Abstract

In the past, nonlinear unconstrained optimization of the optical imaging problem has focused on Newton–Raphson techniques. Besides requiring expensive computation of the Jacobian, the unconstrained minimization with Tikhonov regularization can pose significant storage problems for large-scale reconstructions, involving a large number of unknowns necessary for realization of optical imaging. We formulate the inverse optical imaging problem as both simple-bound constrained and unconstrained minimization problems in order to illustrate the reduction in computational time and storage associated with constrained image reconstructions. The forward simulator of excitation and generated fluorescence, consisting of the Galerkin finite-element formulation, is used in an inverse algorithm to find the spatial distribution of absorption and lifetime that minimizes the difference between predicted and synthetic frequency-domain measurements. The inverse approach employs the truncated Newton method with trust region and a modification of automatic reverse differentiation to speed the computation of the optimization problem. The reconstruction results confirm that the physically based, constrained minimization with efficient optimization schemes may offer a more logical approach to the large-scale optical imaging problem than unconstrained minimization with regularization.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. S. Reynolds, T. L. Troy, E. M. Sevick-Muraca, “Multi-pixel techniques for frequency-domain photon migration imaging,” Biotechnol. Prog. 13, 669–680 (1997).
    [CrossRef] [PubMed]
  2. E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol., B 16, 169–185 (1992).
    [CrossRef]
  3. J. R. Lakowicz, K. W. Berndt, “Lifetime-selective fluorescence imaging using an rf phase-sensitive camera,” Rev. Sci. Instrum. 62, 1727–1734 (1991).
    [CrossRef]
  4. A. M. Siegel, J. J. A. Marota, D. A. Boas, “Design and evaluation of a continuous-wave diffuse optical tomography system,” Opt. Express 4, 287–298 (1999).
    [CrossRef] [PubMed]
  5. V. Ntziachristos, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
    [CrossRef]
  6. R. L. Barbour, R. Andronics, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPI scanner, a general-purpose optical tomography imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.
  7. K. Wells, J. C. Hebden, F. E. W. Schmidt, D. T. Delpy, “The UCL multichannel time-resolved system for optical tomography,” in Optical Tomography and Spectroscopy of Tissue, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 590–607 (1997).
  8. M. Miwa, Y. Ueda, “Development of time-resolved spectroscopy system for quantitative noninvasive tissue measurement,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 142–149 (1995).
  9. S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
    [CrossRef]
  10. 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]
  11. E. M. Sevick-Muraca, C. L. Hutchinson, D. Y. Paithankar, “Optical tissue biodiagnostics using fluorescence lifetime,” Opt. Photonics News, July1996, pp. 25–28.
  12. M. A. O’Leary, D. A. Boas, D. X. L. B. Chance, A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996).
    [CrossRef] [PubMed]
  13. D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, E. M. Sevick-Muraca, “Imaging of fluorescent yield and lifetime from multiply scattered light re-emitted from tissues and other random media,” Appl. Opt. 36, 2260–2272 (1997).
    [CrossRef] [PubMed]
  14. J. Chang, H. L. Graberm, R. L. Barbour, “Luminescence optical tomography of dense scattering media,” J. Opt. Soc. Am. A 14, 288–299 (1997).
    [CrossRef]
  15. E. M. Sevick-Muraca, G. Lopez, T. L. Troy, J. S. Reynolds, C. L. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
    [CrossRef] [PubMed]
  16. D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical heterogeneities within turbid media: analytic solutions and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
    [CrossRef]
  17. M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusion photon tomography,” Opt. Lett. 20, 426–428 (1995).
    [CrossRef]
  18. T. M. Durduran, J. P. Culver, M. J. Holboke, X. D. Li, L. Zubkov, B. Chance, D. Pattanayak, A. G. Yodh, “Algorithms for 3D localization and imaging using near-field diffraction tomography with diffuse light,” Opt. Express 4, 247–262 (1999).
    [CrossRef] [PubMed]
  19. S. A. Walker, S. Fantini, E. Gratton, “Back-projection reconstructions in cylindrical inhomogeneities from frequency-domain optical measurements in turbid media,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C.), 1992, pp. 137–141.
  20. S. B. Colak, G. W. Hooft, D. G. Papaioannou, M. B. van der Mark, “3D backprojection tomography for medical optical imaging,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1992), pp. 294–298.
  21. 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. Muller, B. Chance, R. Alfano, J. Beuthan, E. Gratton, M. Kashke, B. Masters, S. Svanberg, P. van der Zee, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.
  22. Y. Yao, Y. Wang, Y. Pei, W. Zhu, R. L. Barbour, “Frequency-domain optical imaging of absorption and scattering by a Born iterative method,” J. Opt. Soc. Am. A 14, 325–342 (1997).
    [CrossRef]
  23. W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1995).
    [CrossRef]
  24. J. C. Ye, K. J. Webb, R. P. Millane, T. J. Downar, “Modified distorted Born iterative method with an approximate Frechet derivative for optical diffusion tomography,” J. Opt. Soc. Am. A 16, 1814–1830 (1999).
    [CrossRef]
  25. S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
    [CrossRef]
  26. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Optical image reconstruction using frequency-domain data simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
    [CrossRef]
  27. K. D. Paulsen, H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–710 (1995).
    [CrossRef] [PubMed]
  28. R. Roy, “Image reconstruction from light measurements on biological tissue,” Ph.D. thesis (in Mathematics) (University of Hertfordshire, Hatfield, England, 1996).
  29. S. R. Arridge, M. Schweiger, “A gradient-based optimization scheme for optical tomography,” Opt. Express 2, 213–226 (1997).
    [CrossRef]
  30. A. H. Hielscher, A. D. Klose, K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
    [CrossRef] [PubMed]
  31. A. D. Klose, A. H. Hielscher, “Iterative reconstructions scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).
    [CrossRef] [PubMed]
  32. R. Roy, E. M. Sevick-Muraca, “Truncated Newton’s optimization scheme for absorption and fluorescence opticaltomography: Part I: Theory and formulation,” Opt. Express 4, 353–371 (1999).
    [CrossRef] [PubMed]
  33. R. Roy, E. M. Sevick-Muraca, “Truncated Newton’s optimization scheme for absorption and fluorescence optical tomography: Part II: Reconstruction from synthetic measurements,” Opt. Express 4, 372–382 (1999).
    [CrossRef] [PubMed]
  34. A. Tikhonov, V. Arsenin, Solution of Ill-Posed Problems (Wiley, New York, 1977).
  35. V. A. Morozov, “On the solution of functional equations by the method of regularization,” Sov. Math. Dokl. 7, 414–417 (1966).
  36. G. Wahba, Spline Models of Observational Data (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1990).
  37. P. C. Hansen, “Analysis of discrete ill-posed problem by means of the L-curve,” SIAM Rev. 34, 561–580 (1992).
    [CrossRef]
  38. A. H. Hielscher, A. D. Klose, “Use of a priori information and penalty terms in gradient-based iterative reconstruction schemes,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. Tromberg, ed., Proc. SPIE3597, 36–44 (1999).
  39. B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38, 2950–2961 (1999).
    [CrossRef]
  40. M. J. Eppstein, D. E. Dougherty, T. L. Troy, E. M. Sevick-Muraca, “Biomedical optical tomography using dynamic parameterization and Bayesian conditioning on photon migration measurements,” Appl. Opt. 38, 2138–2150 (1999).
    [CrossRef]
  41. B. A. Murtagh, M. A. Saunders“Large-scale linearly constrained optimization,” Math. Program. 14, 41–72 (1978).
    [CrossRef]
  42. B. A. Murtagh, M. A. Saunders, “A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints,” Math. Program. 16, 4–117 (1982).
  43. R. Fletcher, M. P. Jackson, “Minimization of a quadratic function on many variables subject only to upper and lower bounds,” J. Inst. Math. Appl. 14, 159–174 (1974).
    [CrossRef]
  44. P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, London, 1981).
  45. A. R. Conn, I. M. Gould, Ph. L. Toint, LANCELOT: a Fortran Package for Large-Scale Nonlinear Optimization (release A), Vol. 17 of Computational Mathematics Series (Springer-Verlag, New York, 1992).
    [CrossRef]
  46. A. R. Conn, I. M. Gould, Ph. L. Toint, “Testing a class of methods for solving minimization problems with simply bounds on the variables,” Math. Comput. 50, 399–430 (1988).
    [CrossRef]
  47. F. Facchine, J. Judice, J. Soares, “An active set Newton algorithm for large-scale nonlinear programs with box constraints,” SIAM J. Optim. 8, 158–186 (1998).
    [CrossRef]
  48. R. Pytlak, “An efficient algorithm for large-scale nonlinear programming problems with simple bounds on the variables,” SIAM J. Optim. 8, 532–560 (1998).
    [CrossRef]
  49. M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “Three-dimensional optical tomography,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 97–105 (1999).
    [CrossRef]
  50. B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
    [CrossRef]
  51. S. R. Arridge, M. R. Schweiger, “Image reconstruction in optical tomography,” Philos. Trans. R. Soc. London, Ser. B 352, 717–726 (1997).
    [CrossRef] [PubMed]
  52. J. C. Hebden, S. Arridge, D. T. Delpy, “Optical imagingeb in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
    [CrossRef] [PubMed]
  53. S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
    [CrossRef] [PubMed]
  54. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  55. O. C. Zienkiewcz, R. L. Taylor, The Finite Element Methods in Engineering Science (McGraw-Hill, New York, 1989).
  56. D. P. Bertsekas, “Projected Newton method for optimization problems with simple contraints,” SIAM J. Control Optim. 20, 221–246 (1982).
    [CrossRef]
  57. Q. Ni, Y. Yuan, “A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization,” Math. Comput. 66, 1509–1520 (1997).
    [CrossRef]
  58. L. Armijo, “Minimization of functions having Lipschitz continuous first partial derivatives,” Pacific J. Math. 16, 1–3 (1966).
    [CrossRef]
  59. R. S. Dembo, T. Steihaug, “Truncated Newton algorithms for large-scale unconstrained optimization,” Math. Program. 26, 190–212 (1983).
    [CrossRef]
  60. L. C. W. Dixon, R. C. Price, “Numerical experience with the truncated Newton method for unconstrained optimization,” J. Optim. Theory Appl. 56, 245–255 (1988).
    [CrossRef]
  61. P. Wolfe, “Convergence condition for ascent method,” SIAM Rev. 11, 226–253 (1969).
    [CrossRef]
  62. A. Griewank, “On automatic differentiation,” in Mathematical Programming: Recent Developments and Applications, M. Iri, K. Tanaka, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1989), pp. 83–108.
  63. B. Christianson, A. J. Davies, L. C. W. Dixon, R. Roy, P. van der Zee, “Giving reverse differentiation a helping hand,” Opt. Meth. Software 8, 53–67 (1997).
    [CrossRef]
  64. A. J. Davies, B. Christianson, L. C. W. Dixon, R. Roy, P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Adv. Eng. Softw. 28, 217–221 (1997).
    [CrossRef]
  65. J. Lee, E. M. Sevick-Muraca, “Lifetime and absorption imaging with fluorescence FDPM,” in Time-Resolved Fluorescence Spectroscopy and Imaging in Tissues, E. M. Sevick-Muraca, ed. Proc. SPIE3600, 246–254 (1999).
  66. R. Cubeddu, G. Canti, A. Pifferi, P. Taroni, G. Valentini, “Fluorescence lifetime imaging of experimental tumors in the matoporhyrin derivate–sensitized mice,” Photochem. Photobiol. 66, 229–236 (1997).
    [CrossRef] [PubMed]
  67. H. Jiang, “Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations,” Appl. Opt. 37, 5337–5343 (1998).
    [CrossRef]
  68. M. Schweiger, S. R. Arridge, “Comparison of two- and three-dimensional reconstruction methods in optical tomography,” Appl. Opt. 37, 7419–7428 (1998).
    [CrossRef]
  69. Y. Yao, Y. Pei, Y. Wang, R. L. Barbour, “Born-iterative methods for imaging of heterogeneous scattering media and its application to simulated breast tissue,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 231–239 (1997).
  70. W. Cai, B. B. Das, F. Liu, F. A. Feng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds. Proc. SPIE2979, 241–249 (1997).

1999 (9)

A. M. Siegel, J. J. A. Marota, D. A. Boas, “Design and evaluation of a continuous-wave diffuse optical tomography system,” Opt. Express 4, 287–298 (1999).
[CrossRef] [PubMed]

R. Roy, E. M. Sevick-Muraca, “Truncated Newton’s optimization scheme for absorption and fluorescence optical tomography: Part II: Reconstruction from synthetic measurements,” Opt. Express 4, 372–382 (1999).
[CrossRef] [PubMed]

A. H. Hielscher, A. D. Klose, K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef] [PubMed]

A. D. Klose, A. H. Hielscher, “Iterative reconstructions scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).
[CrossRef] [PubMed]

J. C. Ye, K. J. Webb, R. P. Millane, T. J. Downar, “Modified distorted Born iterative method with an approximate Frechet derivative for optical diffusion tomography,” J. Opt. Soc. Am. A 16, 1814–1830 (1999).
[CrossRef]

M. J. Eppstein, D. E. Dougherty, T. L. Troy, E. M. Sevick-Muraca, “Biomedical optical tomography using dynamic parameterization and Bayesian conditioning on photon migration measurements,” Appl. Opt. 38, 2138–2150 (1999).
[CrossRef]

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

T. M. Durduran, J. P. Culver, M. J. Holboke, X. D. Li, L. Zubkov, B. Chance, D. Pattanayak, A. G. Yodh, “Algorithms for 3D localization and imaging using near-field diffraction tomography with diffuse light,” Opt. Express 4, 247–262 (1999).
[CrossRef] [PubMed]

R. Roy, E. M. Sevick-Muraca, “Truncated Newton’s optimization scheme for absorption and fluorescence opticaltomography: Part I: Theory and formulation,” Opt. Express 4, 353–371 (1999).
[CrossRef] [PubMed]

1998 (5)

H. Jiang, “Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations,” Appl. Opt. 37, 5337–5343 (1998).
[CrossRef]

M. Schweiger, S. R. Arridge, “Comparison of two- and three-dimensional reconstruction methods in optical tomography,” Appl. Opt. 37, 7419–7428 (1998).
[CrossRef]

F. Facchine, J. Judice, J. Soares, “An active set Newton algorithm for large-scale nonlinear programs with box constraints,” SIAM J. Optim. 8, 158–186 (1998).
[CrossRef]

R. Pytlak, “An efficient algorithm for large-scale nonlinear programming problems with simple bounds on the variables,” SIAM J. Optim. 8, 532–560 (1998).
[CrossRef]

V. Ntziachristos, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[CrossRef]

1997 (13)

J. S. Reynolds, T. L. Troy, E. M. Sevick-Muraca, “Multi-pixel techniques for frequency-domain photon migration imaging,” Biotechnol. Prog. 13, 669–680 (1997).
[CrossRef] [PubMed]

E. M. Sevick-Muraca, G. Lopez, T. L. Troy, J. S. Reynolds, C. L. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. R. Schweiger, “Image reconstruction in optical tomography,” Philos. Trans. R. Soc. London, Ser. B 352, 717–726 (1997).
[CrossRef] [PubMed]

J. C. Hebden, S. Arridge, D. T. Delpy, “Optical imagingeb in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

Q. Ni, Y. Yuan, “A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization,” Math. Comput. 66, 1509–1520 (1997).
[CrossRef]

J. Chang, H. L. Graberm, R. L. Barbour, “Luminescence optical tomography of dense scattering media,” J. Opt. Soc. Am. A 14, 288–299 (1997).
[CrossRef]

Y. Yao, Y. Wang, Y. Pei, W. Zhu, R. L. Barbour, “Frequency-domain optical imaging of absorption and scattering by a Born iterative method,” J. Opt. Soc. Am. A 14, 325–342 (1997).
[CrossRef]

B. Christianson, A. J. Davies, L. C. W. Dixon, R. Roy, P. van der Zee, “Giving reverse differentiation a helping hand,” Opt. Meth. Software 8, 53–67 (1997).
[CrossRef]

A. J. Davies, B. Christianson, L. C. W. Dixon, R. Roy, P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Adv. Eng. Softw. 28, 217–221 (1997).
[CrossRef]

R. Cubeddu, G. Canti, A. Pifferi, P. Taroni, G. Valentini, “Fluorescence lifetime imaging of experimental tumors in the matoporhyrin derivate–sensitized mice,” Photochem. Photobiol. 66, 229–236 (1997).
[CrossRef] [PubMed]

D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, E. M. Sevick-Muraca, “Imaging of fluorescent yield and lifetime from multiply scattered light re-emitted from tissues and other random media,” Appl. Opt. 36, 2260–2272 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “A gradient-based optimization scheme for optical tomography,” Opt. Express 2, 213–226 (1997).
[CrossRef]

1996 (3)

1995 (4)

W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1995).
[CrossRef]

K. D. Paulsen, H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–710 (1995).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

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

1994 (2)

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

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]

1992 (3)

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol., B 16, 169–185 (1992).
[CrossRef]

P. C. Hansen, “Analysis of discrete ill-posed problem by means of the L-curve,” SIAM Rev. 34, 561–580 (1992).
[CrossRef]

1991 (1)

J. R. Lakowicz, K. W. Berndt, “Lifetime-selective fluorescence imaging using an rf phase-sensitive camera,” Rev. Sci. Instrum. 62, 1727–1734 (1991).
[CrossRef]

1988 (2)

A. R. Conn, I. M. Gould, Ph. L. Toint, “Testing a class of methods for solving minimization problems with simply bounds on the variables,” Math. Comput. 50, 399–430 (1988).
[CrossRef]

L. C. W. Dixon, R. C. Price, “Numerical experience with the truncated Newton method for unconstrained optimization,” J. Optim. Theory Appl. 56, 245–255 (1988).
[CrossRef]

1983 (1)

R. S. Dembo, T. Steihaug, “Truncated Newton algorithms for large-scale unconstrained optimization,” Math. Program. 26, 190–212 (1983).
[CrossRef]

1982 (2)

B. A. Murtagh, M. A. Saunders, “A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints,” Math. Program. 16, 4–117 (1982).

D. P. Bertsekas, “Projected Newton method for optimization problems with simple contraints,” SIAM J. Control Optim. 20, 221–246 (1982).
[CrossRef]

1978 (1)

B. A. Murtagh, M. A. Saunders“Large-scale linearly constrained optimization,” Math. Program. 14, 41–72 (1978).
[CrossRef]

1974 (1)

R. Fletcher, M. P. Jackson, “Minimization of a quadratic function on many variables subject only to upper and lower bounds,” J. Inst. Math. Appl. 14, 159–174 (1974).
[CrossRef]

1969 (1)

P. Wolfe, “Convergence condition for ascent method,” SIAM Rev. 11, 226–253 (1969).
[CrossRef]

1966 (2)

L. Armijo, “Minimization of functions having Lipschitz continuous first partial derivatives,” Pacific J. Math. 16, 1–3 (1966).
[CrossRef]

V. A. Morozov, “On the solution of functional equations by the method of regularization,” Sov. Math. Dokl. 7, 414–417 (1966).

Alfano, R. R.

W. Cai, B. B. Das, F. Liu, F. A. Feng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds. Proc. SPIE2979, 241–249 (1997).

Anderson, E. R.

Andronics, R.

R. L. Barbour, R. Andronics, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPI scanner, a general-purpose optical tomography imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Armijo, L.

L. Armijo, “Minimization of functions having Lipschitz continuous first partial derivatives,” Pacific J. Math. 16, 1–3 (1966).
[CrossRef]

Aronson, R.

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. Muller, B. Chance, R. Alfano, J. Beuthan, E. Gratton, M. Kashke, B. Masters, S. Svanberg, P. van der Zee, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

Arridge, S.

J. C. Hebden, S. Arridge, D. T. Delpy, “Optical imagingeb in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

Arridge, S. R.

M. Schweiger, S. R. Arridge, “Comparison of two- and three-dimensional reconstruction methods in optical tomography,” Appl. Opt. 37, 7419–7428 (1998).
[CrossRef]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. R. Schweiger, “Image reconstruction in optical tomography,” Philos. Trans. R. Soc. London, Ser. B 352, 717–726 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “A gradient-based optimization scheme for optical tomography,” Opt. Express 2, 213–226 (1997).
[CrossRef]

S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
[CrossRef]

Arsenin, V.

A. Tikhonov, V. Arsenin, Solution of Ill-Posed Problems (Wiley, New York, 1977).

Barbieri, B.

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

Barbour, R. L.

J. Chang, H. L. Graberm, R. L. Barbour, “Luminescence optical tomography of dense scattering media,” J. Opt. Soc. Am. A 14, 288–299 (1997).
[CrossRef]

Y. Yao, Y. Wang, Y. Pei, W. Zhu, R. L. Barbour, “Frequency-domain optical imaging of absorption and scattering by a Born iterative method,” J. Opt. Soc. Am. A 14, 325–342 (1997).
[CrossRef]

Y. Yao, Y. Pei, Y. Wang, R. L. Barbour, “Born-iterative methods for imaging of heterogeneous scattering media and its application to simulated breast tissue,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 231–239 (1997).

R. L. Barbour, R. Andronics, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPI scanner, a general-purpose optical tomography imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

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. Muller, B. Chance, R. Alfano, J. Beuthan, E. Gratton, M. Kashke, B. Masters, S. Svanberg, P. van der Zee, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

Berndt, K. W.

J. R. Lakowicz, K. W. Berndt, “Lifetime-selective fluorescence imaging using an rf phase-sensitive camera,” Rev. Sci. Instrum. 62, 1727–1734 (1991).
[CrossRef]

Bertsekas, D. P.

D. P. Bertsekas, “Projected Newton method for optimization problems with simple contraints,” SIAM J. Control Optim. 20, 221–246 (1982).
[CrossRef]

Boas, D. A.

A. M. Siegel, J. J. A. Marota, D. A. Boas, “Design and evaluation of a continuous-wave diffuse optical tomography system,” Opt. Express 4, 287–298 (1999).
[CrossRef] [PubMed]

M. A. O’Leary, D. A. Boas, D. X. L. B. Chance, A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996).
[CrossRef] [PubMed]

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

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

Cai, W.

W. Cai, B. B. Das, F. Liu, F. A. Feng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds. Proc. SPIE2979, 241–249 (1997).

Canti, G.

R. Cubeddu, G. Canti, A. Pifferi, P. Taroni, G. Valentini, “Fluorescence lifetime imaging of experimental tumors in the matoporhyrin derivate–sensitized mice,” Photochem. Photobiol. 66, 229–236 (1997).
[CrossRef] [PubMed]

Chance, B.

T. M. Durduran, J. P. Culver, M. J. Holboke, X. D. Li, L. Zubkov, B. Chance, D. Pattanayak, A. G. Yodh, “Algorithms for 3D localization and imaging using near-field diffraction tomography with diffuse light,” Opt. Express 4, 247–262 (1999).
[CrossRef] [PubMed]

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

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

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

Chance, D. X. L. B.

Chang, J.

J. Chang, H. L. Graberm, R. L. Barbour, “Luminescence optical tomography of dense scattering media,” J. Opt. Soc. Am. A 14, 288–299 (1997).
[CrossRef]

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. Muller, B. Chance, R. Alfano, J. Beuthan, E. Gratton, M. Kashke, B. Masters, S. Svanberg, P. van der Zee, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

Chen, A. U.

Chew, W. C.

W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1995).
[CrossRef]

Christianson, B.

B. Christianson, A. J. Davies, L. C. W. Dixon, R. Roy, P. van der Zee, “Giving reverse differentiation a helping hand,” Opt. Meth. Software 8, 53–67 (1997).
[CrossRef]

A. J. Davies, B. Christianson, L. C. W. Dixon, R. Roy, P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Adv. Eng. Softw. 28, 217–221 (1997).
[CrossRef]

Colak, S. B.

S. B. Colak, G. W. Hooft, D. G. Papaioannou, M. B. van der Mark, “3D backprojection tomography for medical optical imaging,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1992), pp. 294–298.

Conn, A. R.

A. R. Conn, I. M. Gould, Ph. L. Toint, “Testing a class of methods for solving minimization problems with simply bounds on the variables,” Math. Comput. 50, 399–430 (1988).
[CrossRef]

A. R. Conn, I. M. Gould, Ph. L. Toint, LANCELOT: a Fortran Package for Large-Scale Nonlinear Optimization (release A), Vol. 17 of Computational Mathematics Series (Springer-Verlag, New York, 1992).
[CrossRef]

Cubeddu, R.

R. Cubeddu, G. Canti, A. Pifferi, P. Taroni, G. Valentini, “Fluorescence lifetime imaging of experimental tumors in the matoporhyrin derivate–sensitized mice,” Photochem. Photobiol. 66, 229–236 (1997).
[CrossRef] [PubMed]

Culver, J. P.

Das, B. B.

W. Cai, B. B. Das, F. Liu, F. A. Feng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds. Proc. SPIE2979, 241–249 (1997).

Davies, A. J.

B. Christianson, A. J. Davies, L. C. W. Dixon, R. Roy, P. van der Zee, “Giving reverse differentiation a helping hand,” Opt. Meth. Software 8, 53–67 (1997).
[CrossRef]

A. J. Davies, B. Christianson, L. C. W. Dixon, R. Roy, P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Adv. Eng. Softw. 28, 217–221 (1997).
[CrossRef]

Delpy, D. T.

J. C. Hebden, S. Arridge, D. T. Delpy, “Optical imagingeb in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
[CrossRef]

K. Wells, J. C. Hebden, F. E. W. Schmidt, D. T. Delpy, “The UCL multichannel time-resolved system for optical tomography,” in Optical Tomography and Spectroscopy of Tissue, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 590–607 (1997).

Dembo, R. S.

R. S. Dembo, T. Steihaug, “Truncated Newton algorithms for large-scale unconstrained optimization,” Math. Program. 26, 190–212 (1983).
[CrossRef]

Dixon, L. C. W.

B. Christianson, A. J. Davies, L. C. W. Dixon, R. Roy, P. van der Zee, “Giving reverse differentiation a helping hand,” Opt. Meth. Software 8, 53–67 (1997).
[CrossRef]

A. J. Davies, B. Christianson, L. C. W. Dixon, R. Roy, P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Adv. Eng. Softw. 28, 217–221 (1997).
[CrossRef]

L. C. W. Dixon, R. C. Price, “Numerical experience with the truncated Newton method for unconstrained optimization,” J. Optim. Theory Appl. 56, 245–255 (1988).
[CrossRef]

Dougherty, D. E.

M. J. Eppstein, D. E. Dougherty, T. L. Troy, E. M. Sevick-Muraca, “Biomedical optical tomography using dynamic parameterization and Bayesian conditioning on photon migration measurements,” Appl. Opt. 38, 2138–2150 (1999).
[CrossRef]

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “Three-dimensional optical tomography,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 97–105 (1999).
[CrossRef]

Downar, T. J.

Durduran, T. M.

Eppstein, M. J.

M. J. Eppstein, D. E. Dougherty, T. L. Troy, E. M. Sevick-Muraca, “Biomedical optical tomography using dynamic parameterization and Bayesian conditioning on photon migration measurements,” Appl. Opt. 38, 2138–2150 (1999).
[CrossRef]

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “Three-dimensional optical tomography,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 97–105 (1999).
[CrossRef]

Facchine, F.

F. Facchine, J. Judice, J. Soares, “An active set Newton algorithm for large-scale nonlinear programs with box constraints,” SIAM J. Optim. 8, 158–186 (1998).
[CrossRef]

Fantini, S.

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

S. A. Walker, S. Fantini, E. Gratton, “Back-projection reconstructions in cylindrical inhomogeneities from frequency-domain optical measurements in turbid media,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C.), 1992, pp. 137–141.

Feng, F. A.

W. Cai, B. B. Das, F. Liu, F. A. Feng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds. Proc. SPIE2979, 241–249 (1997).

Fletcher, R.

R. Fletcher, M. P. Jackson, “Minimization of a quadratic function on many variables subject only to upper and lower bounds,” J. Inst. Math. Appl. 14, 159–174 (1974).
[CrossRef]

Franceschini, M. A.

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

Gill, P. E.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, London, 1981).

Gould, I. M.

A. R. Conn, I. M. Gould, Ph. L. Toint, “Testing a class of methods for solving minimization problems with simply bounds on the variables,” Math. Comput. 50, 399–430 (1988).
[CrossRef]

A. R. Conn, I. M. Gould, Ph. L. Toint, LANCELOT: a Fortran Package for Large-Scale Nonlinear Optimization (release A), Vol. 17 of Computational Mathematics Series (Springer-Verlag, New York, 1992).
[CrossRef]

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. Muller, B. Chance, R. Alfano, J. Beuthan, E. Gratton, M. Kashke, B. Masters, S. Svanberg, P. van der Zee, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

Graber, H. L.

R. L. Barbour, R. Andronics, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPI scanner, a general-purpose optical tomography imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Graberm, H. L.

Gratton, E.

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

S. A. Walker, S. Fantini, E. Gratton, “Back-projection reconstructions in cylindrical inhomogeneities from frequency-domain optical measurements in turbid media,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C.), 1992, pp. 137–141.

Griewank, A.

A. Griewank, “On automatic differentiation,” in Mathematical Programming: Recent Developments and Applications, M. Iri, K. Tanaka, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1989), pp. 83–108.

Hansen, P. C.

P. C. Hansen, “Analysis of discrete ill-posed problem by means of the L-curve,” SIAM Rev. 34, 561–580 (1992).
[CrossRef]

Hanson, K. M.

A. H. Hielscher, A. D. Klose, K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef] [PubMed]

Haskell, R. C.

Hawrysz, D. J.

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “Three-dimensional optical tomography,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 97–105 (1999).
[CrossRef]

Hebden, J. C.

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

J. C. Hebden, S. Arridge, D. T. Delpy, “Optical imagingeb in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

K. Wells, J. C. Hebden, F. E. W. Schmidt, D. T. Delpy, “The UCL multichannel time-resolved system for optical tomography,” in Optical Tomography and Spectroscopy of Tissue, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 590–607 (1997).

Hielscher, A. H.

A. D. Klose, A. H. Hielscher, “Iterative reconstructions scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).
[CrossRef] [PubMed]

A. H. Hielscher, A. D. Klose, K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef] [PubMed]

A. H. Hielscher, A. D. Klose, “Use of a priori information and penalty terms in gradient-based iterative reconstruction schemes,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. Tromberg, ed., Proc. SPIE3597, 36–44 (1999).

Holboke, M. J.

Hooft, G. W.

S. B. Colak, G. W. Hooft, D. G. Papaioannou, M. B. van der Mark, “3D backprojection tomography for medical optical imaging,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1992), pp. 294–298.

Hutchinson, C. L.

E. M. Sevick-Muraca, G. Lopez, T. L. Troy, J. S. Reynolds, C. L. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

E. M. Sevick-Muraca, C. L. Hutchinson, D. Y. Paithankar, “Optical tissue biodiagnostics using fluorescence lifetime,” Opt. Photonics News, July1996, pp. 25–28.

Ishimaru, A.

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

Jackson, M. P.

R. Fletcher, M. P. Jackson, “Minimization of a quadratic function on many variables subject only to upper and lower bounds,” J. Inst. Math. Appl. 14, 159–174 (1974).
[CrossRef]

Jiang, H.

Johnson, M. L.

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol., B 16, 169–185 (1992).
[CrossRef]

Judice, J.

F. Facchine, J. Judice, J. Soares, “An active set Newton algorithm for large-scale nonlinear programs with box constraints,” SIAM J. Optim. 8, 158–186 (1998).
[CrossRef]

Klose, A. D.

A. H. Hielscher, A. D. Klose, K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef] [PubMed]

A. D. Klose, A. H. Hielscher, “Iterative reconstructions scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).
[CrossRef] [PubMed]

A. H. Hielscher, A. D. Klose, “Use of a priori information and penalty terms in gradient-based iterative reconstruction schemes,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. Tromberg, ed., Proc. SPIE3597, 36–44 (1999).

Lakowicz, J. R.

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol., B 16, 169–185 (1992).
[CrossRef]

J. R. Lakowicz, K. W. Berndt, “Lifetime-selective fluorescence imaging using an rf phase-sensitive camera,” Rev. Sci. Instrum. 62, 1727–1734 (1991).
[CrossRef]

Lax, M.

W. Cai, B. B. Das, F. Liu, F. A. Feng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds. Proc. SPIE2979, 241–249 (1997).

Lee, J.

J. Lee, E. M. Sevick-Muraca, “Lifetime and absorption imaging with fluorescence FDPM,” in Time-Resolved Fluorescence Spectroscopy and Imaging in Tissues, E. M. Sevick-Muraca, ed. Proc. SPIE3600, 246–254 (1999).

Li, X. D.

Liu, F.

W. Cai, B. B. Das, F. Liu, F. A. Feng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds. Proc. SPIE2979, 241–249 (1997).

Lopez, G.

E. M. Sevick-Muraca, G. Lopez, T. L. Troy, J. S. Reynolds, C. L. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

Madsen, S. J.

Maier, J. S.

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

Marota, J. J. A.

A. M. Siegel, J. J. A. Marota, D. A. Boas, “Design and evaluation of a continuous-wave diffuse optical tomography system,” Opt. Express 4, 287–298 (1999).
[CrossRef] [PubMed]

McBride, T. O.

Millane, R. P.

Miwa, M.

M. Miwa, Y. Ueda, “Development of time-resolved spectroscopy system for quantitative noninvasive tissue measurement,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 142–149 (1995).

Morozov, V. A.

V. A. Morozov, “On the solution of functional equations by the method of regularization,” Sov. Math. Dokl. 7, 414–417 (1966).

Murray, W.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, London, 1981).

Murtagh, B. A.

B. A. Murtagh, M. A. Saunders, “A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints,” Math. Program. 16, 4–117 (1982).

B. A. Murtagh, M. A. Saunders“Large-scale linearly constrained optimization,” Math. Program. 14, 41–72 (1978).
[CrossRef]

Ni, Q.

Q. Ni, Y. Yuan, “A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization,” Math. Comput. 66, 1509–1520 (1997).
[CrossRef]

Nowaczyk, K.

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol., B 16, 169–185 (1992).
[CrossRef]

Ntziachristos, V.

V. Ntziachristos, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[CrossRef]

O’Leary, M. A.

Osterberg, U. L.

Paithankar, D. Y.

Papaioannou, D. G.

S. B. Colak, G. W. Hooft, D. G. Papaioannou, M. B. van der Mark, “3D backprojection tomography for medical optical imaging,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1992), pp. 294–298.

Pattanayak, D.

Patterson, M. S.

Paulsen, K. D.

Pei, Y.

Y. Yao, Y. Wang, Y. Pei, W. Zhu, R. L. Barbour, “Frequency-domain optical imaging of absorption and scattering by a Born iterative method,” J. Opt. Soc. Am. A 14, 325–342 (1997).
[CrossRef]

Y. Yao, Y. Pei, Y. Wang, R. L. Barbour, “Born-iterative methods for imaging of heterogeneous scattering media and its application to simulated breast tissue,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 231–239 (1997).

Pifferi, A.

R. Cubeddu, G. Canti, A. Pifferi, P. Taroni, G. Valentini, “Fluorescence lifetime imaging of experimental tumors in the matoporhyrin derivate–sensitized mice,” Photochem. Photobiol. 66, 229–236 (1997).
[CrossRef] [PubMed]

Pogue, B. W.

Prewitt, J.

Price, R. C.

L. C. W. Dixon, R. C. Price, “Numerical experience with the truncated Newton method for unconstrained optimization,” J. Optim. Theory Appl. 56, 245–255 (1988).
[CrossRef]

Pytlak, R.

R. Pytlak, “An efficient algorithm for large-scale nonlinear programming problems with simple bounds on the variables,” SIAM J. Optim. 8, 532–560 (1998).
[CrossRef]

Reynolds, J. S.

E. M. Sevick-Muraca, G. Lopez, T. L. Troy, J. S. Reynolds, C. L. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

J. S. Reynolds, T. L. Troy, E. M. Sevick-Muraca, “Multi-pixel techniques for frequency-domain photon migration imaging,” Biotechnol. Prog. 13, 669–680 (1997).
[CrossRef] [PubMed]

Roy, R.

R. Roy, E. M. Sevick-Muraca, “Truncated Newton’s optimization scheme for absorption and fluorescence optical tomography: Part II: Reconstruction from synthetic measurements,” Opt. Express 4, 372–382 (1999).
[CrossRef] [PubMed]

R. Roy, E. M. Sevick-Muraca, “Truncated Newton’s optimization scheme for absorption and fluorescence opticaltomography: Part I: Theory and formulation,” Opt. Express 4, 353–371 (1999).
[CrossRef] [PubMed]

A. J. Davies, B. Christianson, L. C. W. Dixon, R. Roy, P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Adv. Eng. Softw. 28, 217–221 (1997).
[CrossRef]

B. Christianson, A. J. Davies, L. C. W. Dixon, R. Roy, P. van der Zee, “Giving reverse differentiation a helping hand,” Opt. Meth. Software 8, 53–67 (1997).
[CrossRef]

R. Roy, “Image reconstruction from light measurements on biological tissue,” Ph.D. thesis (in Mathematics) (University of Hertfordshire, Hatfield, England, 1996).

Saunders, M. A.

B. A. Murtagh, M. A. Saunders, “A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints,” Math. Program. 16, 4–117 (1982).

B. A. Murtagh, M. A. Saunders“Large-scale linearly constrained optimization,” Math. Program. 14, 41–72 (1978).
[CrossRef]

Schmidt, F. E. W.

K. Wells, J. C. Hebden, F. E. W. Schmidt, D. T. Delpy, “The UCL multichannel time-resolved system for optical tomography,” in Optical Tomography and Spectroscopy of Tissue, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 590–607 (1997).

Schweiger, M.

Schweiger, M. R.

S. R. Arridge, M. R. Schweiger, “Image reconstruction in optical tomography,” Philos. Trans. R. Soc. London, Ser. B 352, 717–726 (1997).
[CrossRef] [PubMed]

Sevick, E. M.

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol., B 16, 169–185 (1992).
[CrossRef]

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

Sevick-Muraca, E. M.

R. Roy, E. M. Sevick-Muraca, “Truncated Newton’s optimization scheme for absorption and fluorescence opticaltomography: Part I: Theory and formulation,” Opt. Express 4, 353–371 (1999).
[CrossRef] [PubMed]

R. Roy, E. M. Sevick-Muraca, “Truncated Newton’s optimization scheme for absorption and fluorescence optical tomography: Part II: Reconstruction from synthetic measurements,” Opt. Express 4, 372–382 (1999).
[CrossRef] [PubMed]

M. J. Eppstein, D. E. Dougherty, T. L. Troy, E. M. Sevick-Muraca, “Biomedical optical tomography using dynamic parameterization and Bayesian conditioning on photon migration measurements,” Appl. Opt. 38, 2138–2150 (1999).
[CrossRef]

E. M. Sevick-Muraca, G. Lopez, T. L. Troy, J. S. Reynolds, C. L. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, E. M. Sevick-Muraca, “Imaging of fluorescent yield and lifetime from multiply scattered light re-emitted from tissues and other random media,” Appl. Opt. 36, 2260–2272 (1997).
[CrossRef] [PubMed]

J. S. Reynolds, T. L. Troy, E. M. Sevick-Muraca, “Multi-pixel techniques for frequency-domain photon migration imaging,” Biotechnol. Prog. 13, 669–680 (1997).
[CrossRef] [PubMed]

E. M. Sevick-Muraca, C. L. Hutchinson, D. Y. Paithankar, “Optical tissue biodiagnostics using fluorescence lifetime,” Opt. Photonics News, July1996, pp. 25–28.

J. Lee, E. M. Sevick-Muraca, “Lifetime and absorption imaging with fluorescence FDPM,” in Time-Resolved Fluorescence Spectroscopy and Imaging in Tissues, E. M. Sevick-Muraca, ed. Proc. SPIE3600, 246–254 (1999).

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “Three-dimensional optical tomography,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 97–105 (1999).
[CrossRef]

Sha, Q.

R. L. Barbour, R. Andronics, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPI scanner, a general-purpose optical tomography imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Siegel, A. M.

A. M. Siegel, J. J. A. Marota, D. A. Boas, “Design and evaluation of a continuous-wave diffuse optical tomography system,” Opt. Express 4, 287–298 (1999).
[CrossRef] [PubMed]

Soares, J.

F. Facchine, J. Judice, J. Soares, “An active set Newton algorithm for large-scale nonlinear programs with box constraints,” SIAM J. Optim. 8, 158–186 (1998).
[CrossRef]

Soller, I.

R. L. Barbour, R. Andronics, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPI scanner, a general-purpose optical tomography imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

Steihaug, T.

R. S. Dembo, T. Steihaug, “Truncated Newton algorithms for large-scale unconstrained optimization,” Math. Program. 26, 190–212 (1983).
[CrossRef]

Szmacinski, H.

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol., B 16, 169–185 (1992).
[CrossRef]

Taroni, P.

R. Cubeddu, G. Canti, A. Pifferi, P. Taroni, G. Valentini, “Fluorescence lifetime imaging of experimental tumors in the matoporhyrin derivate–sensitized mice,” Photochem. Photobiol. 66, 229–236 (1997).
[CrossRef] [PubMed]

Taylor, R. L.

O. C. Zienkiewcz, R. L. Taylor, The Finite Element Methods in Engineering Science (McGraw-Hill, New York, 1989).

Tikhonov, A.

A. Tikhonov, V. Arsenin, Solution of Ill-Posed Problems (Wiley, New York, 1977).

Toint, Ph. L.

A. R. Conn, I. M. Gould, Ph. L. Toint, “Testing a class of methods for solving minimization problems with simply bounds on the variables,” Math. Comput. 50, 399–430 (1988).
[CrossRef]

A. R. Conn, I. M. Gould, Ph. L. Toint, LANCELOT: a Fortran Package for Large-Scale Nonlinear Optimization (release A), Vol. 17 of Computational Mathematics Series (Springer-Verlag, New York, 1992).
[CrossRef]

Tromberg, B. J.

Troy, T. L.

M. J. Eppstein, D. E. Dougherty, T. L. Troy, E. M. Sevick-Muraca, “Biomedical optical tomography using dynamic parameterization and Bayesian conditioning on photon migration measurements,” Appl. Opt. 38, 2138–2150 (1999).
[CrossRef]

E. M. Sevick-Muraca, G. Lopez, T. L. Troy, J. S. Reynolds, C. L. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

J. S. Reynolds, T. L. Troy, E. M. Sevick-Muraca, “Multi-pixel techniques for frequency-domain photon migration imaging,” Biotechnol. Prog. 13, 669–680 (1997).
[CrossRef] [PubMed]

Ueda, Y.

M. Miwa, Y. Ueda, “Development of time-resolved spectroscopy system for quantitative noninvasive tissue measurement,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 142–149 (1995).

Valentini, G.

R. Cubeddu, G. Canti, A. Pifferi, P. Taroni, G. Valentini, “Fluorescence lifetime imaging of experimental tumors in the matoporhyrin derivate–sensitized mice,” Photochem. Photobiol. 66, 229–236 (1997).
[CrossRef] [PubMed]

van der Mark, M. B.

S. B. Colak, G. W. Hooft, D. G. Papaioannou, M. B. van der Mark, “3D backprojection tomography for medical optical imaging,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1992), pp. 294–298.

van der Zee, P.

A. J. Davies, B. Christianson, L. C. W. Dixon, R. Roy, P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Adv. Eng. Softw. 28, 217–221 (1997).
[CrossRef]

B. Christianson, A. J. Davies, L. C. W. Dixon, R. Roy, P. van der Zee, “Giving reverse differentiation a helping hand,” Opt. Meth. Software 8, 53–67 (1997).
[CrossRef]

Wahba, G.

G. Wahba, Spline Models of Observational Data (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1990).

Walker, S. A.

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

S. A. Walker, S. Fantini, E. Gratton, “Back-projection reconstructions in cylindrical inhomogeneities from frequency-domain optical measurements in turbid media,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C.), 1992, pp. 137–141.

Wang, Y.

Y. Yao, Y. Wang, Y. Pei, W. Zhu, R. L. Barbour, “Frequency-domain optical imaging of absorption and scattering by a Born iterative method,” J. Opt. Soc. Am. A 14, 325–342 (1997).
[CrossRef]

Y. Yao, Y. Pei, Y. Wang, R. L. Barbour, “Born-iterative methods for imaging of heterogeneous scattering media and its application to simulated breast tissue,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 231–239 (1997).

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. Muller, B. Chance, R. Alfano, J. Beuthan, E. Gratton, M. Kashke, B. Masters, S. Svanberg, P. van der Zee, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

Wang, Y. M.

W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1995).
[CrossRef]

Webb, K. J.

Wells, K.

K. Wells, J. C. Hebden, F. E. W. Schmidt, D. T. Delpy, “The UCL multichannel time-resolved system for optical tomography,” in Optical Tomography and Spectroscopy of Tissue, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 590–607 (1997).

Wilson, B. C.

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

Wolfe, P.

P. Wolfe, “Convergence condition for ascent method,” SIAM Rev. 11, 226–253 (1969).
[CrossRef]

Wright, M. H.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, London, 1981).

Yao, Y.

Y. Yao, Y. Wang, Y. Pei, W. Zhu, R. L. Barbour, “Frequency-domain optical imaging of absorption and scattering by a Born iterative method,” J. Opt. Soc. Am. A 14, 325–342 (1997).
[CrossRef]

Y. Yao, Y. Pei, Y. Wang, R. L. Barbour, “Born-iterative methods for imaging of heterogeneous scattering media and its application to simulated breast tissue,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 231–239 (1997).

Ye, J. C.

Yodh, A. G.

Yuan, Y.

Q. Ni, Y. Yuan, “A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization,” Math. Comput. 66, 1509–1520 (1997).
[CrossRef]

Zhu, W.

Zienkiewcz, O. C.

O. C. Zienkiewcz, R. L. Taylor, The Finite Element Methods in Engineering Science (McGraw-Hill, New York, 1989).

Zubkov, L.

Adv. Eng. Softw. (1)

A. J. Davies, B. Christianson, L. C. W. Dixon, R. Roy, P. van der Zee, “Reverse differentiation and the inverse diffusion problem,” Adv. Eng. Softw. 28, 217–221 (1997).
[CrossRef]

Appl. Opt. (5)

Biotechnol. Prog. (1)

J. S. Reynolds, T. L. Troy, E. M. Sevick-Muraca, “Multi-pixel techniques for frequency-domain photon migration imaging,” Biotechnol. Prog. 13, 669–680 (1997).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging (2)

W. C. Chew, Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1995).
[CrossRef]

A. H. Hielscher, A. D. Klose, K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef] [PubMed]

J. Optim. Theory Appl. (1)

L. C. W. Dixon, R. C. Price, “Numerical experience with the truncated Newton method for unconstrained optimization,” J. Optim. Theory Appl. 56, 245–255 (1988).
[CrossRef]

J. Inst. Math. Appl. (1)

R. Fletcher, M. P. Jackson, “Minimization of a quadratic function on many variables subject only to upper and lower bounds,” J. Inst. Math. Appl. 14, 159–174 (1974).
[CrossRef]

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

J. Photochem. Photobiol., B (1)

E. M. Sevick, J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, M. L. Johnson, “Frequency domain imaging of absorbers obscured by scattering,” J. Photochem. Photobiol., B 16, 169–185 (1992).
[CrossRef]

Math. Program. (1)

R. S. Dembo, T. Steihaug, “Truncated Newton algorithms for large-scale unconstrained optimization,” Math. Program. 26, 190–212 (1983).
[CrossRef]

Math. Comput. (2)

Q. Ni, Y. Yuan, “A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization,” Math. Comput. 66, 1509–1520 (1997).
[CrossRef]

A. R. Conn, I. M. Gould, Ph. L. Toint, “Testing a class of methods for solving minimization problems with simply bounds on the variables,” Math. Comput. 50, 399–430 (1988).
[CrossRef]

Math. Program. (2)

B. A. Murtagh, M. A. Saunders“Large-scale linearly constrained optimization,” Math. Program. 14, 41–72 (1978).
[CrossRef]

B. A. Murtagh, M. A. Saunders, “A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints,” Math. Program. 16, 4–117 (1982).

Med. Phys. (2)

A. D. Klose, A. H. Hielscher, “Iterative reconstructions scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).
[CrossRef] [PubMed]

K. D. Paulsen, H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–710 (1995).
[CrossRef] [PubMed]

Opt. Express (2)

R. Roy, E. M. Sevick-Muraca, “Truncated Newton’s optimization scheme for absorption and fluorescence optical tomography: Part II: Reconstruction from synthetic measurements,” Opt. Express 4, 372–382 (1999).
[CrossRef] [PubMed]

A. M. Siegel, J. J. A. Marota, D. A. Boas, “Design and evaluation of a continuous-wave diffuse optical tomography system,” Opt. Express 4, 287–298 (1999).
[CrossRef] [PubMed]

Opt. Eng. (Bellingham) (1)

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Opt. Meth. Software (1)

B. Christianson, A. J. Davies, L. C. W. Dixon, R. Roy, P. van der Zee, “Giving reverse differentiation a helping hand,” Opt. Meth. Software 8, 53–67 (1997).
[CrossRef]

Opt. Photonics News (1)

E. M. Sevick-Muraca, C. L. Hutchinson, D. Y. Paithankar, “Optical tissue biodiagnostics using fluorescence lifetime,” Opt. Photonics News, July1996, pp. 25–28.

Pacific J. Math. (1)

L. Armijo, “Minimization of functions having Lipschitz continuous first partial derivatives,” Pacific J. Math. 16, 1–3 (1966).
[CrossRef]

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

S. R. Arridge, M. R. Schweiger, “Image reconstruction in optical tomography,” Philos. Trans. R. Soc. London, Ser. B 352, 717–726 (1997).
[CrossRef] [PubMed]

Photochem. Photobiol. (2)

R. Cubeddu, G. Canti, A. Pifferi, P. Taroni, G. Valentini, “Fluorescence lifetime imaging of experimental tumors in the matoporhyrin derivate–sensitized mice,” Photochem. Photobiol. 66, 229–236 (1997).
[CrossRef] [PubMed]

E. M. Sevick-Muraca, G. Lopez, T. L. Troy, J. S. Reynolds, C. L. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” Photochem. Photobiol. 66, 55–64 (1997).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

J. C. Hebden, S. Arridge, D. T. Delpy, “Optical imagingeb in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

Proc. IEEE (1)

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

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 heterogeneities within turbid media: analytic solutions and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Rev. Sci. Instrum. (1)

J. R. Lakowicz, K. W. Berndt, “Lifetime-selective fluorescence imaging using an rf phase-sensitive camera,” Rev. Sci. Instrum. 62, 1727–1734 (1991).
[CrossRef]

Rev. Sci. Instrum. (1)

V. Ntziachristos, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[CrossRef]

SIAM J. Control Optim. (1)

D. P. Bertsekas, “Projected Newton method for optimization problems with simple contraints,” SIAM J. Control Optim. 20, 221–246 (1982).
[CrossRef]

SIAM J. Optim. (2)

F. Facchine, J. Judice, J. Soares, “An active set Newton algorithm for large-scale nonlinear programs with box constraints,” SIAM J. Optim. 8, 158–186 (1998).
[CrossRef]

R. Pytlak, “An efficient algorithm for large-scale nonlinear programming problems with simple bounds on the variables,” SIAM J. Optim. 8, 532–560 (1998).
[CrossRef]

SIAM Rev. (2)

P. C. Hansen, “Analysis of discrete ill-posed problem by means of the L-curve,” SIAM Rev. 34, 561–580 (1992).
[CrossRef]

P. Wolfe, “Convergence condition for ascent method,” SIAM Rev. 11, 226–253 (1969).
[CrossRef]

Sov. Math. Dokl. (1)

V. A. Morozov, “On the solution of functional equations by the method of regularization,” Sov. Math. Dokl. 7, 414–417 (1966).

Other (20)

G. Wahba, Spline Models of Observational Data (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1990).

A. H. Hielscher, A. D. Klose, “Use of a priori information and penalty terms in gradient-based iterative reconstruction schemes,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. Tromberg, ed., Proc. SPIE3597, 36–44 (1999).

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, E. M. Sevick-Muraca, “Three-dimensional optical tomography,” in Optical Tomography and Spectroscopy of Tissue III, B. Chance, R. R. Alfano, B. J. Tromberg, eds., Proc. SPIE3597, 97–105 (1999).
[CrossRef]

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, London, 1981).

A. R. Conn, I. M. Gould, Ph. L. Toint, LANCELOT: a Fortran Package for Large-Scale Nonlinear Optimization (release A), Vol. 17 of Computational Mathematics Series (Springer-Verlag, New York, 1992).
[CrossRef]

R. L. Barbour, R. Andronics, Q. Sha, H. L. Graber, I. Soller, “Development and evaluation of the IRIS-OPI scanner, a general-purpose optical tomography imaging system,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 251–255.

K. Wells, J. C. Hebden, F. E. W. Schmidt, D. T. Delpy, “The UCL multichannel time-resolved system for optical tomography,” in Optical Tomography and Spectroscopy of Tissue, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 590–607 (1997).

M. Miwa, Y. Ueda, “Development of time-resolved spectroscopy system for quantitative noninvasive tissue measurement,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 142–149 (1995).

S. A. Walker, S. Fantini, E. Gratton, “Back-projection reconstructions in cylindrical inhomogeneities from frequency-domain optical measurements in turbid media,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C.), 1992, pp. 137–141.

S. B. Colak, G. W. Hooft, D. G. Papaioannou, M. B. van der Mark, “3D backprojection tomography for medical optical imaging,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1992), pp. 294–298.

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. Muller, B. Chance, R. Alfano, J. Beuthan, E. Gratton, M. Kashke, B. Masters, S. Svanberg, P. van der Zee, eds. (SPIE Press, Bellingham, Wash., 1993), pp. 87–120.

S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
[CrossRef]

A. Tikhonov, V. Arsenin, Solution of Ill-Posed Problems (Wiley, New York, 1977).

R. Roy, “Image reconstruction from light measurements on biological tissue,” Ph.D. thesis (in Mathematics) (University of Hertfordshire, Hatfield, England, 1996).

A. Griewank, “On automatic differentiation,” in Mathematical Programming: Recent Developments and Applications, M. Iri, K. Tanaka, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1989), pp. 83–108.

J. Lee, E. M. Sevick-Muraca, “Lifetime and absorption imaging with fluorescence FDPM,” in Time-Resolved Fluorescence Spectroscopy and Imaging in Tissues, E. M. Sevick-Muraca, ed. Proc. SPIE3600, 246–254 (1999).

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

O. C. Zienkiewcz, R. L. Taylor, The Finite Element Methods in Engineering Science (McGraw-Hill, New York, 1989).

Y. Yao, Y. Pei, Y. Wang, R. L. Barbour, “Born-iterative methods for imaging of heterogeneous scattering media and its application to simulated breast tissue,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 231–239 (1997).

W. Cai, B. B. Das, F. Liu, F. A. Feng, M. Lax, R. R. Alfano, “Three-dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance, R. R. Alfano, eds. Proc. SPIE2979, 241–249 (1997).

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 (5)

Fig. 1
Fig. 1

(a) Solution through active constrained optimization, (b) solution through unconstrained optimization, (c) iterative active constrained optimization.  

Fig. 2
Fig. 2

(a) Actual distribution of absorption μ a xf in the two-dimensional domain; (b) reconstructed absorption μ a xf with the unconstrained optimization method; (c) reconstructed absorption μ a xf with the simple-bound constrained optimization method, with = 0.01 ; (d) reconstructed absorption μ a xf with the simple-bound constrained optimization method, with = 0.001 ; (e) reconstructed absorption μ a xf with the simple-bound constrained optimization method, with = 0.0001 ; (f ) reconstructed absorption μ a xf with the simple-bound constrained optimization method, with = 0.00001 ; (g) reconstructed absorption μ a xf with the simple-bound constrained optimization method, with = 0.0001 and upper bound greater than that of targets.

Fig. 3
Fig. 3

(a) Actual distribution of lifetime τ in the two-dimensional domain having longer fluorescence lifetime in three heterogeneities that have tenfold uptake of fluorescent dye; (b) reconstructed lifetime τ with the unconstrained optimization method; (c) reconstructed lifetime τ with the simple-bound constrained optimization method, with = 0.001 ; (d) reconstructed lifetime τ with the simple-bound constrained optimization method, with = 0.0001 .

Fig. 4
Fig. 4

(a) Actual distribution of lifetime τ in the two-dimensional domain with fluorescence quenching in three heterogeneities having tenfold uptake of fluorescent dye; (b) reconstructed lifetime τ with the unconstrained optimization method; (c) reconstructed lifetime τ with the simple-bound constrained optimization method, with = 0.01 ; (d) reconstructed lifetime τ with the simple-bound constrained optimization method, with = 0.001 .

Fig. 5
Fig. 5

Physical location of targets.

Tables (8)

Tables Icon

Table 1 Optical Parameters Used for the Optimization Problems [See Eqs. (1 ) and (2 )]

Tables Icon

Table 2 Computation Time Required for Reconstruction of Absorption Coefficients μ a xf (Problem 1) in the Two-Dimensional Domain with the Unconstrained and Simple-Bound Constrained Optimization Methods

Tables Icon

Table 3 Active and Free Variables of Absorption Coefficients after Each Iteration (Problem 1) with the Constrained Optimization Method

Tables Icon

Table 4 Computation Time for Reconstruction of Lifetime τ (Background 1 ns, Problem 2) in the Two-Dimensional Domain with Longer Fluorescence Lifetime in Three Heterogeneities Having Tenfold Uptake of Fluorescent Dye with the Unconstrained and Simple-Bound Constrained Optimization Methods

Tables Icon

Table 5 Active and Free Variables of Lifetimes after Each Iteration (Background 1 ns, Problem 2) with the Constrained Optimization Method

Tables Icon

Table 6 Computation Time Required for Reconstruction of Lifetime τ (Background 10 ns, Problem 3) in the Two-Dimensional Domain with Fluorescence Quenching in Three Heterogeneities Having Tenfold Uptake of Fluorescent Dye with the Unconstrained and Simple-Bound Constrained Optimization Methods

Tables Icon

Table 7 Active and Free Variables of Lifetimes after Each Iteration (Background 10 ns, Problem 3) with the Constrained Optimization Method

Tables Icon

Table 8 Computation Time Required for Finding the Background Absorption Coefficient μ a xf in the Two-Dimensional Domain with the Unconstrained Optimization Methods

Equations (33)

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

- [ D x ( r ) Φ x ( r ,   ω ) ]
+ i ω c + μ a xi ( r ) + μ a xf ( r ) Φ x ( r ,   ω )
= 0 on Ω ,
- [ D m ( r ) Φ m ( r ,   ω ) ] + i ω c + μ a m ( r ) Φ m ( r ,   ω )
= ϕ μ a xf 1 1 - i ω τ   Φ x ( r ,   ω ) on Ω ,
2 D x Φ x n   + Φ x + S δ ( r ¯ ,   r ¯ s ) = 0 on   d Ω ,
K Φ ¯ x , m = b .
E ( μ ¯ a xf   ,   τ ¯ ) = 1 2 l = 1 N q j = 1 j l N B { [ ( Φ m ) l ] j } c - { [ ( Φ m ) l ] j } me { [ ( Φ m ) l ] j } me
× { [ ( Φ m * ) l ] j } c - { [ ( Φ m * ) l ] j } me { [ ( Φ m * ) l ] j } me .
l i ( μ a ) i u i , i = 1 , ,   N ,
l i τ i u i , i = 1 , ,   N .
A ( μ ¯ a ) = [ i   :   ( μ a ) i = l i , E ( μ a ) i 0 ]     [ i   :   ( μ a ) i = u i ,
E ( μ a ) i 0 ] ,
E ( μ a ) i = 0 , i A ( μ ¯ a ) .
w T 2 E ( μ ¯ a ) w > 0
A 1 ( μ ¯ a ) = A ( μ ¯ a )     [ i   :   E ( μ a ) i 0 ] .
B ( μ ¯ a ) = ( i   :   l i μ a i l i + ) ,
B ( μ ¯ a ) = ( i   :   u i - μ a i μ i ) ,
C ( μ ¯ a ) = ( i   :   l i + μ a i u i - ) ,
= a i ( μ a ) E i ( μ a ) ,
= b i ( μ a ) E i ( μ a ) ,
l i + < u i - for i = 1 , ,   N .
min E ( μ ¯ a k ) T d k + 1 2 d k T G k d k   :   d k i = 0 ,   i B k ,   B k ,
min g k T w + 1 2 w T G k w   :   w     R m k ,
μ ¯ a k + 1 = μ ¯ a k + λ k d k ,
μ ¯ a k + 1 = μ ¯ a k + δ k d k
R 1 = 0.01 ,
R k + 1 = 2 R k   if λ k 1.0 ,
R k + 1 = 1 3   R k   if λ k < 1.0 .
E = j 1 2 ( Φ m ) c - ( Φ m ) me ( Φ m ) me j ( Φ m * ) c - ( Φ m * ) me ( Φ m * ) me j .
F = F + E .
Φ ¯ ^ m = E Φ m = ( Φ m * ) c - ( Φ m * ) me ( Φ m ) me ( Φ m * ) me j for all j d Ω 0 for all j d Ω
( μ ^ a ) p = E ( μ a ) p = E K K ( μ a ) p + E b b ( μ a ) p = el i ,   j ( K ^ el ) i ,   j K i ,   j el ( μ a ) p + el j b ^ j b j ( μ a ) p .

Metrics