Abstract

We present a carefully designed phantom experimental study aimed to provide solid evidence that both absorption and scattering images of heterogeneous scattering media can be reconstructed independently from dc data. We also study the important absorption–scattering cross-talk issue. In this regard, we develop a simple normalizing scheme that is incorporated into our nonlinear finite-element-based reconstruction algorithm. Our results from the controlled phantom experiments show that the cross talk of an absorption object appearing in scattering images can be eliminated and that the cross talk of a scattering object appearing in absorption images can be reduced considerably. In addition, these carefully designed phantom experiments clearly suggest that both absorption and scattering images can be simultaneously recovered and quantitatively separated in highly scattering media by use of dc measurements. Finally, we discuss our results in light of recent theoretical findings on nonuniqueness for dc image reconstruction.

© 2002 Optical Society of America

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  22. Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2002 (2)

H. Jiang, N. Iftimia, Y. Xu, J. Eggert, L. Fajardo, K. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef] [PubMed]

2001 (7)

2000 (3)

1999 (5)

1998 (2)

H. Jiang, K. Paulsen, U. Osterberg, M. Patterson, “Improved continuous light diffusion imaging in single- and multi-target tissue-like phantoms,” Phys. Med. Biol. 43, 675–693 (1998).
[CrossRef] [PubMed]

S. Arridge, W. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998).
[CrossRef]

1997 (5)

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
[CrossRef] [PubMed]

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

B. Chance, Q. Luo, S. Nioka, D. Alsop, J. Detre, “Optical investigations of physiology: a study of biomedical intrinsic and extrinsic contrast,” Phil. Trans. R. Soc. London Ser. B 352, 707–716 (1997).
[CrossRef]

J. Zhang, H. L. Graber, P. C. Kou, R. Aronson, S. S. Barbour, R. L. Barbour, “Optical imaging of anatomical maps derived from magnetic resonance images using time-independent optical source,” IEEE Trans. Med. Imaging 16, 68–77 (1997).
[CrossRef]

S. Colak, D. Papaioannou, G. t’ Hooft, M. vander Mark, H. Schomberg, J. Paasschens, J. Melissen, N. VanAsten, “Tomographic image reconstruction from optical projections in light diffusing media,” Appl. Opt. 36, 180–213 (1997).
[CrossRef] [PubMed]

1996 (1)

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using dc data: simulations and experiments,” Phys. Med. Biol. 41, 1483–1498 (1996).
[CrossRef] [PubMed]

1995 (4)

Alfano, R.

Alrubaiee, M.

Alsop, D.

B. Chance, Q. Luo, S. Nioka, D. Alsop, J. Detre, “Optical investigations of physiology: a study of biomedical intrinsic and extrinsic contrast,” Phil. Trans. R. Soc. London Ser. B 352, 707–716 (1997).
[CrossRef]

Aronson, R.

Y. Pei, H. L. Graber, R. L. Barbour, R. Aronson, “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]

J. Zhang, H. L. Graber, P. C. Kou, R. Aronson, S. S. Barbour, R. L. Barbour, “Optical imaging of anatomical maps derived from magnetic resonance images using time-independent optical source,” IEEE Trans. Med. Imaging 16, 68–77 (1997).
[CrossRef]

Arridge, S.

Banks, H. T.

H. T. Banks, K. Kunisch, Estimation Techniques for Distributed Parameter Systems (Birkhauser, Boston, 1989).
[CrossRef]

Barbour, R.

H. L. Graber, Y. Pei, R. Barbour, “Imaging of spatiotemporal coincident states by dc optical tomography,” IEEE Trans. Med. Imaging (to be published).

Barbour, R. L.

Barbour, S. S.

J. Zhang, H. L. Graber, P. C. Kou, R. Aronson, S. S. Barbour, R. L. Barbour, “Optical imaging of anatomical maps derived from magnetic resonance images using time-independent optical source,” IEEE Trans. Med. Imaging 16, 68–77 (1997).
[CrossRef]

Baron, L.

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 60–66 (2001).

Bjorck, A.

G. Dahlquist, A. Bjorck, Numerical Methods (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Boas, D.

Boas, D. A.

Bolster, M.

Bolster, M. B.

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef] [PubMed]

Bulirsch, R.

J. Stoer, R. Bulirsch, Introduction to Numerical Analysis (Springer-Verlag, Berlin, 1980).

Cai, W.

Chance, B.

V. Ntziachristos, A. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).
[CrossRef] [PubMed]

B. Chance, Q. Luo, S. Nioka, D. Alsop, J. Detre, “Optical investigations of physiology: a study of biomedical intrinsic and extrinsic contrast,” Phil. Trans. R. Soc. London Ser. B 352, 707–716 (1997).
[CrossRef]

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

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

Colak, S.

S. Colak, M. van der Mark, G. t’ Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

S. Colak, D. Papaioannou, G. t’ Hooft, M. vander Mark, H. Schomberg, J. Paasschens, J. Melissen, N. VanAsten, “Tomographic image reconstruction from optical projections in light diffusing media,” Appl. Opt. 36, 180–213 (1997).
[CrossRef] [PubMed]

Cubeddu, R.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
[CrossRef] [PubMed]

Dahlquist, G.

G. Dahlquist, A. Bjorck, Numerical Methods (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Delpy, D.

Detre, J.

B. Chance, Q. Luo, S. Nioka, D. Alsop, J. Detre, “Optical investigations of physiology: a study of biomedical intrinsic and extrinsic contrast,” Phil. Trans. R. Soc. London Ser. B 352, 707–716 (1997).
[CrossRef]

Eggert, J.

H. Jiang, N. Iftimia, Y. Xu, J. Eggert, L. Fajardo, K. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 60–66 (2001).

Fajardo, L.

H. Jiang, N. Iftimia, Y. Xu, J. Eggert, L. Fajardo, K. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 60–66 (2001).

Fry, M.

Gayen, S.

Graber, H. L.

Y. Pei, H. L. Graber, R. L. Barbour, R. Aronson, “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]

Y. Pei, H. L. Graber, R. L. Barbour, “Normalized-constraint algorithm for minimizing inter-parameter crosstalk in dc optical tomography,” Opt. Express 9, 97–109 (2001).
[CrossRef] [PubMed]

J. Zhang, H. L. Graber, P. C. Kou, R. Aronson, S. S. Barbour, R. L. Barbour, “Optical imaging of anatomical maps derived from magnetic resonance images using time-independent optical source,” IEEE Trans. Med. Imaging 16, 68–77 (1997).
[CrossRef]

H. L. Graber, Y. Pei, R. Barbour, “Imaging of spatiotemporal coincident states by dc optical tomography,” IEEE Trans. Med. Imaging (to be published).

Hebden, J.

Hillman, E.

Hoogenraad, J.

S. Colak, M. van der Mark, G. t’ Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Iftimia, N.

H. Jiang, N. Iftimia, Y. Xu, J. Eggert, L. Fajardo, K. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef] [PubMed]

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 60–66 (2001).

Y. Xu, N. Iftimia, H. Jiang, L. Key, M. Bolster, “Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography,” Opt. Express 8, 447–451 (2001).
[CrossRef] [PubMed]

N. Iftimia, H. Jiang, “Quantitative optical image reconstruction of turbid media using dc measurements,” Appl. Opt. 39, 5256–5261 (2000).
[CrossRef]

H. Jiang, Y. Xu, N. Iftimia, “Experimental three-dimensional optical image reconstruction of heterogeneous turbid media,” Opt. Express 7, 204–209 (2000).
[CrossRef] [PubMed]

Jiang, H.

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef] [PubMed]

H. Jiang, N. Iftimia, Y. Xu, J. Eggert, L. Fajardo, K. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

Y. Xu, N. Iftimia, H. Jiang, L. Key, M. Bolster, “Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography,” Opt. Express 8, 447–451 (2001).
[CrossRef] [PubMed]

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 60–66 (2001).

N. Iftimia, H. Jiang, “Quantitative optical image reconstruction of turbid media using dc measurements,” Appl. Opt. 39, 5256–5261 (2000).
[CrossRef]

H. Jiang, Y. Xu, N. Iftimia, “Experimental three-dimensional optical image reconstruction of heterogeneous turbid media,” Opt. Express 7, 204–209 (2000).
[CrossRef] [PubMed]

H. Jiang, K. Paulsen, U. Osterberg, M. Patterson, “Improved continuous light diffusion imaging in single- and multi-target tissue-like phantoms,” Phys. Med. Biol. 43, 675–693 (1998).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using dc data: simulations and experiments,” Phys. Med. Biol. 41, 1483–1498 (1996).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of absorption and scattering maps in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[CrossRef] [PubMed]

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–702 (1995).
[CrossRef] [PubMed]

Jiang, S.

Key, L.

Key, L. L.

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef] [PubMed]

Klove, K.

H. Jiang, N. Iftimia, Y. Xu, J. Eggert, L. Fajardo, K. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
[CrossRef] [PubMed]

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 60–66 (2001).

Kou, P. C.

J. Zhang, H. L. Graber, P. C. Kou, R. Aronson, S. S. Barbour, R. L. Barbour, “Optical imaging of anatomical maps derived from magnetic resonance images using time-independent optical source,” IEEE Trans. Med. Imaging 16, 68–77 (1997).
[CrossRef]

Kuijpers, F.

S. Colak, M. van der Mark, G. t’ Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Kunisch, K.

H. T. Banks, K. Kunisch, Estimation Techniques for Distributed Parameter Systems (Birkhauser, Boston, 1989).
[CrossRef]

Lax, M.

Lionheart, W.

Luo, Q.

B. Chance, Q. Luo, S. Nioka, D. Alsop, J. Detre, “Optical investigations of physiology: a study of biomedical intrinsic and extrinsic contrast,” Phil. Trans. R. Soc. London Ser. B 352, 707–716 (1997).
[CrossRef]

Marota, J.

Matson, C. L.

McBride, T. O.

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

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

Melissen, J.

Nioka, S.

B. Chance, Q. Luo, S. Nioka, D. Alsop, J. Detre, “Optical investigations of physiology: a study of biomedical intrinsic and extrinsic contrast,” Phil. Trans. R. Soc. London Ser. B 352, 707–716 (1997).
[CrossRef]

Ntziachristos, V.

V. Ntziachristos, A. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).
[CrossRef] [PubMed]

O’Leary, M. A.

Osterberg, U.

H. Jiang, K. Paulsen, U. Osterberg, M. Patterson, “Improved continuous light diffusion imaging in single- and multi-target tissue-like phantoms,” Phys. Med. Biol. 43, 675–693 (1998).
[CrossRef] [PubMed]

Osterberg, U. L.

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

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using dc data: simulations and experiments,” Phys. Med. Biol. 41, 1483–1498 (1996).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of absorption and scattering maps in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[CrossRef] [PubMed]

Osterman, K. S.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

Paasschens, J.

Papaioannou, D.

Patterson, M.

H. Jiang, K. Paulsen, U. Osterberg, M. Patterson, “Improved continuous light diffusion imaging in single- and multi-target tissue-like phantoms,” Phys. Med. Biol. 43, 675–693 (1998).
[CrossRef] [PubMed]

Patterson, M. S.

Paulsen, K.

H. Jiang, K. Paulsen, U. Osterberg, M. Patterson, “Improved continuous light diffusion imaging in single- and multi-target tissue-like phantoms,” Phys. Med. Biol. 43, 675–693 (1998).
[CrossRef] [PubMed]

Paulsen, K. D.

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

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using dc data: simulations and experiments,” Phys. Med. Biol. 41, 1483–1498 (1996).
[CrossRef] [PubMed]

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–702 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of absorption and scattering maps in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
[CrossRef] [PubMed]

Pei, Y.

Pifferi, A.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
[CrossRef] [PubMed]

Pogue, B. W.

Poplack, S. P.

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R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
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R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “A solid tissue phantom for photon migration studies,” Phys. Med. Biol. 42, 1971–1979 (1997).
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S. Colak, M. van der Mark, G. t’ Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

van der Mark, M.

S. Colak, M. van der Mark, G. t’ Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

VanAsten, N.

vander Mark, M.

Wells, W. A.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
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Xu, Y.

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V. Ntziachristos, A. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).
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H. Jiang, N. Iftimia, Y. Xu, J. Eggert, L. Fajardo, K. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. 9, 186–194 (2002).
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Appl. Opt. (5)

IEEE J. Sel. Top. Quantum Electron. (1)

S. Colak, M. van der Mark, G. t’ Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
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IEEE Trans. Med. Imaging (2)

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 60–66 (2001).

J. Zhang, H. L. Graber, P. C. Kou, R. Aronson, S. S. Barbour, R. L. Barbour, “Optical imaging of anatomical maps derived from magnetic resonance images using time-independent optical source,” IEEE Trans. Med. Imaging 16, 68–77 (1997).
[CrossRef]

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Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
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Phys. Today (1)

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

V. Ntziachristos, A. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).
[CrossRef] [PubMed]

Radiology (1)

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
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Figures (12)

Fig. 1
Fig. 1

Schematic of the DOT system.

Fig. 2
Fig. 2

Phantom geometry for (a) cases 1–6 and (b) case 7.

Fig. 3
Fig. 3

Reconstructed absorption and scattering images by use of the existing algorithm (without the normalizing scheme): (a) absorption image for case 2, (b) scattering image for case 2, (c) absorption image for case 4, and (d) scattering image for case 4.

Fig. 4
Fig. 4

Reconstructed absorption and scattering images by use of the normalizing scheme–based algorithm: (a) absorption image for case 1, (b) scattering image for case 1, (c) absorption image for case 2, and (d) scattering image for case 2.

Fig. 5
Fig. 5

Reconstructed absorption and scattering images by use of the normalizing scheme–based algorithm: (a) absorption image for case 3, (b) scattering image for case 3, (c) absorption image for case 4, and (d) scattering image for case 4.

Fig. 6
Fig. 6

Reconstructed absorption and scattering images by use of the normalizing scheme–based algorithm: (a) absorption image for case 5, (b) scattering image for case 5, (c) absorption image for case 6, and (d) scattering image for case 6.

Fig. 7
Fig. 7

Reconstructed absorption and scattering images by use of the normalizing scheme–based algorithm: (a) absorption image for case 7 and (b) scattering image for case 7.

Fig. 8
Fig. 8

Comparison of exact (dashed line) and reconstructed (solid curve) optical property distribution along transects CD and EF shown in Fig. 2(a) for the images appearing in Fig. 4: (a) absorption profiles along transect CD for case 1, (b) absorption profiles along transect EF for case 1, (c) absorption profiles along transect CD for case 2, and (d) absorption profiles along transect EF for case 2.

Fig. 9
Fig. 9

Comparison of exact (dashed line) and reconstructed (solid curve) optical property distribution along transects CD and EF shown in Fig. 2(a) for the images appearing in Fig. 5: (a) scattering profiles along transect CD for case 3, (b) scattering profiles along transect EF for case 3, (c) scattering profiles along transect CD for case 4, and (d) scattering profiles along transect EF for case 4.

Fig. 10
Fig. 10

Comparison of exact (dashed line) and reconstructed (solid curve) optical property distribution along transects CD and EF shown in Fig. 2(a) for the images appearing in Fig. 6: (a) absorption profiles along transect CD for case 5, (b) absorption profiles along transect EF for case 5, (c) scattering profiles along transect CD for case 5, (d) scattering profiles along transect EF for case 5, (e) absorption profiles along transect CD for case 6, (f) absorption profiles along transect EF for case 6, (g) scattering profiles along transect CD for case 6, and (h) scattering profiles along transect EF for case 6.

Fig. 11
Fig. 11

Comparison of exact (dashed line) and reconstructed (solid curve) optical property distribution along transects CD and EF or C* D* and E* F* shown in Fig. 2(b) for the images appearing in Fig. 7: (a) absorption profiles along transect C* D* for target B, (b) absorption profiles along transect E* F* for target B, (c) absorption profiles along transect CD for target A, (d) absorption profiles along transect EF for target A, (e) scattering profiles along transect C* D* for target B, and (f) scattering profiles along transect E* F* for target B.

Fig. 12
Fig. 12

Effect of regularization. The simulation of the 1D diffusion approximation on the interval (0, 43.0) with Rubin or type III boundary conditions for a homogeneous background medium with q = μa/D. We computed cost functional F λ(q) = |Φ(0; q 0) - Φ(0; q)| + λ‖q2 for q 0 = 0.1907 mm-1 (corresponding to μ a = 0.012 mm-1 and D = 0.33 mm) over a range of q starting from 0.14 to 0.4, where Φ(x; q) is the Green’s function for a delta source located at x = 42.0. The solid curve represents F without regularization (λ = 0), and the broken curve represents F λ with regularization parameter λ = 10-6.

Equations (10)

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T+λIΔq=TΦm-Φc,
=Φ1D1Φ1D2Φ1DNΦ1μa,1Φ1μa,2Φ1μa,NΦ2D1Φ2D2Φ2DNΦ2μa,1Φ2μa,2Φ2μa,NΦMD1ΦMD2ΦMDNΦMμa,1ΦMμa,2ΦMμa,N.
mD=MaxΦ1D1, Φ1D2,  Φ1DN, Φ2D1, Φ2D2,  Φ2DN,  ΦMD1, ΦMD2,  ΦMDN,
mμ=MaxΦ1μa,1, Φ1μa,2,  Φ1μa,N, Φ2μa,1, Φ2μa,2,  ΦNμa,N,ΦMμa,1,  ΦMμa,2,  ΦMμa,N,
Φ¯D=1mDΦD,
Φ¯μa=1mμΦμa
¯T¯+λIΔq¯=¯TΦm-Φc,
Δq¯=mDΔD1, mDΔD2,  mDΔDN, mμΔμa,1, mμΔμa,2,  mμΔμa,NT,
¯=1mDΦ1D11mDΦ1D21mDΦ1DN1mμΦ1μa,11mμΦ1μa,21mμΦ1μa,N1mDΦ2D11mDΦ2D21mDΦ2DN1mμΦ2μa,11mμΦa,2μa,21mμΦ2μa,N1mDΦMD11mDΦMD21mDΦMDN1mμΦMμa,11mμΦMμa,21mμΦMμa,N.
FλΦm, Φc; q=j=1M |Φjm-Φjc|+λq2,

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