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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 5 — May. 1, 2003
  • pp: 890–902

Optics InfoBase > JOSA A > Volume 20 > Issue 5 > Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition

Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition

Vadim A. Markel, Vivek Mital, and John C. Schotland  »View Author Affiliations


JOSA A, Vol. 20, Issue 5, pp. 890-902 (2003)
http://dx.doi.org/10.1364/JOSAA.20.000890


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Abstract

We continue our study of the inverse scattering problem for diffuse light. In particular, we derive inversion formulas for this problem that are based on the functional singular-value decomposition of the linearized forward-scattering operator in the slab, cylindrical, and spherical geometries. Computer simulations are used to illustrate our results in model systems.

© 2003 Optical Society of America

OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.6960) Medical optics and biotechnology : Tomography

History
Original Manuscript: June 19, 2002
Revised Manuscript: November 11, 2002
Manuscript Accepted: November 11, 2002
Published: May 1, 2003

Citation
Vadim A. Markel, Vivek Mital, and John C. Schotland, "Inverse problem in optical diffusion tomography. III. Inversion formulas and singular-value decomposition," J. Opt. Soc. Am. A 20, 890-902 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-5-890


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References

  1. B. Chance, R. R. Alfano, M. Tamura, E. M. Sevick-Muraca, Optical Tomography and Spectroscopy of Tissue, Proc. SPIE 4250, (2001).
  2. Biomedical Optics, Vol. 71 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002).
  3. V. A. Markel, J. C. Schotland, “The inverse problem in optical diffusion tomography. I. Fourier–Laplace inversion formulas,” J. Opt. Soc. Am. A 18, 1336–1347 (2001). [CrossRef]
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  6. J. C. Schotland, V. A. Markel, “Inverse scattering with diffusing waves,” J. Opt. Soc. Am. A 18, 2767–2777 (2001). [CrossRef]
  7. V. A. Markel, J. C. Schotland, “Inverse scattering for the diffusion equation with general boundary conditions,” Phys. Rev. E 64, R035601 (2001). [CrossRef]
  8. R. Aronson, “Boundary conditions for diffuse light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995). [CrossRef]
  9. F. Natterer, The Mathematics of Computerized Tomography (Wiley, New York, 1986).

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