction," Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, "Improved quantification of small objects in near-infrared diffuse optical tomography," J. Biomed. Opt. 9, 1161-1171 (2004).
[CrossRef] [PubMed]

Eppstein, M. J.

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

Fajardo, L.

Franco, N.

Gaudette, T.

D. A. Boas, T. Gaudette, G. Strangman, X. Cheng, J. J. A. Marota, and J. B. Mandeville, "The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics," Neuroimage 13, 76-90 (2001).
[CrossRef] [PubMed]

Godavarty, A.

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

Gopinath, S.

S. Gopinath, C. S. Robertson, R. G. Grossman, and B. Chance, "Near-infrared spectroscopic localization of intracranial hematomas," J. Neurosurg. 79, 43-47 (1993).
[CrossRef] [PubMed]

Graber, H.

Graber, H. L.

Y. Pey, H. L. Graber, and R. L. Barbour, "Influence of systematic errors in reference states on image quality and on stability of derived information for DC optical imaging," Appl. Opt. 40, 5755-5769 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, "MRI-guided optical tomography: prospects and computation for a new imaging method," IEEE Comput. Sci. Eng. 2, 63-77 (1995).
[CrossRef]

Greenberg, J. H.

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

Grossman, R. G.

S. Gopinath, C. S. Robertson, R. G. Grossman, and B. Chance, "Near-infrared spectroscopic localization of intracranial hematomas," J. Neurosurg. 79, 43-47 (1993).
[CrossRef] [PubMed]

Gryazin, Y. A.

Y. A. Gryazin, M. V. Klibanov, and T. R. Lucas, "Numerical solution of a subsurface imaging inverse problem," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 664-683 (2001).
[CrossRef]

Gu, X.

Gurfinkel, M.

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

Hanson, K. M.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, "Gradient-based iterative reconstruction scheme for time-resolved optical tomography," IEEE Trans. Med. Imaging 18, 262-271 (1999).
[CrossRef] [PubMed]

Hardin, R.

Hebden, J. C.

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

Hielscher, A. H.

G. S. Abdoulaev, K. Ren, and A. H. Hielscher, "Optical tomography as a PDE-constrained optimization problem," Inverse Probl. 21, 1507-1530 (2005).
[CrossRef]

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, and A. H. Hielscher, "Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia," J. Biomed. Opt. 9, 1046-1062 (2004).
[CrossRef] [PubMed]

A. H. Hielscher, A. D. Klose, and K. M. Hanson, "Gradient-based iterative reconstruction scheme for time-resolved optical tomography," IEEE Trans. Med. Imaging 18, 262-271 (1999).
[CrossRef] [PubMed]

Hong, L.

Jiang, H.

Jiang, S.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally constrained reconstruction," Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, "Improved quantification of small objects in near-infrared diffuse optical tomography," J. Biomed. Opt. 9, 1161-1171 (2004).
[CrossRef] [PubMed]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, and K. D. Paulsen, "Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging," Opt. Lett. 26, 822-824 (2001).
[CrossRef]

Katz, A.

G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
[CrossRef] [PubMed]

Katz, M.

Klemer, D.

Klibanov, M. V.

Y. A. Gryazin, M. V. Klibanov, and T. R. Lucas, "Numerical solution of a subsurface imaging inverse problem," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 664-683 (2001).
[CrossRef]

M. V. Klibanov and A. Timonov, Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (Brill Academic, 2004).

Klose, A. D.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, "Gradient-based iterative reconstruction scheme for time-resolved optical tomography," IEEE Trans. Med. Imaging 18, 262-271 (1999).
[CrossRef] [PubMed]

Kofinas, A. D.

G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
[CrossRef] [PubMed]

Kogel, C.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally constrained reconstruction," Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

Koo, P. C.

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, "MRI-guided optical tomography: prospects and computation for a new imaging method," IEEE Comput. Sci. Eng. 2, 63-77 (1995).
[CrossRef]

Lasker, J.

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, and A. H. Hielscher, "Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia," J. Biomed. Opt. 9, 1046-1062 (2004).
[CrossRef] [PubMed]

Leigh, J.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, "Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation," Anal. Biochem. 195, 330-351 (1991).
[CrossRef] [PubMed]

Levin, M.

Levina, R.

Li, C.

Lucas, T. R.

Y. A. Gryazin, M. V. Klibanov, and T. R. Lucas, "Numerical solution of a subsurface imaging inverse problem," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 664-683 (2001).
[CrossRef]

Mandeville, J. B.

D. A. Boas, T. Gaudette, G. Strangman, X. Cheng, J. J. A. Marota, and J. B. Mandeville, "The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics," Neuroimage 13, 76-90 (2001).
[CrossRef] [PubMed]

Maris, M.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, "Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation," Anal. Biochem. 195, 330-351 (1991).
[CrossRef] [PubMed]

Marota, J. J. A.

D. A. Boas, T. Gaudette, G. Strangman, X. Cheng, J. J. A. Marota, and J. B. Mandeville, "The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics," Neuroimage 13, 76-90 (2001).
[CrossRef] [PubMed]

Maulik, D.

G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
[CrossRef] [PubMed]

McBride, T. O.

Murray, T.

Nioka, S.

B. Chance, E. Anday, S. Nioka, S. Zhou, L. Hong, K. Worden, C. Li, T. Murray, Y. Ovetsky, D. Pidikiti, and R. Thomas, "A novel method for fast imaging of brain function, noninvasively, with light," Opt. Express 2, 411-423 (1998).
[CrossRef] [PubMed]

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, "Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation," Anal. Biochem. 195, 330-351 (1991).
[CrossRef] [PubMed]

O'Leary, M. A.

Österberg, U. L.

Ovetsky, Y.

Paulsen, K. D.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally constrained reconstruction," Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, "Improved quantification of small objects in near-infrared diffuse optical tomography," J. Biomed. Opt. 9, 1161-1171 (2004).
[CrossRef] [PubMed]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, and K. D. Paulsen, "Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging," Opt. Lett. 26, 822-824 (2001).
[CrossRef]

Pei, Y.

Pey, Y.

Pidikiti, D.

Pogue, B. W.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally constrained reconstruction," Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, "Improved quantification of small objects in near-infrared diffuse optical tomography," J. Biomed. Opt. 9, 1161-1171 (2004).
[CrossRef] [PubMed]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Österberg, and K. D. Paulsen, "Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging," Opt. Lett. 26, 822-824 (2001).
[CrossRef]

Poplack, S. P.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally constrained reconstruction," Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

Ren, K.

G. S. Abdoulaev, K. Ren, and A. H. Hielscher, "Optical tomography as a PDE-constrained optimization problem," Inverse Probl. 21, 1507-1530 (2005).
[CrossRef]

Robertson, C. S.

S. Gopinath, C. S. Robertson, R. G. Grossman, and B. Chance, "Near-infrared spectroscopic localization of intracranial hematomas," J. Neurosurg. 79, 43-47 (1993).
[CrossRef] [PubMed]

Rosenfeld, W.

G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
[CrossRef] [PubMed]

Roy, R.

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

Schmitz, C.

Schotland, J. C.

Sevick, E. M.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, "Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation," Anal. Biochem. 195, 330-351 (1991).
[CrossRef] [PubMed]

Sevick-Muraka, E. M.

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

Solomon, W.

Song, X.

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, "Improved quantification of small objects in near-infrared diffuse optical tomography," J. Biomed. Opt. 9, 1161-1171 (2004).
[CrossRef] [PubMed]

Srinivasan, S.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally constrained reconstruction," Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, "Improved quantification of small objects in near-infrared diffuse optical tomography," J. Biomed. Opt. 9, 1161-1171 (2004).
[CrossRef] [PubMed]

Stankovic, M. R.

G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
[CrossRef] [PubMed]

Stewart, M.

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, and A. H. Hielscher, "Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia," J. Biomed. Opt. 9, 1046-1062 (2004).
[CrossRef] [PubMed]

Strangman, G.

D. A. Boas, T. Gaudette, G. Strangman, X. Cheng, J. J. A. Marota, and J. B. Mandeville, "The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics," Neuroimage 13, 76-90 (2001).
[CrossRef] [PubMed]

Stubblefield, P. G.

G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
[CrossRef] [PubMed]

Takahashi, K.

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

Thomas, R.

Thompson, A. B.

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

Timonov, A.

M. V. Klibanov and A. Timonov, Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (Brill Academic, 2004).

Worden, K.

Xu, Y.

Yodh, A. G.

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, "Experimental images of heterogeneous turbid media by frequency-domain diffusion-photon tomography," Opt. Lett. 20, 426-428 (1995).
[CrossRef] [PubMed]

A. G. Yodh and D. A. Boas, "Functional imaging with diffusing light," in Biomedical Photonics Handbook, T.Vo-Dinh, ed. (CRC, 2003).
[CrossRef]

Zhang, C.

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

Zhang, G.

G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
[CrossRef] [PubMed]

Zhou, S.

Anal. Biochem. (1)

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, and M. Maris, "Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation," Anal. Biochem. 195, 330-351 (1991).
[CrossRef] [PubMed]

Appl. Opt. (3)

IEEE Comput. Sci. Eng. (1)

R. L. Barbour, H. L. Graber, J. W. Chang, S. L. S. Barbour, P. C. Koo, and R. Aronson, "MRI-guided optical tomography: prospects and computation for a new imaging method," IEEE Comput. Sci. Eng. 2, 63-77 (1995).
[CrossRef]

IEEE Trans. Med. Imaging (1)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, "Gradient-based iterative reconstruction scheme for time-resolved optical tomography," IEEE Trans. Med. Imaging 18, 262-271 (1999).
[CrossRef] [PubMed]

Inverse Probl. (1)

G. S. Abdoulaev, K. Ren, and A. H. Hielscher, "Optical tomography as a PDE-constrained optimization problem," Inverse Probl. 21, 1507-1530 (2005).
[CrossRef]

J. Biomed. Opt. (3)

S. Srinivasan, B. W. Pogue, H. Dehghani, S. Jiang, X. Song, and K. D. Paulsen, "Improved quantification of small objects in near-infrared diffuse optical tomography," J. Biomed. Opt. 9, 1161-1171 (2004).
[CrossRef] [PubMed]

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

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, and A. H. Hielscher, "Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia," J. Biomed. Opt. 9, 1046-1062 (2004).
[CrossRef] [PubMed]

J. Neurosurg. (1)

S. Gopinath, C. S. Robertson, R. G. Grossman, and B. Chance, "Near-infrared spectroscopic localization of intracranial hematomas," J. Neurosurg. 79, 43-47 (1993).
[CrossRef] [PubMed]

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

Neuroimage (1)

D. A. Boas, T. Gaudette, G. Strangman, X. Cheng, J. J. A. Marota, and J. B. Mandeville, "The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics," Neuroimage 13, 76-90 (2001).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Med. Biol. (3)

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

G. Zhang, A. Katz, R. R. Alfano, A. D. Kofinas, P. G. Stubblefield, W. Rosenfeld, D. Beyer, D. Maulik, and M. R. Stankovic, "Brain perfusion monitoring with frequency-domain and continuous-wave near-infrared spectroscopy: a cross-correlation study in newborn piglets," Phys. Med. Biol. 45, 3143-3158 (2000).
[CrossRef] [PubMed]

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

SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. (1)

Y. A. Gryazin, M. V. Klibanov, and T. R. Lucas, "Numerical solution of a subsurface imaging inverse problem," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 62, 664-683 (2001).
[CrossRef]

Technol. Cancer Res. Treat. (1)

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally constrained reconstruction," Technol. Cancer Res. Treat. 4, 513-526 (2005).
[PubMed]

Other (3)

A. G. Yodh and D. A. Boas, "Functional imaging with diffusing light," in Biomedical Photonics Handbook, T.Vo-Dinh, ed. (CRC, 2003).
[CrossRef]

B. Chance, "High sensitivity and specificity in human breast cancer detection with near-infrared imaging," in Biomedical Topical Meetings, Postconference Digest, Vol. 71, OSA Trends in Optics and Photonics Series (Optical Society of America, 2002), pp. 450-455.

M. V. Klibanov and A. Timonov, Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (Brill Academic, 2004).

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Figures (8)

Fig. 1
Fig. 1

Light source and domain.

Fig. 2
Fig. 2

Finite element mesh.

Fig. 3
Fig. 3

Comparison of the reconstructed and the actual data. (a) Actual absorption distribution in the grid; the absorption coefficient μ a = 1 inside the target region and μ a = 0.1 otherwise. The color of the absorbing object is to show the location and is not scaled to show quantitative absorption coefficient. (b) Reconstructed absorption distribution (shown in cross section). The peak μ a value inside target region reaches 0.832. The color is scaled to show quantitative absorption coefficient.

Fig. 4
Fig. 4

Comparison of the reconstructed and the actual data. (a) Actual absorption distribution in the grid. The absorption coefficient μ a = 1 inside the target region and μ a = 0.1 otherwise. The color of the absorbing object is to show the location and is not scaled to show quantitative absorption coefficient. (b) Reconstructed absorption distribution (shown in cross section). The peak μ a value inside target region reaches 0.824. The color is scaled to show quantitative absorption coefficient.

Fig. 5
Fig. 5

Three-dimensional finite element mesh.

Fig. 6
Fig. 6

Comparison between the reconstructed data and actual data. (a) Actual absorption distribution; the color is scaled to show quantitative absorption coefficient. (b) Reconstructed data with 90% initial value and 2% white noise, namely, a = a 0 ( 0.9 + 0.02 W ) with a 0 = the original data, and W = white noise between 1 and 1. The color is scaled to show quantitative absorption coefficient.

Fig. 7
Fig. 7

Comparison of the actual and the reconstructed data on a cross section at x = 0.025 through their level curves. (a) Actual absorption distribution. (b) Reconstructed absorption.

Fig. 8
Fig. 8

Reconstructed data with disturbed initial value by noise in the form of a = a 0 ( r 1 + r 2 W ) with a 0 = the original data, and W = white noise between 1 and 1. The color is scaled to show quantitative absorption coefficient. (a) r 1 = 0.8 , r 2 = 0.02 ; (b) r 1 = 0.7 , r 2 = 0.02 ; (c) r 1 = 0.8 , r 2 = 0.02 , and 2% noise is used on the detection side.

Tables (1)

Tables Icon

Table 1 Comparison of Relative Errors for the Reconstructed Data a

Equations (14)

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

[ D ( x , y , z ) w ( x , y , z ) ] μ a ( x , y , z ) w ( x , y , z ) = δ ( x , r , y , z ) ,
Δ u ( x , y , z ) + u ( x , y , z ) u ( x , y , z ) a ( x , y , z ) = 0 ,
a ( x , y , z ) = 1 2 Δ [ ln D ( x , y , z ) ] + 1 4 [ ln D ( x , y , z ) ] [ ln D ( x , y , z ) ] + μ a ( x , y , z ) D ( x , y , z ) .
u ( x , y , z , r ) = r 1 r v ( x , y , z , τ ) d τ + u ( x , y , z ) .
Δ v ( x , y , z , r ) + 2 Δ v ( x , y , z , r ) [ r 1 r v ( x , y , z , τ ) d τ + u ( x , y , z ) ] = 0 .
D ( w n ) μ a w = ϕ f , at x = 0 ; D ( w x ) μ a w = 0 , others .
Δ v ( x , y , z , r i ) + 2 Δ v ( x , y , z , r i ) [ u ( x , y , z ) ] = 0 , i = 1 ,
Δ v ( x , y , z , r i ) + 2 Δ v ( x , y , z , r i ) [ 1 2 v ( x , y , z , r l ) Δ r + j = 2 i 1 v ( x , y , z , r j ) Δ r + 1 2 v ( x , y , z , r i ) Δ r + u ( x , y , z ) ] = 0 , i = 2 , 3 , 4 .
Δ v ( k ) ( x , y , z , r i ) + 2 Δ v ( k ) ( x , y , z , r i ) [ u ( x , y , z ) ] = 0 , i = 1 ,
Δ v ( k ) ( x , y , z , r i ) + 2 Δ v ( k ) ( x , y , z , r i ) [ 1 2 v ( x , y , z , r l ) Δ r + j = 2 i 1 v ( x , y , z , r j ) Δ r + 1 2 v ( k 1 ) ( x , y , z , r i ) Δ r + u ( x , y , z ) ] = 0 , i = 2 , 3 , 4 .
v ( k ) ( x , y , z , r i ) η + 2 v ( k ) ( x , y , z , r i ) [ u ( x , y , z ) ] η = 0 , i = 1 ,
v ( k ) ( x , y , z , r i ) η + 2 v ( k ) ( x , y , z , r i ) [ 1 2 v ( x , y , z , r l ) Δ r + j = 2 i 1 v ( x , y , z , r j ) Δ r + 1 2 v ( k 1 ) ( x , y , z , r i ) Δ r + u ( x , y , z ) ] η = 0 , i = 2 , 3 , 4 ,
η w ( x , y , z , r i ) a ( x , y , z ) w ( x , y , z ) η d V = 0 ,
a ( x , y , z ) = l = 1 N a l η l ,

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