Abstract

Optical image reconstruction in heterogeneous turbid media is sensitive to noise, especially when the signal-to-noise ratio of a measurement system is low. A total-variation-minimization-based iterative algorithm is described in this paper that enhances the quality of reconstructed images with frequency-domain data over that obtained previously with a regularized least-squares approach. Simulation experiments in an 8.6-cm-diameter circular heterogeneous region with low- and high-contrast levels between the target and the background show that the quality of the reconstructed images can be improved considerably when total-variation minimization is included. These simulated results are further verified and confirmed by images reconstructed from experimental data by the use of the same geometry and optically tissue-equivalent phantoms. Measures of imaging performance, including the location, size, and shape of the reconstructed heterogeneity, along with absolute errors in the predicted optical-property values are used to quantify the enhancements afforded by this new approach to optical image reconstruction with diffuse light. The results show improvements of up to 5 mm in terms of geometric information and an order of magnitude or more decrease in the absolute errors in the reconstructed optical-property values for the test cases examined.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), p. 3.
  2. Y. Yamishita, M Kaneko, “Infrared diaphanoscopy for medical diagnosis,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 283–316.
  3. T. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state, diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
    [CrossRef] [PubMed]
  4. H. Jiang, K. D. Paulsen, U. L. Osterberg, “Indirect optical image reconstruction with a cw He–Ne laser for breast cancer detection,” 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, 615–620 (1995).
    [CrossRef]
  5. B. B. Das, K. M. Yoo, R. R. Alfano, “Ultrafast time-gated imaging in thick tissues—a step towards optical mammography,” Opt. Lett. 18, 1092–1094 (1993).
    [CrossRef] [PubMed]
  6. J. C. Hebden, D. T. Delpy, “Enhanced time-resolved imaging with a diffusion model of photon transport,” Opt. Lett. 19, 311–313 (1994).
    [CrossRef] [PubMed]
  7. R. Berg, S. Andersson-Engels, S. Svanberg, “Time-resolved transillumination imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 397–424.
  8. J. B. Fishkin, E. Gratton, “Propagation of photon density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A 10, 127–140 (1993).
    [CrossRef] [PubMed]
  9. S. J. Madsen, E. R. Anderson, R. C. Haskell, B. J. Tromberg, “Portable, high-bandwidth frequency-domain photon migration instrument for tissue spectroscopy,” Opt. Lett. 19, 1934–1936 (1994).
    [CrossRef] [PubMed]
  10. E. M. Sevick, J. J. Frisoli, C. L. Burch, J. R. Lakowicz, “Localization of absorbers in scattering media by use of frequency-domain measurements of time-dependent photon migration,” Appl. Opt. 33, 3562–3570 (1994).
    [CrossRef] [PubMed]
  11. M. S. Patterson, B. W. Pogue, B. C. Wilson, “Computer simulation and experimental studies of optical imaging with photon density waves,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Belling-ham, Wash., 1993), pp. 513–533.
  12. E. Gratton, M. Limkeman, “A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution,” Biophys. J. 44, 315–324 (1983).
    [CrossRef] [PubMed]
  13. S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: light-emitting-diode based technique,” Appl. Opt. 33, 5204–5213 (1994).
    [CrossRef] [PubMed]
  14. E. Gratton, W. Mantulin, M. J. van de Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to laser tomography,” Bioimaging 1, 40–46 (1993).
    [CrossRef]
  15. R. L. Barbour, H. Graber, Y. Wang, J. Chang, R. Aronson, “Perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.
  16. 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]
  17. B. W. Pogue, M.S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
    [CrossRef] [PubMed]
  18. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of absorption and scattering profiles in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995).
    [CrossRef] [PubMed]
  19. H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
    [CrossRef]
  20. 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]
  21. S. R. Arridge, “Forward and inverse problems in time-resolved infrared imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 35–64.
  22. H. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: Derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 121–143.
  23. L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60, 259–268 (1992).
    [CrossRef]
  24. D. C. Dobson, F. Santosa, “An image-enhancement technique for electrical impedance tomography,” Inverse Probl. 10, 317–334 (1994).
    [CrossRef]
  25. P. M. van den Berg, R. E. Kleinmann, “A total variation enhanced modified gradient algorithm for profile reconstruction,” Inverse Probl. 11, L5–L10 (1995).
    [CrossRef]
  26. C. R. Vogel, M. E. Oman, “Iterative methods for total variation denoising,” SIAM J. Sci. Comput. 17, 227–238 (1996).
    [CrossRef]
  27. D. C. Dobson, F. Santosa, “Recovery of blocky images from noisy and blurred data,” SIAM J. Numer. Anal. (to be published).
  28. D. C. Dobson, “Exploiting ill-posedness in the design of diffractive optical structures,” in Smart Structures and Materials 1993: Mathematics in Smart Structures, H. Banks, eds., Proc. SPIE1919, 248–257 (1993).
    [CrossRef]
  29. R. Acar, C. R. Vogel, “Analysis of bounded variation penalty methods for ill-posed problems,” Inverse Probl. 10, 1217–1229 (1994).
    [CrossRef]
  30. S. R. Arridge, P. van der Zee, M. Cope, D. Delpy, “Reconstruction methods for infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
    [CrossRef]
  31. R. C. Haskell, L. O. Svaasand, T. Tsay, T. C. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).
    [CrossRef]
  32. R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995).
    [CrossRef]
  33. D. W. Marquardt, “An algorithm for least squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
    [CrossRef]

1996 (2)

1995 (6)

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]

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

B. W. Pogue, M.S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (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]

P. M. van den Berg, R. E. Kleinmann, “A total variation enhanced modified gradient algorithm for profile reconstruction,” Inverse Probl. 11, L5–L10 (1995).
[CrossRef]

R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995).
[CrossRef]

1994 (7)

1993 (3)

1992 (2)

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60, 259–268 (1992).
[CrossRef]

T. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state, diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

1983 (1)

E. Gratton, M. Limkeman, “A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution,” Biophys. J. 44, 315–324 (1983).
[CrossRef] [PubMed]

1963 (1)

D. W. Marquardt, “An algorithm for least squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Acar, R.

R. Acar, C. R. Vogel, “Analysis of bounded variation penalty methods for ill-posed problems,” Inverse Probl. 10, 1217–1229 (1994).
[CrossRef]

Alfano, R. R.

Anderson, E. R.

Andersson-Engels, S.

R. Berg, S. Andersson-Engels, S. Svanberg, “Time-resolved transillumination imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 397–424.

Aronson, R.

R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995).
[CrossRef]

H. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: Derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 121–143.

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

Arridge, S. R.

S. R. Arridge, P. van der Zee, M. Cope, D. Delpy, “Reconstruction methods for infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

S. R. Arridge, “Forward and inverse problems in time-resolved infrared imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 35–64.

Barbieri, B.

Barbour, R. L.

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

H. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: Derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 121–143.

Berg, R.

R. Berg, S. Andersson-Engels, S. Svanberg, “Time-resolved transillumination imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 397–424.

Boas, D. A.

Burch, C. L.

Chance, B.

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]

E. Gratton, W. Mantulin, M. J. van de Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to laser tomography,” Bioimaging 1, 40–46 (1993).
[CrossRef]

Chang, J.

H. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: Derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 121–143.

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

Cope, M.

S. R. Arridge, P. van der Zee, M. Cope, D. Delpy, “Reconstruction methods for infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

Das, B. B.

Delpy, D.

S. R. Arridge, P. van der Zee, M. Cope, D. Delpy, “Reconstruction methods for infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

Delpy, D. T.

Dobson, D. C.

D. C. Dobson, F. Santosa, “An image-enhancement technique for electrical impedance tomography,” Inverse Probl. 10, 317–334 (1994).
[CrossRef]

D. C. Dobson, “Exploiting ill-posedness in the design of diffractive optical structures,” in Smart Structures and Materials 1993: Mathematics in Smart Structures, H. Banks, eds., Proc. SPIE1919, 248–257 (1993).
[CrossRef]

D. C. Dobson, F. Santosa, “Recovery of blocky images from noisy and blurred data,” SIAM J. Numer. Anal. (to be published).

Fantini, S.

Farrell, T.

T. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state, diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

Fatemi, E.

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60, 259–268 (1992).
[CrossRef]

Feng, T. C.

Fishkin, J.

E. Gratton, W. Mantulin, M. J. van de Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to laser tomography,” Bioimaging 1, 40–46 (1993).
[CrossRef]

Fishkin, J. B.

Franceschini, M. A.

Frisoli, J. J.

Graber, H.

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

H. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: Derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 121–143.

Gratton, E.

Haskell, R. C.

Hebden, J. C.

Jiang, H.

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

B. W. Pogue, M.S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of absorption and scattering profiles 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]

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Indirect optical image reconstruction with a cw He–Ne laser for breast cancer detection,” 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, 615–620 (1995).
[CrossRef]

Kaneko, M

Y. Yamishita, M Kaneko, “Infrared diaphanoscopy for medical diagnosis,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 283–316.

Kleinmann, R. E.

P. M. van den Berg, R. E. Kleinmann, “A total variation enhanced modified gradient algorithm for profile reconstruction,” Inverse Probl. 11, L5–L10 (1995).
[CrossRef]

Lakowicz, J. R.

Limkeman, M.

E. Gratton, M. Limkeman, “A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution,” Biophys. J. 44, 315–324 (1983).
[CrossRef] [PubMed]

Madsen, S. J.

Mantulin, W.

E. Gratton, W. Mantulin, M. J. van de Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to laser tomography,” Bioimaging 1, 40–46 (1993).
[CrossRef]

Maris, M.

E. Gratton, W. Mantulin, M. J. van de Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to laser tomography,” Bioimaging 1, 40–46 (1993).
[CrossRef]

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

McAdams, M. S.

O'Leary, M. A.

Oman, M. E.

C. R. Vogel, M. E. Oman, “Iterative methods for total variation denoising,” SIAM J. Sci. Comput. 17, 227–238 (1996).
[CrossRef]

Osher, S.

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60, 259–268 (1992).
[CrossRef]

Osterberg, U. L.

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

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

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Indirect optical image reconstruction with a cw He–Ne laser for breast cancer detection,” 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, 615–620 (1995).
[CrossRef]

Patterson, M. S.

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

T. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state, diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

M. S. Patterson, B. W. Pogue, B. C. Wilson, “Computer simulation and experimental studies of optical imaging with photon density waves,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Belling-ham, Wash., 1993), pp. 513–533.

Patterson, M.S.

B. W. Pogue, M.S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

Paulsen, K. D.

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

B. W. Pogue, M.S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (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]

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

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Indirect optical image reconstruction with a cw He–Ne laser for breast cancer detection,” 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, 615–620 (1995).
[CrossRef]

Pogue, B. W.

B. W. Pogue, M.S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

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

M. S. Patterson, B. W. Pogue, B. C. Wilson, “Computer simulation and experimental studies of optical imaging with photon density waves,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Belling-ham, Wash., 1993), pp. 513–533.

Rudin, L. I.

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60, 259–268 (1992).
[CrossRef]

Santosa, F.

D. C. Dobson, F. Santosa, “An image-enhancement technique for electrical impedance tomography,” Inverse Probl. 10, 317–334 (1994).
[CrossRef]

D. C. Dobson, F. Santosa, “Recovery of blocky images from noisy and blurred data,” SIAM J. Numer. Anal. (to be published).

Sevick, E. M.

Svaasand, L. O.

Svanberg, S.

R. Berg, S. Andersson-Engels, S. Svanberg, “Time-resolved transillumination imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 397–424.

Tromberg, B. J.

Tsay, T.

van de Ven, M. J.

E. Gratton, W. Mantulin, M. J. van de Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to laser tomography,” Bioimaging 1, 40–46 (1993).
[CrossRef]

van den Berg, P. M.

P. M. van den Berg, R. E. Kleinmann, “A total variation enhanced modified gradient algorithm for profile reconstruction,” Inverse Probl. 11, L5–L10 (1995).
[CrossRef]

van der Zee, P.

S. R. Arridge, P. van der Zee, M. Cope, D. Delpy, “Reconstruction methods for infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

Vogel, C. R.

C. R. Vogel, M. E. Oman, “Iterative methods for total variation denoising,” SIAM J. Sci. Comput. 17, 227–238 (1996).
[CrossRef]

R. Acar, C. R. Vogel, “Analysis of bounded variation penalty methods for ill-posed problems,” Inverse Probl. 10, 1217–1229 (1994).
[CrossRef]

Wang, Y.

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

Wilson, B. C.

T. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state, diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

M. S. Patterson, B. W. Pogue, B. C. Wilson, “Computer simulation and experimental studies of optical imaging with photon density waves,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Belling-ham, Wash., 1993), pp. 513–533.

Yamishita, Y.

Y. Yamishita, M Kaneko, “Infrared diaphanoscopy for medical diagnosis,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 283–316.

Yodh, A. G.

Yoo, K. M.

Appl. Opt. (2)

Bioimaging (1)

E. Gratton, W. Mantulin, M. J. van de Ven, J. Fishkin, M. Maris, B. Chance, “A novel approach to laser tomography,” Bioimaging 1, 40–46 (1993).
[CrossRef]

Biophys. J. (1)

E. Gratton, M. Limkeman, “A continuously variable frequency cross-correlation phase fluorometer with picosecond resolution,” Biophys. J. 44, 315–324 (1983).
[CrossRef] [PubMed]

Inverse Probl. (3)

R. Acar, C. R. Vogel, “Analysis of bounded variation penalty methods for ill-posed problems,” Inverse Probl. 10, 1217–1229 (1994).
[CrossRef]

D. C. Dobson, F. Santosa, “An image-enhancement technique for electrical impedance tomography,” Inverse Probl. 10, 317–334 (1994).
[CrossRef]

P. M. van den Berg, R. E. Kleinmann, “A total variation enhanced modified gradient algorithm for profile reconstruction,” Inverse Probl. 11, L5–L10 (1995).
[CrossRef]

J. Opt. Soc. Am. A (4)

Med. Phys. (2)

T. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state, diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[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]

Opt. Lett. (5)

Phys. Med. Biol. (1)

B. W. Pogue, M.S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

Physica D (1)

L. I. Rudin, S. Osher, E. Fatemi, “Nonlinear total variation based noise removal algorithm,” Physica D 60, 259–268 (1992).
[CrossRef]

SIAM J. Appl. Math. (1)

D. W. Marquardt, “An algorithm for least squares estimation of nonlinear parameters,” SIAM J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

SIAM J. Sci. Comput. (1)

C. R. Vogel, M. E. Oman, “Iterative methods for total variation denoising,” SIAM J. Sci. Comput. 17, 227–238 (1996).
[CrossRef]

Other (11)

D. C. Dobson, F. Santosa, “Recovery of blocky images from noisy and blurred data,” SIAM J. Numer. Anal. (to be published).

D. C. Dobson, “Exploiting ill-posedness in the design of diffractive optical structures,” in Smart Structures and Materials 1993: Mathematics in Smart Structures, H. Banks, eds., Proc. SPIE1919, 248–257 (1993).
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Indirect optical image reconstruction with a cw He–Ne laser for breast cancer detection,” 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, 615–620 (1995).
[CrossRef]

R. Berg, S. Andersson-Engels, S. Svanberg, “Time-resolved transillumination imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 397–424.

G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), p. 3.

Y. Yamishita, M Kaneko, “Infrared diaphanoscopy for medical diagnosis,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 283–316.

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

S. R. Arridge, “Forward and inverse problems in time-resolved infrared imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 35–64.

H. Graber, J. Chang, R. Aronson, R. L. Barbour, “A perturbation model for imaging in dense scattering media: Derivation and evaluation of imaging operators,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Bellingham, Wash., 1993), pp. 121–143.

S. R. Arridge, P. van der Zee, M. Cope, D. Delpy, “Reconstruction methods for infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

M. S. Patterson, B. W. Pogue, B. C. Wilson, “Computer simulation and experimental studies of optical imaging with photon density waves,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. B. Arridge, J. Beuthen, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of the SPIE Institute Series (SPIE Press, Belling-ham, Wash., 1993), pp. 513–533.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Diagram of the phantom geometry for the off-center-target case under study: R 1 = 43 mm, R 2 = 12.5 mm.

Fig. 2
Fig. 2

Simulated simultaneous reconstructions of both the diffusion and absorption coefficients with a 2:1 contrast level for an eccentrically located target without added random noise: (a) exact image of D, (b) reconstruction of D with no total-variation (TV) minimization, (c) reconstruction of D with TV minimization, (d) exact image of μ a , (e) reconstruction of μ a with no TV minimization, and (f) reconstruction of μ a with TV minimization.

Fig. 3
Fig. 3

Comparison of exact and simulated reconstructions along transects AB and CD (Fig. 1) for the images appearing in Fig. 2. Profiles of (a) D along transect AB, (b) μ a along transect AB, (c) D along transect CD, and (d) μ a along transect CD. The vertical axes indicate values of either D or μ a in millimeters and inverse millimeters, respectively, and the horizontal axes indicate the distance along either transect AB or CD in millimeters.

Fig. 4
Fig. 4

Simulated simultaneous reconstructions of both the diffusion and absorption coefficients with a 2:1 contrast level for an eccentrically located target with an added 10% random noise: (a) exact image of D, (b) reconstruction of D with no total-variation (TV) minimization, (c) reconstruction of D with TV minimization, (d) exact image of μ a , (e) reconstruction of μ a with no TV minimization, and (f) reconstruction of μ a with TV minimization.

Fig. 5
Fig. 5

Comparison of exact and simulated reconstructions along transects AB and CD (Fig. 1) for the images appearing in Fig. 4. Profiles of (a) D along transect AB, (b) μ a along transect AB, (c) D along transect CD, and (d) μ a along transect CD. The vertical axes indicate values of either D or μ a in millimeters and inverse millimeters, respectively, and the horizontal axes indicate the distance along either transect AB or CD in millimeters.

Fig. 6
Fig. 6

Simulated simultaneous reconstructions of both the diffusion and absorption coefficients with a 10:1 contrast level for an eccentrically located target without added random noise: (a) exact image of D, (b) reconstruction of D with no total-variation (TV) minimization, (c) reconstruction of D with TV minimization, (d) exact image of μ a , (e) reconstruction of μ a with no TV minimization, and (f) reconstruction of μ a with TV minimization.

Fig. 7
Fig. 7

Simultaneous reconstructions of both the diffusion and absorption coefficients from the experimental data with a 2:1 contrast level for an eccentrically located target: (a) exact image of D, (b) reconstruction of D with no total-variation (TV) minimization, (c) reconstruction of D with TV minimization, (d) exact image of μ a , (e) reconstruction of μ a with no TV minimization, and (f) reconstruction of μ a with TV minimization.

Fig. 8
Fig. 8

Comparison of the exact and reconstructed profiles along transects AB and CD (Fig. 1) for the images appearing in Fig. 7. Profiles of (a) D along transect AB, (b) μ a along transect AB, (c) D along transect CD, and (d) μ a along transect CD. The vertical axes indicate values of either D or μ a in millimeters and inverse millimeters, respectively, and the horizontal axes indicate the distance along either transect AB or CD in millimeters.

Fig. 9
Fig. 9

Simultaneous reconstructions of both the diffusion and absorption coefficients from the experimental data with a 10:1 contrast level for an eccentrically located target: (a) exact image of D, (b) reconstruction of D with no total-variation (TV) minimization, (c) reconstruction of D with TV minimization, (d) exact image of μ a , (e) reconstruction of μ a with no TV minimization, and (f) reconstruction of μ a with TV minimization.

Tables (4)

Tables Icon

Table 1 Comparison of Image Errors for Simulated-Data Images with Differing Noise and Contrast Levels, both with and without the Total-Variation (TV) Minimization a

Tables Icon

Table 2 Geometric Information for Reconstructed Simulated-Data Images with Differing Noise and Contrast Levels, both with and without the Total-Variation (TV) Minimization a

Tables Icon

Table 3 Image Errors a for Experimental-Data Images with Differing Contrast Levels between the Target and the Background, both with and without the Total-Variation (TV) Minimization

Tables Icon

Table 4 Geometric Information for Reconstructed Experimental-Data Images with Differing Contrast Levels, both with and without the Total-Variation (TV) Minimization a

Equations (16)

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

D Φ ( μ a i ω c ) Φ = S ,
D Φ ψ i + ( μ a i ω c ) Φ ψ i = S ψ i + D Φ n ̂ ψ i d s ,
[ A ] { Φ } = { b } ,
a i j = k = 1 K D k ψ k ψ j ψ i + l = 1 L ( μ l ψ l i ω c ) ψ j ψ i , i = 1 , 2 , , N , j = 1 , 2 , , N ,
b i = S ψ i α j = 1 B Φ j ψ j ψ i d s , Φ = { Φ 1 , Φ 2 , , Φ N } T ,
F ( Φ , D , μ a ) = j = 1 M ( Φ j o Φ j c ) 2 ,
( J T J + λ I ) Δ χ = J T ( Φ o Φ c ) ,
F ( Φ , D , μ a ) = F ( Φ , D , μ a ) + ( w D 2 | D | 2 + w μ 2 | μ a | 2 + δ 2 ) 1 / 2 ,
F χ 1 = j = 1 M ( Φ j o Φ j c ) Φ j c χ 1 + V 1 = 0 , F χ 2 = j = 1 M ( Φ j o Φ j c ) Φ j c χ 2 + V 2 = 0 , F χ 2 N = j = 1 M ( Φ j o Φ j c ) Φ j c χ 2 N + V 2 N = 0 ,
V i = w D 2 ( ψ i x k = 1 N D k ψ k x + ψ i y k = 1 N D k ψ k y ) { w D 2 [ ( k = 1 N D k ψ k x ) 2 + ( k = 1 N D k ψ k y ) 2 ] + w μ 2 [ ( l = 1 N μ l ψ l x ) 2 + ( l = 1 N μ l ψ l y ) 2 ] + δ 2 } 1 / 2 d x d y ,
V i = w μ 2 ( ψ i x l = 1 N μ l ψ l x + ψ i y l = 1 N μ l ψ l y ) { w D 2 [ ( k = 1 N D k ψ k x ) 2 + ( k = 1 N D k ψ k y ) 2 ] + w μ 2 [ ( l = 1 N μ l ψ l x ) 2 + ( l = 1 N μ l ψ l y ) 2 ] + δ 2 } 1 / 2 d x d y ,
Γ = ( F χ 1 , F χ 2 , , F χ 2 N ) T = ( f 1 , f 2 , , f 2 N ) T
( G + λ I ) Δ χ = Γ ,
G = [ f 1 χ 1 f 1 χ 2 f 1 χ 2 N f 2 χ 1 f 2 χ 2 f 2 χ 2 N f 2 N χ 1 f 2 N χ 2 f 2 N χ 2 N ] .
( J T J + R + λ I ) Δ χ = J T ( Φ o Φ c ) V ,
R = [ V 1 D 1 V 1 D N V 1 μ 1 V 1 μ N V N D 1 V N D N V N μ 1 V N μ N V N + 1 D 1 V N + 1 D N V N + 1 μ 1 V N + 1 μ N V 2 N D 1 V 2 N D N V 2 N μ 1 V 2 N μ N ] ,

Metrics