Abstract

The reconstruction method presented here is based on diffusion approximation for light propagation in turbid media and on a minimization strategy for the output-least-squares problem. A perturbation approach is introduced for the optical properties. Here we can strongly reduce the number of free variables of the inverse problem by exploiting a priori information such as the search for single inhomogeneities within a relatively homogeneous object, a typical situation for breast cancer detection. We achieve higher accuracy and a considerable reduction in computational effort by solving a parabolic differential equation for a perturbation density, i.e., the difference between the photon density in an inhomogeneous object and the density in the homogeneous case being given by an analytic expression. The calculations are performed by a two-dimensional finite-element-method algorithm. However, as a time-dependent correction factor is applied, the three-dimensional situation is well approximated. The method was successfully tested by use of the University of Pennsylvania standard data set. Data noise was generated and taken into account in a modified data set. The influence of different noise on the reconstruction results is discussed.

© 1998 Optical Society of America

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References

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  1. G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der. Zee, eds., Medical Optical Tomography: Functional Imaging and Monitoring, SPIE Institutes Series, Vol. IS11 (SPIE, Bellingham, Wash., 1993).
  2. R. Model, R. Hünlich, M. Orlt, M. Walzel, “Reconstruction algorithm for near-infrared imaging in turbid media by means of time-domain data,” J. Opt. Soc. Am. A 14, 313–324 (1997).
    [CrossRef]
  3. R. Model, R. Hünlich, M. Orlt, M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 400–410 (1995).
    [CrossRef]
  4. M. Orlt, M. Walzel, R. Model, “Transillumination imaging performance using time domain data,” in Photon Propagation in Tissue, B. Chance, D. T. Delpy, G. J. Müller, eds., Proc. SPIE2626, 346–357 (1995).
    [CrossRef]
  5. S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “Performance of an iterative reconstruction algorithm for near-infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissue, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 360–371 (1993).
    [CrossRef]
  6. B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse iterative calculations for 3-D frequency diffuse optical tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 328–339 (1995).
    [CrossRef]
  7. M. V. Klibanow, T. R. Lucas, R. M. Frank, “New imaging algorithm in diffusion tomography,” in Biological Imaging and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, D. A. Benaron, B. Chance, eds., Proc. SPIE2979, 272–283 (1997).
    [CrossRef]
  8. A. Ishimaru, Wave Propagation in Random Scattering Media (Academic, New York, 1978).
  9. D. Boas, Time-Domain Standard Data Series (University of Pennsylvania, URL http://www.lrsm.upenn.edu .
  10. S. R. Arridge, M. Cope, P. van der Zee, P. J. Hillson, D. T. Delpy, “Visualization of the oxygenation state of brain and muscle in newborn infants by near infrared transillumination,” in Information Processing in Medical Imaging, S. L. Bacharach, ed. (Nijhoff, Dordrecht, The Netherlands, 1985), pp. 155–176.
  11. Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of scattering media by diffusion tomography: an iterative perturbative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE1641, 58–71 (1992).
    [CrossRef]
  12. S. C. Feng, F.-A. Zeng, B. Chance, “Analytical perturbation theory of photon migration in the presence of a single absorbing or scattering defect sphere,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 54–63 (1995).
    [CrossRef]
  13. M. R. Ostermeyer, S. T. Jacques, “Perturbation theory for optical diffusion theory: a general approach for absorbing and scattering objects in tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 98–102 (1995).
    [CrossRef]
  14. M. Orlt, M. Walzel, R. Model, “Influence of different kind of error on imaging results in optical tomography,” in Advanced Mathematical Tools in Metrology II, P. Ciarlini, M. Cox, F. Pavese, D. Richter, eds. (World Scientific, Singapore, 1997), pp. 277–279.
  15. R. Model, R. Hünlich, “Parameter sensitivity in near infrared imaging,” in Photon Propagation in Tissue, B. Chance, D. T. Delpy, G. J. Müller, eds., Proc. SPIE2626, 56–65 (1995).
    [CrossRef]
  16. D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
    [CrossRef] [PubMed]
  17. D. V. O’Conner, D. Phillips, Time-Correlated Single Photon Counting (Academic, London, 1984).
  18. R. Model, R. Hünlich, “Optical imaging of highly scattering media,” Z. Angew. Math. Mech. 76, 483–484 (1996).
  19. J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983).

1997 (1)

1996 (1)

R. Model, R. Hünlich, “Optical imaging of highly scattering media,” Z. Angew. Math. Mech. 76, 483–484 (1996).

1994 (1)

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Aronson, R.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of scattering media by diffusion tomography: an iterative perturbative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE1641, 58–71 (1992).
[CrossRef]

Arridge, S. R.

S. R. Arridge, M. Cope, P. van der Zee, P. J. Hillson, D. T. Delpy, “Visualization of the oxygenation state of brain and muscle in newborn infants by near infrared transillumination,” in Information Processing in Medical Imaging, S. L. Bacharach, ed. (Nijhoff, Dordrecht, The Netherlands, 1985), pp. 155–176.

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “Performance of an iterative reconstruction algorithm for near-infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissue, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

Barbour, R. L.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of scattering media by diffusion tomography: an iterative perturbative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE1641, 58–71 (1992).
[CrossRef]

Boas, D. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Chance, B.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

S. C. Feng, F.-A. Zeng, B. Chance, “Analytical perturbation theory of photon migration in the presence of a single absorbing or scattering defect sphere,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 54–63 (1995).
[CrossRef]

Chang, J.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of scattering media by diffusion tomography: an iterative perturbative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE1641, 58–71 (1992).
[CrossRef]

Cope, M.

S. R. Arridge, M. Cope, P. van der Zee, P. J. Hillson, D. T. Delpy, “Visualization of the oxygenation state of brain and muscle in newborn infants by near infrared transillumination,” in Information Processing in Medical Imaging, S. L. Bacharach, ed. (Nijhoff, Dordrecht, The Netherlands, 1985), pp. 155–176.

Delpy, D. T.

S. R. Arridge, M. Cope, P. van der Zee, P. J. Hillson, D. T. Delpy, “Visualization of the oxygenation state of brain and muscle in newborn infants by near infrared transillumination,” in Information Processing in Medical Imaging, S. L. Bacharach, ed. (Nijhoff, Dordrecht, The Netherlands, 1985), pp. 155–176.

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “Performance of an iterative reconstruction algorithm for near-infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissue, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

Dennis, J. E.

J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983).

Farrell, T. J.

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse iterative calculations for 3-D frequency diffuse optical tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 328–339 (1995).
[CrossRef]

Feng, S. C.

S. C. Feng, F.-A. Zeng, B. Chance, “Analytical perturbation theory of photon migration in the presence of a single absorbing or scattering defect sphere,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 54–63 (1995).
[CrossRef]

Frank, R. M.

M. V. Klibanow, T. R. Lucas, R. M. Frank, “New imaging algorithm in diffusion tomography,” in Biological Imaging and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, D. A. Benaron, B. Chance, eds., Proc. SPIE2979, 272–283 (1997).
[CrossRef]

Graber, H. L.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of scattering media by diffusion tomography: an iterative perturbative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE1641, 58–71 (1992).
[CrossRef]

Hillson, P. J.

S. R. Arridge, M. Cope, P. van der Zee, P. J. Hillson, D. T. Delpy, “Visualization of the oxygenation state of brain and muscle in newborn infants by near infrared transillumination,” in Information Processing in Medical Imaging, S. L. Bacharach, ed. (Nijhoff, Dordrecht, The Netherlands, 1985), pp. 155–176.

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “Performance of an iterative reconstruction algorithm for near-infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissue, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

Hünlich, R.

R. Model, R. Hünlich, M. Orlt, M. Walzel, “Reconstruction algorithm for near-infrared imaging in turbid media by means of time-domain data,” J. Opt. Soc. Am. A 14, 313–324 (1997).
[CrossRef]

R. Model, R. Hünlich, “Optical imaging of highly scattering media,” Z. Angew. Math. Mech. 76, 483–484 (1996).

R. Model, R. Hünlich, “Parameter sensitivity in near infrared imaging,” in Photon Propagation in Tissue, B. Chance, D. T. Delpy, G. J. Müller, eds., Proc. SPIE2626, 56–65 (1995).
[CrossRef]

R. Model, R. Hünlich, M. Orlt, M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 400–410 (1995).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation in Random Scattering Media (Academic, New York, 1978).

Jacques, S. T.

M. R. Ostermeyer, S. T. Jacques, “Perturbation theory for optical diffusion theory: a general approach for absorbing and scattering objects in tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 98–102 (1995).
[CrossRef]

Klibanow, M. V.

M. V. Klibanow, T. R. Lucas, R. M. Frank, “New imaging algorithm in diffusion tomography,” in Biological Imaging and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, D. A. Benaron, B. Chance, eds., Proc. SPIE2979, 272–283 (1997).
[CrossRef]

Lubowsky, J.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of scattering media by diffusion tomography: an iterative perturbative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE1641, 58–71 (1992).
[CrossRef]

Lucas, T. R.

M. V. Klibanow, T. R. Lucas, R. M. Frank, “New imaging algorithm in diffusion tomography,” in Biological Imaging and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, D. A. Benaron, B. Chance, eds., Proc. SPIE2979, 272–283 (1997).
[CrossRef]

Model, R.

R. Model, R. Hünlich, M. Orlt, M. Walzel, “Reconstruction algorithm for near-infrared imaging in turbid media by means of time-domain data,” J. Opt. Soc. Am. A 14, 313–324 (1997).
[CrossRef]

R. Model, R. Hünlich, “Optical imaging of highly scattering media,” Z. Angew. Math. Mech. 76, 483–484 (1996).

M. Orlt, M. Walzel, R. Model, “Influence of different kind of error on imaging results in optical tomography,” in Advanced Mathematical Tools in Metrology II, P. Ciarlini, M. Cox, F. Pavese, D. Richter, eds. (World Scientific, Singapore, 1997), pp. 277–279.

R. Model, R. Hünlich, “Parameter sensitivity in near infrared imaging,” in Photon Propagation in Tissue, B. Chance, D. T. Delpy, G. J. Müller, eds., Proc. SPIE2626, 56–65 (1995).
[CrossRef]

R. Model, R. Hünlich, M. Orlt, M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 400–410 (1995).
[CrossRef]

M. Orlt, M. Walzel, R. Model, “Transillumination imaging performance using time domain data,” in Photon Propagation in Tissue, B. Chance, D. T. Delpy, G. J. Müller, eds., Proc. SPIE2626, 346–357 (1995).
[CrossRef]

O’Conner, D. V.

D. V. O’Conner, D. Phillips, Time-Correlated Single Photon Counting (Academic, London, 1984).

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Orlt, M.

R. Model, R. Hünlich, M. Orlt, M. Walzel, “Reconstruction algorithm for near-infrared imaging in turbid media by means of time-domain data,” J. Opt. Soc. Am. A 14, 313–324 (1997).
[CrossRef]

R. Model, R. Hünlich, M. Orlt, M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 400–410 (1995).
[CrossRef]

M. Orlt, M. Walzel, R. Model, “Transillumination imaging performance using time domain data,” in Photon Propagation in Tissue, B. Chance, D. T. Delpy, G. J. Müller, eds., Proc. SPIE2626, 346–357 (1995).
[CrossRef]

M. Orlt, M. Walzel, R. Model, “Influence of different kind of error on imaging results in optical tomography,” in Advanced Mathematical Tools in Metrology II, P. Ciarlini, M. Cox, F. Pavese, D. Richter, eds. (World Scientific, Singapore, 1997), pp. 277–279.

Ostermeyer, M. R.

M. R. Ostermeyer, S. T. Jacques, “Perturbation theory for optical diffusion theory: a general approach for absorbing and scattering objects in tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 98–102 (1995).
[CrossRef]

Patterson, M. S.

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse iterative calculations for 3-D frequency diffuse optical tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 328–339 (1995).
[CrossRef]

Phillips, D.

D. V. O’Conner, D. Phillips, Time-Correlated Single Photon Counting (Academic, London, 1984).

Pogue, B. W.

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse iterative calculations for 3-D frequency diffuse optical tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 328–339 (1995).
[CrossRef]

Schnabel, R. B.

J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983).

Schweiger, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “Performance of an iterative reconstruction algorithm for near-infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissue, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

van der Zee, P.

S. R. Arridge, M. Cope, P. van der Zee, P. J. Hillson, D. T. Delpy, “Visualization of the oxygenation state of brain and muscle in newborn infants by near infrared transillumination,” in Information Processing in Medical Imaging, S. L. Bacharach, ed. (Nijhoff, Dordrecht, The Netherlands, 1985), pp. 155–176.

Walzel, M.

R. Model, R. Hünlich, M. Orlt, M. Walzel, “Reconstruction algorithm for near-infrared imaging in turbid media by means of time-domain data,” J. Opt. Soc. Am. A 14, 313–324 (1997).
[CrossRef]

M. Orlt, M. Walzel, R. Model, “Transillumination imaging performance using time domain data,” in Photon Propagation in Tissue, B. Chance, D. T. Delpy, G. J. Müller, eds., Proc. SPIE2626, 346–357 (1995).
[CrossRef]

R. Model, R. Hünlich, M. Orlt, M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 400–410 (1995).
[CrossRef]

M. Orlt, M. Walzel, R. Model, “Influence of different kind of error on imaging results in optical tomography,” in Advanced Mathematical Tools in Metrology II, P. Ciarlini, M. Cox, F. Pavese, D. Richter, eds. (World Scientific, Singapore, 1997), pp. 277–279.

Wang, Y.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of scattering media by diffusion tomography: an iterative perturbative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE1641, 58–71 (1992).
[CrossRef]

Yodh, A. G.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Zeng, F.-A.

S. C. Feng, F.-A. Zeng, B. Chance, “Analytical perturbation theory of photon migration in the presence of a single absorbing or scattering defect sphere,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 54–63 (1995).
[CrossRef]

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

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

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Z. Angew. Math. Mech. (1)

R. Model, R. Hünlich, “Optical imaging of highly scattering media,” Z. Angew. Math. Mech. 76, 483–484 (1996).

Other (16)

J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983).

D. V. O’Conner, D. Phillips, Time-Correlated Single Photon Counting (Academic, London, 1984).

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der. Zee, eds., Medical Optical Tomography: Functional Imaging and Monitoring, SPIE Institutes Series, Vol. IS11 (SPIE, Bellingham, Wash., 1993).

R. Model, R. Hünlich, M. Orlt, M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 400–410 (1995).
[CrossRef]

M. Orlt, M. Walzel, R. Model, “Transillumination imaging performance using time domain data,” in Photon Propagation in Tissue, B. Chance, D. T. Delpy, G. J. Müller, eds., Proc. SPIE2626, 346–357 (1995).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “Performance of an iterative reconstruction algorithm for near-infrared absorption and scatter imaging,” in Photon Migration and Imaging in Random Media and Tissue, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse iterative calculations for 3-D frequency diffuse optical tomography,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. Alfano, eds., Proc. SPIE2389, 328–339 (1995).
[CrossRef]

M. V. Klibanow, T. R. Lucas, R. M. Frank, “New imaging algorithm in diffusion tomography,” in Biological Imaging and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, D. A. Benaron, B. Chance, eds., Proc. SPIE2979, 272–283 (1997).
[CrossRef]

A. Ishimaru, Wave Propagation in Random Scattering Media (Academic, New York, 1978).

D. Boas, Time-Domain Standard Data Series (University of Pennsylvania, URL http://www.lrsm.upenn.edu .

S. R. Arridge, M. Cope, P. van der Zee, P. J. Hillson, D. T. Delpy, “Visualization of the oxygenation state of brain and muscle in newborn infants by near infrared transillumination,” in Information Processing in Medical Imaging, S. L. Bacharach, ed. (Nijhoff, Dordrecht, The Netherlands, 1985), pp. 155–176.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, J. Lubowsky, “Imaging of scattering media by diffusion tomography: an iterative perturbative approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. S. Mang, ed., Proc. SPIE1641, 58–71 (1992).
[CrossRef]

S. C. Feng, F.-A. Zeng, B. Chance, “Analytical perturbation theory of photon migration in the presence of a single absorbing or scattering defect sphere,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 54–63 (1995).
[CrossRef]

M. R. Ostermeyer, S. T. Jacques, “Perturbation theory for optical diffusion theory: a general approach for absorbing and scattering objects in tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 98–102 (1995).
[CrossRef]

M. Orlt, M. Walzel, R. Model, “Influence of different kind of error on imaging results in optical tomography,” in Advanced Mathematical Tools in Metrology II, P. Ciarlini, M. Cox, F. Pavese, D. Richter, eds. (World Scientific, Singapore, 1997), pp. 277–279.

R. Model, R. Hünlich, “Parameter sensitivity in near infrared imaging,” in Photon Propagation in Tissue, B. Chance, D. T. Delpy, G. J. Müller, eds., Proc. SPIE2626, 56–65 (1995).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Three-dimensional measurement geometry: 12 sources and 12 detectors positioned in a plane on a circular curve 8 cm in diameter. Background absorption, μ a = 0.05 cm-1; scattering, μ s ′ = 10.0 cm-1.

Fig. 2
Fig. 2

FEM grid with measurement geometry for the source in position x s = 0 mm, y s = -40 mm.

Fig. 3
Fig. 3

Approximate 3D simulation results for the 10-fold absorber. Comparison is shown between the simulated photon density and the University of Pennsylvania standard data set in five detector positions.

Fig. 4
Fig. 4

Reconstruction results. Comparison is shown between the University of Pennsylvania standard data set with additional noise (dotted curves) for μ a abs = 0.5 cm-1, simulated photon densities after identification when 12 sources, 10 detectors (solid curves) are used, and the densities for a homogenous medium (dashed curve). Source and detectors are chosen as in Fig. 2. Top, 5% noise; bottom, 10% noise.

Fig. 5
Fig. 5

Select iteration solutions starting from a strongly unfavorable initial guess when 12 sources and 10 detectors are used [fac = (μ a abs a0)].

Fig. 6
Fig. 6

Reconstruction results for different absorption coefficients μ a abs of the sphere [fac = (μ a abs a0)] and 10% data noise (the theoretical value of fac is in brackets). Top: 3 sources and 10 detectors; bottom, 12 sources and 10 detectors.

Fig. 7
Fig. 7

Reconstruction results when noisy data are used. The dependence of d (distance between the center of the detected absorber and that of the expected absorber) on the absorption of the sphere and on the noise level is illustrated. Top, 12 sources, 0%, 5%, 10%, and 15% noise; bottom, 3 sources, 0%, 3%, 5%, and 10% noise.

Tables (1)

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Table 1 Reconstruction Results for a 2-fold Absorber, Different Number of Sources, and 10 Detectors used in Each Case by the Original Standard Data Series without Additional Noise

Equations (18)

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t   Φ x ,   t = div D x   grad   Φ x ,   t - c μ a x Φ x ,   t + s x ,   t ,   x Ω ,   0 < t T .
D x = c 3 μ a x + μ s x ,
- D x Φ x ,   t n = ch x Φ x ,   t ,   x Ω ,   0 < t T .
Φ x ,   t n | x |   0 ,   0 < t T
Φ x ,   0 = Φ 0 x = Q δ x - x s ,   x Ω ,
D = D 0 + D 1 ,     μ a = μ a 0 + μ a 1 ,
t   Φ - div D 0 + D 1 grad   Φ + c μ a 0 + μ a 1 Φ = 0 .
t   Φ c - div D 0   grad   Φ c + c μ a 0 Φ c = 0 .
Φ c x ,   t = Φ an 2 D x ,   t = Q 4 π D 0 t exp - | x - x s | 2 4 D 0 t - c μ a 0 t .
Ψ = Φ 2 D - Φ an 2 D ,
t   Ψ - div D 0 + D 1 grad   Ψ + c μ a 0 + μ a 1 Ψ = div D 1   grad   Φ an 2 D - c μ a 1 Φ an 2 D .
Ψ x ,   t = 0 ,     x Ω ,     0 < t T
Ψ x ,   0 = 0 ,       x Ω
Φ an 3 D = 1 2 π D 0 t 1 / 2 Φ an 2 D .
Φ 3 D 1 2 π D 0 t 1 / 2   Φ 2 D = Φ an 3 D + 1 2 π D 0 t 1 / 2   Ψ .
( 1 )   Choose an initial guess for   p . ( 2 )   Solve the forward problem , i.e. ,   compute   Φ sim ( p ) . ( 3 )   Compare   Φ sim ( p )   with   Φ mes ;   if   Φ sim ( p )   -   Φ mes w is small , go to   ( 5 ) . ( 4 )   Correct   p   and go to   ( 2 ) . ( 5 )   End
Φ sim p - Φ mes w 2 = k = 1 m j = 1 n k i = 1 q jk   w ijk | Φ k sim x jk ,   t ijk ,   p - Φ k mes x jk ,   t ijk | 2 l   | F l p | 2 = min ! ,
w ijk = 1 | Φ k mes x jk ,   t ijk |   max 1 l q jk   | Φ k mes x jk ,   t ljk | .

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