Abstract

The information content of data types in time-domain optical tomography is quantified by studying the detectability of signals in the attenuation and reduced scatter coefficients. Detection in both uniform and structured backgrounds is considered, and our results show a complex dependence of spatial detectability maps on the type of signal, data type, and background. In terms of the detectability of lesions, the mean time of arrival of photons and the total number of counts effectively summarize the information content of the full temporal waveform. A methodology for quantifying information content prior to reconstruction without assumptions of linearity is established, and the importance of signal and background characterization is highlighted.

© 2006 Optical Society of America

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  1. A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical tomography," Phys. Med. Biol. 50, R1-R43 (2005).
    [CrossRef] [PubMed]
  2. F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, "A 32-channel time-resolved instrument for medical optical tomography," Rev. Sci. Instrum. 71, 256-265 (2000).
    [CrossRef]
  3. B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, and K. Paulsen, "Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection," Opt. Express 1, 391-403 (1997).
    [CrossRef] [PubMed]
  4. M. Schweiger, A. P. Gibson, and S. R. Arridge, "Computational aspects of diffuse optical tomography," IEEE Comput. Sci. Eng. 5, 33-41 (2003).
  5. J. C. Hebden, S. R. Arridge, and D. T. Delpy, "Optical imaging in medicine: I. Experimental techniques," Phys. Med. Biol. 42, 825-840 (1997).
    [CrossRef] [PubMed]
  6. S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
    [CrossRef]
  7. B. W. Pogue, C. Willscher, T. O. McBride, U. L. Österberg, and K. D. Paulsen, "Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography," Med. Phys. 22, 1779-1792 (1995).
  8. D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, "Detection and characterization of optical inhomogeneities with diffuse photon density wave: a signal-to-noise analysis," Appl. Opt. 36, 75-92 (1997).
    [CrossRef] [PubMed]
  9. H. H. Barrett, "Objective assessment of image quality: effects of quantum noise and object variability," J. Opt. Soc. Am. A 7, 1266-1278 (1990).
    [CrossRef] [PubMed]
  10. H. H. Barrett, C. K. Abbey, and E. Clarkson, "Objective assessment of image quality. II. Fisher information, Fourier crosstalk, and figures of merit for task performance," J. Opt. Soc. Am. A 12, 834-852 (1995).
    [CrossRef]
  11. H. H. Barrett, C. K. Abbey, and E. Clarkson, "Objective assessment of image quality. III. ROC metrics, ideal observers, and likelihood-generating functions," J. Opt. Soc. Am. A 15, 1520-1535 (1998).
    [CrossRef]
  12. H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004).
  13. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22, 1779-1792 (1995).
    [CrossRef] [PubMed]
  14. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, "A finite element approach to modeling photon transport in tissue," Med. Phys. 20, 299-309 (1993).
    [CrossRef] [PubMed]
  15. M. Schweiger and S. R. Arridge, "Optimal data types in optical tomography," in Proceedings of the 15th Conference on Information Processing in Medical Imaging, Lecture Notes in Computer Science, Vol. 1230 (Springer, 1997), pp. 71-84.
  16. M. Gerken and G. W. Faris, "Frequency-domain immersion technique for accurate optical property measurements of turbid media," Opt. Lett. 24, 1726-1728 (1999).
    [CrossRef]
  17. A. R. Pineda, H. H. Barrett, and S. R. Arridge, "Spatially varying detectability for optical tomography," in Proc. SPIE 3977, 77-83 (2000).
    [CrossRef]
  18. B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
    [CrossRef] [PubMed]
  19. S. R. Arridge and W. R. B. Lionheart, "Nonuniqueness in diffusion-based optical tomography," Opt. Lett. 23, 882-884 (1998).
    [CrossRef]
  20. K. J. Myers, J. P. Rolland, H. H. Barrett, and R. F. Wagner, "Aperture optimization for emission imaging: effect of a spatially varying background," J. Opt. Soc. Am. A 7, 1279-1293 (1990).
    [CrossRef] [PubMed]
  21. S. R. Arridge, M. Hiraoka, and M. Schweiger, "Statistical basis for the determination of optical path length in tissue," Phys. Med. Biol. 40, 1539-1558 (1995).
    [CrossRef] [PubMed]
  22. S. R. Arridge and M. Schweiger, "Inverse methods for optical tomography," in Proceedings of the 13th Conference on Information Processing in Medical Imaging, Lecture Notes in Computer Science, Vol. 687 (Springer, 1997), pp. 259-277.
  23. B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, "Spatially variant regularization improves diffuse optical tomography," Appl. Opt. 38, 2950-2961 (1999).
    [CrossRef]
  24. J. Zhou, J. Bai, and P. He, "Spatial location weighted optimization scheme for DC optical tomography," Opt. Express 11, 141-149 (2003).
    [CrossRef] [PubMed]
  25. G. Bal and O. Pinaud, "Time-reversal-based detection in random media," Inverse Probl. 21, 1593-1619 (2005).
    [CrossRef]
  26. M. A. Kupinski, E. Clarkson, J. W. Hoppin, L. Chen, and H. H. Barrett, "Experimental determination of object statistics from noisy images," J. Opt. Soc. Am. A 20, 421-429 (2003).
    [CrossRef]
  27. J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems (Springer, 2005).
  28. S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, "Approximation errors and model reduction with an application in optical diffusion tomography," Inverse Probl. 22, 175-195 (2006).
    [CrossRef]
  29. H. H. Barrett, K. J. Myers, B. Gallas, E. Clarkson, and H. Zhang, "Megalopinakophobia: its symptoms and cures," in Proc. SPIE 4320, 299-307 (2001).
    [CrossRef]
  30. S. R. Arridge and M. Schweiger, "Photon-measurement density-functions. Part 2. Finite-element-method calculations," Appl. Opt. 34, 8026-8037 (1995).
    [CrossRef] [PubMed]
  31. J. A. Swets and R. M. Pickett, Evaluation of Diagnostic Systems: Methods from Signal Detection Theory (Academic, 1982).

2006 (1)

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, "Approximation errors and model reduction with an application in optical diffusion tomography," Inverse Probl. 22, 175-195 (2006).
[CrossRef]

2005 (2)

G. Bal and O. Pinaud, "Time-reversal-based detection in random media," Inverse Probl. 21, 1593-1619 (2005).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical tomography," Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

2003 (3)

2001 (1)

H. H. Barrett, K. J. Myers, B. Gallas, E. Clarkson, and H. Zhang, "Megalopinakophobia: its symptoms and cures," in Proc. SPIE 4320, 299-307 (2001).
[CrossRef]

2000 (2)

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, "A 32-channel time-resolved instrument for medical optical tomography," Rev. Sci. Instrum. 71, 256-265 (2000).
[CrossRef]

A. R. Pineda, H. H. Barrett, and S. R. Arridge, "Spatially varying detectability for optical tomography," in Proc. SPIE 3977, 77-83 (2000).
[CrossRef]

1999 (3)

1998 (2)

1997 (4)

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, "Detection and characterization of optical inhomogeneities with diffuse photon density wave: a signal-to-noise analysis," Appl. Opt. 36, 75-92 (1997).
[CrossRef] [PubMed]

B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, and K. Paulsen, "Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection," Opt. Express 1, 391-403 (1997).
[CrossRef] [PubMed]

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

1995 (5)

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Österberg, and K. D. Paulsen, "Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography," Med. Phys. 22, 1779-1792 (1995).

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

H. H. Barrett, C. K. Abbey, and E. Clarkson, "Objective assessment of image quality. II. Fisher information, Fourier crosstalk, and figures of merit for task performance," J. Opt. Soc. Am. A 12, 834-852 (1995).
[CrossRef]

S. R. Arridge, M. Hiraoka, and M. Schweiger, "Statistical basis for the determination of optical path length in tissue," Phys. Med. Biol. 40, 1539-1558 (1995).
[CrossRef] [PubMed]

S. R. Arridge and M. Schweiger, "Photon-measurement density-functions. Part 2. Finite-element-method calculations," Appl. Opt. 34, 8026-8037 (1995).
[CrossRef] [PubMed]

1993 (1)

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

1990 (2)

Abbey, C. K.

Anderson, E. R.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

Arridge, S. R.

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, "Approximation errors and model reduction with an application in optical diffusion tomography," Inverse Probl. 22, 175-195 (2006).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical tomography," Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

M. Schweiger, A. P. Gibson, and S. R. Arridge, "Computational aspects of diffuse optical tomography," IEEE Comput. Sci. Eng. 5, 33-41 (2003).

A. R. Pineda, H. H. Barrett, and S. R. Arridge, "Spatially varying detectability for optical tomography," in Proc. SPIE 3977, 77-83 (2000).
[CrossRef]

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

S. R. Arridge and W. R. B. Lionheart, "Nonuniqueness in diffusion-based optical tomography," Opt. Lett. 23, 882-884 (1998).
[CrossRef]

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

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Hiraoka, and M. Schweiger, "Statistical basis for the determination of optical path length in tissue," Phys. Med. Biol. 40, 1539-1558 (1995).
[CrossRef] [PubMed]

S. R. Arridge and M. Schweiger, "Photon-measurement density-functions. Part 2. Finite-element-method calculations," Appl. Opt. 34, 8026-8037 (1995).
[CrossRef] [PubMed]

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

M. Schweiger and S. R. Arridge, "Optimal data types in optical tomography," in Proceedings of the 15th Conference on Information Processing in Medical Imaging, Lecture Notes in Computer Science, Vol. 1230 (Springer, 1997), pp. 71-84.

S. R. Arridge and M. Schweiger, "Inverse methods for optical tomography," in Proceedings of the 13th Conference on Information Processing in Medical Imaging, Lecture Notes in Computer Science, Vol. 687 (Springer, 1997), pp. 259-277.

Bai, J.

Bal, G.

G. Bal and O. Pinaud, "Time-reversal-based detection in random media," Inverse Probl. 21, 1593-1619 (2005).
[CrossRef]

Barrett, H. H.

Boas, D. A.

Butler, J.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

Cahn, M.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

Chance, B.

Chen, L.

Clarkson, E.

Coquoz, O.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

Delpy, D. T.

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, "A 32-channel time-resolved instrument for medical optical tomography," Rev. Sci. Instrum. 71, 256-265 (2000).
[CrossRef]

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

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

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

Faris, G. W.

Fishkin, J. B.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

Fry, M. E.

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, "A 32-channel time-resolved instrument for medical optical tomography," Rev. Sci. Instrum. 71, 256-265 (2000).
[CrossRef]

Gallas, B.

H. H. Barrett, K. J. Myers, B. Gallas, E. Clarkson, and H. Zhang, "Megalopinakophobia: its symptoms and cures," in Proc. SPIE 4320, 299-307 (2001).
[CrossRef]

Gerken, M.

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical tomography," Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

M. Schweiger, A. P. Gibson, and S. R. Arridge, "Computational aspects of diffuse optical tomography," IEEE Comput. Sci. Eng. 5, 33-41 (2003).

Gross, J. D.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

He, P.

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical tomography," Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, "A 32-channel time-resolved instrument for medical optical tomography," Rev. Sci. Instrum. 71, 256-265 (2000).
[CrossRef]

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

Hillman, E. M. C.

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, "A 32-channel time-resolved instrument for medical optical tomography," Rev. Sci. Instrum. 71, 256-265 (2000).
[CrossRef]

Hiraoka, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Hiraoka, and M. Schweiger, "Statistical basis for the determination of optical path length in tissue," Phys. Med. Biol. 40, 1539-1558 (1995).
[CrossRef] [PubMed]

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

Hoppin, J. W.

Kaipio, J.

J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems (Springer, 2005).

Kaipio, J. P.

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, "Approximation errors and model reduction with an application in optical diffusion tomography," Inverse Probl. 22, 175-195 (2006).
[CrossRef]

Kolehmainen, V.

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, "Approximation errors and model reduction with an application in optical diffusion tomography," Inverse Probl. 22, 175-195 (2006).
[CrossRef]

Kupinski, M. A.

Lionheart, W. R. B.

McBride, T.

McBride, T. O.

B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, "Spatially variant regularization improves diffuse optical tomography," Appl. Opt. 38, 2950-2961 (1999).
[CrossRef]

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Österberg, and K. D. Paulsen, "Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography," Med. Phys. 22, 1779-1792 (1995).

Myers, K. J.

H. H. Barrett, K. J. Myers, B. Gallas, E. Clarkson, and H. Zhang, "Megalopinakophobia: its symptoms and cures," in Proc. SPIE 4320, 299-307 (2001).
[CrossRef]

K. J. Myers, J. P. Rolland, H. H. Barrett, and R. F. Wagner, "Aperture optimization for emission imaging: effect of a spatially varying background," J. Opt. Soc. Am. A 7, 1279-1293 (1990).
[CrossRef] [PubMed]

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004).

O'Leary, M. A.

Osterberg, U.

Osterberg, U. L.

Österberg, U. L.

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Österberg, and K. D. Paulsen, "Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography," Med. Phys. 22, 1779-1792 (1995).

Paulsen, K.

Paulsen, K. D.

B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, "Spatially variant regularization improves diffuse optical tomography," Appl. Opt. 38, 2950-2961 (1999).
[CrossRef]

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Österberg, and K. D. Paulsen, "Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography," Med. Phys. 22, 1779-1792 (1995).

Pham, D.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

Pham, T.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

Pickett, R. M.

J. A. Swets and R. M. Pickett, Evaluation of Diagnostic Systems: Methods from Signal Detection Theory (Academic, 1982).

Pinaud, O.

G. Bal and O. Pinaud, "Time-reversal-based detection in random media," Inverse Probl. 21, 1593-1619 (2005).
[CrossRef]

Pineda, A. R.

A. R. Pineda, H. H. Barrett, and S. R. Arridge, "Spatially varying detectability for optical tomography," in Proc. SPIE 3977, 77-83 (2000).
[CrossRef]

Pogue, B. W.

Prewitt, J.

Rolland, J. P.

Schmidt, F. E. W.

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, "A 32-channel time-resolved instrument for medical optical tomography," Rev. Sci. Instrum. 71, 256-265 (2000).
[CrossRef]

Schweiger, M.

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, "Approximation errors and model reduction with an application in optical diffusion tomography," Inverse Probl. 22, 175-195 (2006).
[CrossRef]

M. Schweiger, A. P. Gibson, and S. R. Arridge, "Computational aspects of diffuse optical tomography," IEEE Comput. Sci. Eng. 5, 33-41 (2003).

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Hiraoka, and M. Schweiger, "Statistical basis for the determination of optical path length in tissue," Phys. Med. Biol. 40, 1539-1558 (1995).
[CrossRef] [PubMed]

S. R. Arridge and M. Schweiger, "Photon-measurement density-functions. Part 2. Finite-element-method calculations," Appl. Opt. 34, 8026-8037 (1995).
[CrossRef] [PubMed]

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

M. Schweiger and S. R. Arridge, "Optimal data types in optical tomography," in Proceedings of the 15th Conference on Information Processing in Medical Imaging, Lecture Notes in Computer Science, Vol. 1230 (Springer, 1997), pp. 71-84.

S. R. Arridge and M. Schweiger, "Inverse methods for optical tomography," in Proceedings of the 13th Conference on Information Processing in Medical Imaging, Lecture Notes in Computer Science, Vol. 687 (Springer, 1997), pp. 259-277.

Somersalo, E.

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, "Approximation errors and model reduction with an application in optical diffusion tomography," Inverse Probl. 22, 175-195 (2006).
[CrossRef]

J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems (Springer, 2005).

Swets, J. A.

J. A. Swets and R. M. Pickett, Evaluation of Diagnostic Systems: Methods from Signal Detection Theory (Academic, 1982).

Tarvainen, T.

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, "Approximation errors and model reduction with an application in optical diffusion tomography," Inverse Probl. 22, 175-195 (2006).
[CrossRef]

Testorf, M.

Tromberg, B. J.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

Vauhkonen, M.

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, "Approximation errors and model reduction with an application in optical diffusion tomography," Inverse Probl. 22, 175-195 (2006).
[CrossRef]

Venugopalan, V.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

Wagner, R. F.

Willscher, C.

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Österberg, and K. D. Paulsen, "Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography," Med. Phys. 22, 1779-1792 (1995).

Yodh, A. G.

Zhang, H.

H. H. Barrett, K. J. Myers, B. Gallas, E. Clarkson, and H. Zhang, "Megalopinakophobia: its symptoms and cures," in Proc. SPIE 4320, 299-307 (2001).
[CrossRef]

Zhou, J.

Appl. Opt. (3)

IEEE Comput. Sci. Eng. (1)

M. Schweiger, A. P. Gibson, and S. R. Arridge, "Computational aspects of diffuse optical tomography," IEEE Comput. Sci. Eng. 5, 33-41 (2003).

Inverse Probl. (3)

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

G. Bal and O. Pinaud, "Time-reversal-based detection in random media," Inverse Probl. 21, 1593-1619 (2005).
[CrossRef]

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen, and M. Vauhkonen, "Approximation errors and model reduction with an application in optical diffusion tomography," Inverse Probl. 22, 175-195 (2006).
[CrossRef]

J. Opt. Soc. Am. A (5)

Med. Phys. (3)

B. W. Pogue, C. Willscher, T. O. McBride, U. L. Österberg, and K. D. Paulsen, "Contrast-detail analysis for detection and characterization with near-infrared diffuse tomography," Med. Phys. 22, 1779-1792 (1995).

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, "The finite element method for the propagation of light in scattering media: Boundary and source conditions," Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

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

Opt. Express (2)

Opt. Lett. (2)

Philos. Trans. R. Soc. London, Ser. B (1)

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, and D. Pham, "Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration," Philos. Trans. R. Soc. London, Ser. B 352, 661-668 (1997).
[CrossRef] [PubMed]

Phys. Med. Biol. (3)

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

A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical tomography," Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

S. R. Arridge, M. Hiraoka, and M. Schweiger, "Statistical basis for the determination of optical path length in tissue," Phys. Med. Biol. 40, 1539-1558 (1995).
[CrossRef] [PubMed]

Proc. SPIE (2)

H. H. Barrett, K. J. Myers, B. Gallas, E. Clarkson, and H. Zhang, "Megalopinakophobia: its symptoms and cures," in Proc. SPIE 4320, 299-307 (2001).
[CrossRef]

A. R. Pineda, H. H. Barrett, and S. R. Arridge, "Spatially varying detectability for optical tomography," in Proc. SPIE 3977, 77-83 (2000).
[CrossRef]

Rev. Sci. Instrum. (1)

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, "A 32-channel time-resolved instrument for medical optical tomography," Rev. Sci. Instrum. 71, 256-265 (2000).
[CrossRef]

Other (5)

H. H. Barrett and K. J. Myers, Foundations of Image Science (Wiley, 2004).

M. Schweiger and S. R. Arridge, "Optimal data types in optical tomography," in Proceedings of the 15th Conference on Information Processing in Medical Imaging, Lecture Notes in Computer Science, Vol. 1230 (Springer, 1997), pp. 71-84.

J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems (Springer, 2005).

S. R. Arridge and M. Schweiger, "Inverse methods for optical tomography," in Proceedings of the 13th Conference on Information Processing in Medical Imaging, Lecture Notes in Computer Science, Vol. 687 (Springer, 1997), pp. 259-277.

J. A. Swets and R. M. Pickett, Evaluation of Diagnostic Systems: Methods from Signal Detection Theory (Academic, 1982).

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Figures (10)

Fig. 1
Fig. 1

Schematic of the experimental setup. The 32 detectors and 32 sources are uniformly placed in the boundary of a circular domain with a radius of 50 mm . One source and 32 detectors are shown. The 10 detectors nearest to the source (shown with dotted lines) are not used in our calculations.

Fig. 2
Fig. 2

Sample lumpy background (in μ a [ mm 1 ] ) and signal half way from the center to the boundary of the domain. The correlated structure of the background confounds the task of detecting the signal.

Fig. 3
Fig. 3

Detectability of μ a , + signal in a flat background showing only a small angular dependence away from the boundary. The maxima in the boundary occur near the detectors. The arrow pointing into the domain shows the location of one of the sources, and the arrow pointing outward shows the location of a detector. As expected, the detectability is lower in the center of the domain.

Fig. 4
Fig. 4

Detectability of μ a , + signal in a flat background. Note that the normalized waveform and τ plots overlap. For an attenuating inclusion in a flat background, the majority of the information is encoded by the total counts. Peak detectability occurs close to the boundary.

Fig. 5
Fig. 5

Detectability of μ s , + signal in a flat background. For a scattering inclusion the total counts contain the majority of the information, and peak detectability occurs at the boundary.

Fig. 6
Fig. 6

Detectability of μ a , + , μ s , signal in a flat background. For an inclusion that has an increase in attenuation and scatter, the mean time contains most of the information, and we see that the behavior near the boundary depends on the data type.

Fig. 7
Fig. 7

Detectability for μ a , + lesion and the E data type in a flat background. Each curve represents exclusion of a different number of detectors at either side of each source. Note that using all detectors [fan(0)] and only excluding one [fan(1)] produces plots that lie on top of each other.

Fig. 8
Fig. 8

Stability plot for four sets of 500 lumpy backgrounds each. We see that for the random backgrounds our detectability estimate is biased high for a small number of samples but converges as we increase our sample size.

Fig. 9
Fig. 9

Detectability of μ a , + signal in a lumpy background. The randomness in the background reduces the detectability of the inclusions and affects the behavior close to the boundary. We see that the mean time has a lower but more uniform detectability than the total counts in the presence of random fluctuations in the background. The overall decrease in detectability for the mean time was less than that for the total counts when compared to the flat background.

Fig. 10
Fig. 10

Histogram of standardized Hotelling test statistic. The approximate Gaussianity of the test statistic justifies using SNR Hot 2 as our measure of detectability.

Equations (29)

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1 c Φ ( r , t ) t k ( r ) Φ ( r , t ) + μ a ( r ) Φ ( r , t ) = q o ( r , t ) ,
k ( r ) = 1 3 [ μ a ( r ) + μ s ( r ) ] .
Φ ( ξ , t ) + 2 k ( ξ ) A n ̂ Φ ( ξ , t ) = 0 ,
Γ ( ξ m , t ) = c k ( ξ m ) n ̂ Φ ( ξ m , t ) ,
Sampled Waveform : Γ qm with [ Γ q m ] i = t i t i + 1 Γ q m ( t ) d t ,
Total Number of Photons : E q m = 0 Γ q m ( t ) d t ,
Sampled Normalized Waveform : N Γ qm = 10 5 E q m Γ qm ,
Mean Time : τ q m = 1 E q m 0 t Γ q m ( t ) d t .
μ a , + ( r ) = { Δ μ a , max e r r o 2 2 s 2 : r r o < 3 s 0 : otherwise ,
μ s , + ( r ) = { Δ μ s , max e r r o 2 2 s 2 : r r o < 3 s 0 : otherwise ,
b ( r ) = b 0 + i = 1 N lump ( r r i ) ,
lump ( r r i ) = l 0 e r r i 2 2 w 2 1 A ( Ω ) Ω l 0 e r r i 2 2 w 2 d 2 r ,
g 0 = g ( b ) + n if the signal is absent ,
g i = g ( b + s ) + n if the signal is present ,
t Hot ( g ) = Δ g t K g 1 g ,
Δ g = g ( b + s ) g ( b ) ,
SNR t = t 1 t 0 σ ( t ) ,
SNR Hot 2 = Δ g t K g 1 Δ g .
τ = 0 t [ N Γ ( t ) 0 N Γ ( t ) d t ] d t .
σ τ 2 = 1 N a { 0 t 2 [ N Γ ¯ ( t ) 0 N Γ ¯ ( t ) d t ] d t τ ¯ 2 } .
K g = K g , meas b + K g , lumps ,
K g , lumps = ( g ¯ g ¯ ¯ ) ( g ¯ g ¯ ¯ ) t b ,
g ¯ ¯ ̂ ( N ) = 1 N i = 1 N g ¯ i ,
Δ g ̿ ̂ ( N ) = 1 N i = 1 N Δ g ¯ i ,
K ̂ g ( N ) = 1 N i = 1 N K g , meas ( i ) + 1 N 1 i = 1 N ( g ¯ i g ¯ ¯ ̂ ( N ) ) ( g ¯ i g ¯ ¯ ̂ ( N ) ) t ,
SNR Hot 2 ( N ) = Δ g ̿ ̂ ̂ t K ̂ g 1 Δ g ̿ ̂ .
SNR Hot 2 loc = 1 N i = 1 N SNR Hot 2 ( l i ) ,
AUC G ( SNR t ) = 1 2 + 1 2 erf ( SNR t 2 ) ,
AUC MW = 1 N 2 i = 1 N j = 1 N step ( t j 1 t i 0 ) ,

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