Abstract

We propose a new numerical approach to the nonstationary optical (diffusion) tomography (OT) problem. The assumption in the method is that the absorption and/or diffusion coefficients are nonstationary in the sense that they may exhibit significant changes during the time that is needed to measure data for one traditional image frame. In the proposed method, the OT problem is formulated as a state-estimation problem. Within the state-estimation formulation, the absorption and/or diffusion coefficients are considered a stochastic process. The objective is to estimate a sequence of states for the process when the state evolution model for the process, the observation model for OT experiments, and data on the exterior boundary are given. In the proposed method, the state estimates are computed by using Kalman filtering techniques. The performance of the proposed method is evaluated on the basis of synthetic data. The simulations also illustrate that further improvements to the results in nonstationary applications can be obtained by adjustment of the measurement protocol.

© 2003 Optical Society of America

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  1. M. Cutler, “Transillumination as an aid in the diagnosis of breast lesions,” Surg. Gynecol. Obstet. 48, 721–729 (1929).
  2. J. J. Jöbsis, “Noninvasive infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
    [CrossRef]
  3. G. Jarry, S. Ghesquiere, J. M. Maarek, S. Debray, Bui-Mong-Hung, D. Laurent, “Imaging mammalian tissues and organs using laser collimated transillumination,” J. Biomed. Eng. 6, 70–74 (1984).
    [CrossRef] [PubMed]
  4. S. R. Arridge, “The 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. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE, Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 35–64.
  5. A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 38–40 (1995).
    [CrossRef]
  6. J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine: I. Experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
    [CrossRef] [PubMed]
  7. S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
    [CrossRef] [PubMed]
  8. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
    [CrossRef]
  9. D. Hawysz, E. M. Sevick-Muraca, “Developments towards diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2, 388–417 (2000).
    [CrossRef]
  10. D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
    [CrossRef]
  11. S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
    [CrossRef] [PubMed]
  12. K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. A. Franceschini, M. Kaschke, P. M. Schlag, “Contrast features ofbreast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
    [CrossRef] [PubMed]
  13. H. Jess, H. Erdl, K. T. Moesta, S. Fantini, M. A. Franceschini, E. Gratton, “Intensity modulated breast imaging: technology and clinical pilot study results,” 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., 1996), pp. 126–129.
  14. S. R. Arridge, M. Schweiger, “A general framework for iterative reconstruction algorithms in optical tomography, using a finite element method,” in Computational Radiology and Imaging: Therapy and Diagnosis, C. Borgers, F. Natteres, eds., Vol. 110 of IMA Volumes in Mathematics and Its Applications (Springer-Verlag, Berlin, 1998), pp. 45–70.
    [CrossRef]
  15. J. P. van Houten, D. A. Benaron, S. Splilman, D. K. Stevenson, “Imaging brain injury using time-resolved near infrared light scanning,” Pediatr. Res. 39, 470–476 (1996).
    [CrossRef] [PubMed]
  16. J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).
  17. A. Villringer, B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435–442 (1997).
    [CrossRef] [PubMed]
  18. C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).
  19. R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).
    [CrossRef] [PubMed]
  20. K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997).
    [CrossRef]
  21. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffusive reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
    [CrossRef] [PubMed]
  22. M. Kohl, R. Watson, M. Cope, “Determination of absorption-coefficients in highly scattering media from changes in attenuation and phase,” Opt. Lett. 21, 1519–1521 (1996).
    [CrossRef] [PubMed]
  23. B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
    [CrossRef]
  24. R. A. Williams, M. S. Beck, eds., Process Tomography, Principles, Techniques and Applications (Butterworth-Heinemann, Oxford, UK, 1995).
  25. 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 (1995).
    [CrossRef]
  26. 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]
  27. J. C. Ye, K. J. Webb, C. A. Bouman, R. P. Millane, “Optical diffusion tomography by iterative coordinate-descent optimization in a Bayesian framework,” J. Opt. Soc. Am. A 16, 2400–2412 (1999).
    [CrossRef]
  28. R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
    [CrossRef] [PubMed]
  29. J. Chang, H. L. Graber, R. L. Barbour, R. Aronson, “Recovery of optical cross-section perturbations in dense-scattering media by transport theory based imaging operators and steady state simulated data,” Appl. Opt. 35, 3963–3978 (1996).
    [CrossRef] [PubMed]
  30. B. B. Das, J. Dolne, R. L. Barbour, H. L. Graber, J. Chang, M. Zevallos, F. Liu, R. R. Alfano, “Analysis of time-resolved data for tomographical image reconstruction of opaque phantoms and finite absorbers in diffusive media,” 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, 16–28 (1995).
    [CrossRef]
  31. M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995).
    [CrossRef] [PubMed]
  32. J. Chang, H. L. Graber, P. C. Koo, R. Aronson, S. S. Barbour, R. L. Barbour, “Optical imaging of anatomical maps derived from magnetic resonance images using time-independent optical sources,” IEEE Trans. Med. Imaging 16, 68–77 (1997).
    [CrossRef] [PubMed]
  33. K. D. Paulsen, H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total variation minimization,” Appl. Opt. 35, 3447–3458 (1996).
    [CrossRef] [PubMed]
  34. M. Schweiger, S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
    [CrossRef] [PubMed]
  35. V. Kolehmainen, M. Vauhkonen, J. P. Kaipio, S. R. Arridge, “Recovery of piecewise constant coefficients in optical diffusion tomography,” Opt. Express7, 468–480 (2000); http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  36. A. V. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express9, 272–286 (2001); http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  37. C. H. Schmitz, H. L. Graber, H. Lou, I. Arif, J. Ira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, D.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6485 (2000).
    [CrossRef]
  38. J. P. Kaipio, E. Somersalo, “Nonstationary inverse problems and state estimation,” J. Inverse Ill-Posed Probl. 7, 273–282 (1999).
    [CrossRef]
  39. A. Seppänen, M. Vauhkonen, P. J. Vauhkonen, E. Somersalo, J. P. Kaipio, “State estimation with fluid dynamical evolution models in process tomography—an application to impedance tomography,” Inverse Probl. 17, 467–484 (2001).
    [CrossRef]
  40. V. Kolehmainen, A. Voutilainen, J. P. Kaipio, “Estimation of non-stationary region boundaries in EIT—state estimation approach,” Inverse Probl. 17, 1937–1956 (2001).
    [CrossRef]
  41. 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]
  42. M. J. Eppstein, D. E. Dougherty, D. J. Hawysz, E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
    [CrossRef] [PubMed]
  43. S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
    [CrossRef] [PubMed]
  44. J. P. Kaltenbach, M. Kaschke, “Frequency- and time-domain modelling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (Society at Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 65–86.
  45. M. C. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, New York, 1967).
  46. O. Dorn, “A transport–backtransport method for optical tomography,” Inverse Probl. 14, 1107–1130 (1998).
    [CrossRef]
  47. M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
    [CrossRef] [PubMed]
  48. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
  49. R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995).
    [CrossRef]
  50. F. Martelli, D. Contini, A. Taddeucci, G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. 2. Comparison with Monte Carlo results,” Appl. Opt. 36, 4600–4612 (1997).
    [CrossRef] [PubMed]
  51. A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
    [CrossRef] [PubMed]
  52. S. R. Arridge, H. Dehghani, M. Schweiger, E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with non-scattering regions,” Med. Phys. 27, 252–264 (2000).
    [CrossRef] [PubMed]
  53. V. Kolehmainen, “Novel approaches to image reconstruction in diffusion tomography,” Ph.D. thesis (University of Kuopio, Kuopio, Finland, 2001); http://venda.uku.fi/~vkolehma/ .
  54. S. R. Arridge, W. R. B. Lionheart, “Non-uniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998).
    [CrossRef]
  55. B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Östeberg, K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38, 2950–2960 (1999).
    [CrossRef]
  56. R. E. Kalman, R. S. Bucy, “New results in linear filter ing and prediction theory,” Trans. ASME J. Basic Eng. 83, 95–108 (1961).
    [CrossRef]
  57. J. L. Melsa, D. L. Cohn, Decision and Estimation Theory (McGraw-Hill, New York, 1978).
  58. C. K. Chui, G. Chen, Kalman Filtering with Practical Applications (Springer-Verlag, Berlin, 1987).
  59. B. D. O. Anderson, J. B. Moore, Optimal Filtering (Prentice-Hall, Englewood Cliffs, N.J., 1979).
  60. H. W. Sorenson, ed., Kalman Filtering: Theory and Applications (IEEE Press, Piscataway, N.J., 1985).
  61. A. Gelb, ed., Applied Optimal Estimation (MIT Press, Cambridge, Mass., 1974).
  62. A. Seppänen, M. Vauhkonen, E. Somersalo, J. P. Kaipio, “State space models in process tomography—approximation of state noise covariance,” Inverse Probl. Eng. 9, 561–585 (2001).
    [CrossRef]
  63. S. R. Arridge, M. Hiraoka, M. Schweiger, “Statistical basis for the determination of optical pathlength in tissue,” Phys. Med. Biol. 40, 1539–1558 (1995).
    [CrossRef] [PubMed]
  64. M. Cheney, D. Isaacson, J. C. Newell, S. Simske, J. Goble, “NOSER: an algorithm for solving the inverse conductivity problem,” Int. J. Imaging Syst. Technol. 2, 66–75 (1990).
    [CrossRef]
  65. J. E. Brazy, D. V. Lewis, M. H. Mitnick, F. F. Jöbsis van der Vliet, “Noninvasive monitoring of cerebral oxygenation in preterm infants: preliminary observations,” Pediatrics 75, 217–225 (1985).
    [PubMed]
  66. D. T. Delpy, M. Cope, “Quantitation in tissue near infra-red spectroscopy,” Philos. Trans. R. Soc. London Ser. B 352, 649–659 (1997).
    [CrossRef]
  67. S. R. Arridge, M. Hiraoka, M. Schweiger, “Modeling of noise for near-infrared transillumination imaging,” 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, 389–399 (1995).
    [CrossRef]
  68. J. P. Kaipio, V. Kolehmainen, E. Somersalo, M. Vauhkonen, “Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography,” Inverse Probl. 16, 1487–1522 (2000).
    [CrossRef]
  69. S. R. Arridge, “Photon measurement density functions. Part 1: analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
    [CrossRef] [PubMed]
  70. S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delby, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
    [CrossRef]
  71. F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, S. R. Arridge, “Multiple-slice imaging of a tissue-equivalent phantom by use of time-resolved optical tomography,” Appl. Opt. 39, 3380–3387 (2000).
    [CrossRef]
  72. J. Riley, M. Schweiger, S. R. Arridge, J. Ripoll, M. Nieto-Vesperinas, “3D optical tomography in the presence of void regions,” Opt. Express7, 462–467 (2000); http://www.opticsexpress.org .
    [CrossRef] [PubMed]

2001 (5)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

A. Seppänen, M. Vauhkonen, P. J. Vauhkonen, E. Somersalo, J. P. Kaipio, “State estimation with fluid dynamical evolution models in process tomography—an application to impedance tomography,” Inverse Probl. 17, 467–484 (2001).
[CrossRef]

V. Kolehmainen, A. Voutilainen, J. P. Kaipio, “Estimation of non-stationary region boundaries in EIT—state estimation approach,” Inverse Probl. 17, 1937–1956 (2001).
[CrossRef]

M. J. Eppstein, D. E. Dougherty, D. J. Hawysz, E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef] [PubMed]

A. Seppänen, M. Vauhkonen, E. Somersalo, J. P. Kaipio, “State space models in process tomography—approximation of state noise covariance,” Inverse Probl. Eng. 9, 561–585 (2001).
[CrossRef]

2000 (7)

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

D. Hawysz, E. M. Sevick-Muraca, “Developments towards diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2, 388–417 (2000).
[CrossRef]

J. P. Kaipio, V. Kolehmainen, E. Somersalo, M. Vauhkonen, “Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography,” Inverse Probl. 16, 1487–1522 (2000).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delby, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

S. R. Arridge, H. Dehghani, M. Schweiger, E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with non-scattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, S. R. Arridge, “Multiple-slice imaging of a tissue-equivalent phantom by use of time-resolved optical tomography,” Appl. Opt. 39, 3380–3387 (2000).
[CrossRef]

C. H. Schmitz, H. L. Graber, H. Lou, I. Arif, J. Ira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, D.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6485 (2000).
[CrossRef]

1999 (7)

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. Östeberg, K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38, 2950–2960 (1999).
[CrossRef]

J. C. Ye, K. J. Webb, C. A. Bouman, R. P. Millane, “Optical diffusion tomography by iterative coordinate-descent optimization in a Bayesian framework,” J. Opt. Soc. Am. A 16, 2400–2412 (1999).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

M. Schweiger, S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

J. P. Kaipio, E. Somersalo, “Nonstationary inverse problems and state estimation,” J. Inverse Ill-Posed Probl. 7, 273–282 (1999).
[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]

1998 (4)

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

O. Dorn, “A transport–backtransport method for optical tomography,” Inverse Probl. 14, 1107–1130 (1998).
[CrossRef]

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. A. Franceschini, M. Kaschke, P. M. Schlag, “Contrast features ofbreast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

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

1997 (7)

F. Martelli, D. Contini, A. Taddeucci, G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. 2. Comparison with Monte Carlo results,” Appl. Opt. 36, 4600–4612 (1997).
[CrossRef] [PubMed]

D. T. Delpy, M. Cope, “Quantitation in tissue near infra-red spectroscopy,” Philos. Trans. R. Soc. London Ser. B 352, 649–659 (1997).
[CrossRef]

A. Villringer, B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435–442 (1997).
[CrossRef] [PubMed]

K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997).
[CrossRef]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging 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. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

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

1996 (8)

C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).

R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).
[CrossRef] [PubMed]

J. P. van Houten, D. A. Benaron, S. Splilman, D. K. Stevenson, “Imaging brain injury using time-resolved near infrared light scanning,” Pediatr. Res. 39, 470–476 (1996).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
[CrossRef] [PubMed]

M. Kohl, R. Watson, M. Cope, “Determination of absorption-coefficients in highly scattering media from changes in attenuation and phase,” Opt. Lett. 21, 1519–1521 (1996).
[CrossRef] [PubMed]

J. Chang, H. L. Graber, R. L. Barbour, R. Aronson, “Recovery of optical cross-section perturbations in dense-scattering media by transport theory based imaging operators and steady state simulated data,” Appl. Opt. 35, 3963–3978 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffusive reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
[CrossRef] [PubMed]

K. D. Paulsen, H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total variation minimization,” Appl. Opt. 35, 3447–3458 (1996).
[CrossRef] [PubMed]

1995 (7)

1993 (1)

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

1990 (2)

M. Cheney, D. Isaacson, J. C. Newell, S. Simske, J. Goble, “NOSER: an algorithm for solving the inverse conductivity problem,” Int. J. Imaging Syst. Technol. 2, 66–75 (1990).
[CrossRef]

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).

1988 (1)

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

1985 (1)

J. E. Brazy, D. V. Lewis, M. H. Mitnick, F. F. Jöbsis van der Vliet, “Noninvasive monitoring of cerebral oxygenation in preterm infants: preliminary observations,” Pediatrics 75, 217–225 (1985).
[PubMed]

1984 (1)

G. Jarry, S. Ghesquiere, J. M. Maarek, S. Debray, Bui-Mong-Hung, D. Laurent, “Imaging mammalian tissues and organs using laser collimated transillumination,” J. Biomed. Eng. 6, 70–74 (1984).
[CrossRef] [PubMed]

1977 (1)

J. J. Jöbsis, “Noninvasive infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
[CrossRef]

1961 (1)

R. E. Kalman, R. S. Bucy, “New results in linear filter ing and prediction theory,” Trans. ASME J. Basic Eng. 83, 95–108 (1961).
[CrossRef]

1929 (1)

M. Cutler, “Transillumination as an aid in the diagnosis of breast lesions,” Surg. Gynecol. Obstet. 48, 721–729 (1929).

Alcouffe, R. E.

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

Alfano, R. R.

B. B. Das, J. Dolne, R. L. Barbour, H. L. Graber, J. Chang, M. Zevallos, F. Liu, R. R. Alfano, “Analysis of time-resolved data for tomographical image reconstruction of opaque phantoms and finite absorbers in diffusive media,” 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, 16–28 (1995).
[CrossRef]

Anderson, B. D. O.

B. D. O. Anderson, J. B. Moore, Optimal Filtering (Prentice-Hall, Englewood Cliffs, N.J., 1979).

Andronica, R.

Arif, I.

Aronson, R.

Arridge, S. R.

F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, S. R. Arridge, “Multiple-slice imaging of a tissue-equivalent phantom by use of time-resolved optical tomography,” Appl. Opt. 39, 3380–3387 (2000).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delby, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

S. R. Arridge, H. Dehghani, M. Schweiger, E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with non-scattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

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

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

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

S. R. Arridge, “Photon measurement density functions. Part 1: analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Hiraoka, M. Schweiger, “Statistical basis for the determination of optical pathlength in tissue,” Phys. Med. Biol. 40, 1539–1558 (1995).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

S. R. Arridge, “The 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. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE, Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 35–64.

S. R. Arridge, M. Schweiger, “A general framework for iterative reconstruction algorithms in optical tomography, using a finite element method,” in Computational Radiology and Imaging: Therapy and Diagnosis, C. Borgers, F. Natteres, eds., Vol. 110 of IMA Volumes in Mathematics and Its Applications (Springer-Verlag, Berlin, 1998), pp. 45–70.
[CrossRef]

S. R. Arridge, M. Hiraoka, M. Schweiger, “Modeling of noise for near-infrared transillumination imaging,” 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, 389–399 (1995).
[CrossRef]

Barbour, D.-L. S.

Barbour, R. L.

C. H. Schmitz, H. L. Graber, H. Lou, I. Arif, J. Ira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, D.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6485 (2000).
[CrossRef]

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

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

J. Chang, H. L. Graber, R. L. Barbour, R. Aronson, “Recovery of optical cross-section perturbations in dense-scattering media by transport theory based imaging operators and steady state simulated data,” Appl. Opt. 35, 3963–3978 (1996).
[CrossRef] [PubMed]

B. B. Das, J. Dolne, R. L. Barbour, H. L. Graber, J. Chang, M. Zevallos, F. Liu, R. R. Alfano, “Analysis of time-resolved data for tomographical image reconstruction of opaque phantoms and finite absorbers in diffusive media,” 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, 16–28 (1995).
[CrossRef]

Barbour, S. S.

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

Benaron, D. A.

J. P. van Houten, D. A. Benaron, S. Splilman, D. K. Stevenson, “Imaging brain injury using time-resolved near infrared light scanning,” Pediatr. Res. 39, 470–476 (1996).
[CrossRef] [PubMed]

Bernarding, J.

R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).
[CrossRef] [PubMed]

C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).

Bluestone, A.

Boas, D. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

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

Boretsky, R.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Bouman, C. A.

Brazy, J. E.

J. E. Brazy, D. V. Lewis, M. H. Mitnick, F. F. Jöbsis van der Vliet, “Noninvasive monitoring of cerebral oxygenation in preterm infants: preliminary observations,” Pediatrics 75, 217–225 (1985).
[PubMed]

Brooks, D. H.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

Bucy, R. S.

R. E. Kalman, R. S. Bucy, “New results in linear filter ing and prediction theory,” Trans. ASME J. Basic Eng. 83, 95–108 (1961).
[CrossRef]

Bui-Mong-Hung,

G. Jarry, S. Ghesquiere, J. M. Maarek, S. Debray, Bui-Mong-Hung, D. Laurent, “Imaging mammalian tissues and organs using laser collimated transillumination,” J. Biomed. Eng. 6, 70–74 (1984).
[CrossRef] [PubMed]

Case, M. C.

M. C. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, New York, 1967).

Chance, B.

A. Villringer, B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435–442 (1997).
[CrossRef] [PubMed]

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 38–40 (1995).
[CrossRef]

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

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Chang, J.

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

J. Chang, H. L. Graber, R. L. Barbour, R. Aronson, “Recovery of optical cross-section perturbations in dense-scattering media by transport theory based imaging operators and steady state simulated data,” Appl. Opt. 35, 3963–3978 (1996).
[CrossRef] [PubMed]

B. B. Das, J. Dolne, R. L. Barbour, H. L. Graber, J. Chang, M. Zevallos, F. Liu, R. R. Alfano, “Analysis of time-resolved data for tomographical image reconstruction of opaque phantoms and finite absorbers in diffusive media,” 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, 16–28 (1995).
[CrossRef]

Chen, G.

C. K. Chui, G. Chen, Kalman Filtering with Practical Applications (Springer-Verlag, Berlin, 1987).

Cheney, M.

M. Cheney, D. Isaacson, J. C. Newell, S. Simske, J. Goble, “NOSER: an algorithm for solving the inverse conductivity problem,” Int. J. Imaging Syst. Technol. 2, 66–75 (1990).
[CrossRef]

Chui, C. K.

C. K. Chui, G. Chen, Kalman Filtering with Practical Applications (Springer-Verlag, Berlin, 1987).

Cohn, D. L.

J. L. Melsa, D. L. Cohn, Decision and Estimation Theory (McGraw-Hill, New York, 1978).

Cohne, P.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Contini, D.

Cope, M.

D. T. Delpy, M. Cope, “Quantitation in tissue near infra-red spectroscopy,” Philos. Trans. R. Soc. London Ser. B 352, 649–659 (1997).
[CrossRef]

M. Kohl, R. Watson, M. Cope, “Determination of absorption-coefficients in highly scattering media from changes in attenuation and phase,” Opt. Lett. 21, 1519–1521 (1996).
[CrossRef] [PubMed]

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).

Cutler, M.

M. Cutler, “Transillumination as an aid in the diagnosis of breast lesions,” Surg. Gynecol. Obstet. 48, 721–729 (1929).

Das, B. B.

B. B. Das, J. Dolne, R. L. Barbour, H. L. Graber, J. Chang, M. Zevallos, F. Liu, R. R. Alfano, “Analysis of time-resolved data for tomographical image reconstruction of opaque phantoms and finite absorbers in diffusive media,” 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, 16–28 (1995).
[CrossRef]

Debray, S.

G. Jarry, S. Ghesquiere, J. M. Maarek, S. Debray, Bui-Mong-Hung, D. Laurent, “Imaging mammalian tissues and organs using laser collimated transillumination,” J. Biomed. Eng. 6, 70–74 (1984).
[CrossRef] [PubMed]

Dehghani, H.

F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, S. R. Arridge, “Multiple-slice imaging of a tissue-equivalent phantom by use of time-resolved optical tomography,” Appl. Opt. 39, 3380–3387 (2000).
[CrossRef]

S. R. Arridge, H. Dehghani, M. Schweiger, E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with non-scattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delby, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Delby, D. T.

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delby, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Delpy, D. T.

F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, S. R. Arridge, “Multiple-slice imaging of a tissue-equivalent phantom by use of time-resolved optical tomography,” Appl. Opt. 39, 3380–3387 (2000).
[CrossRef]

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

D. T. Delpy, M. Cope, “Quantitation in tissue near infra-red spectroscopy,” Philos. Trans. R. Soc. London Ser. B 352, 649–659 (1997).
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).

DiMarzio, C. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

Dirnagl, U.

R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).
[CrossRef] [PubMed]

C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).

Dolne, J.

B. B. Das, J. Dolne, R. L. Barbour, H. L. Graber, J. Chang, M. Zevallos, F. Liu, R. R. Alfano, “Analysis of time-resolved data for tomographical image reconstruction of opaque phantoms and finite absorbers in diffusive media,” 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, 16–28 (1995).
[CrossRef]

Dorn, O.

O. Dorn, “A transport–backtransport method for optical tomography,” Inverse Probl. 14, 1107–1130 (1998).
[CrossRef]

Dougherty, D. E.

M. J. Eppstein, D. E. Dougherty, D. J. Hawysz, E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[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]

Eberle, K.

K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997).
[CrossRef]

Edwards, A. D.

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).

Eppstein, M. J.

M. J. Eppstein, D. E. Dougherty, D. J. Hawysz, E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[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]

Erdl, H.

H. Jess, H. Erdl, K. T. Moesta, S. Fantini, M. A. Franceschini, E. Gratton, “Intensity modulated breast imaging: technology and clinical pilot study results,” 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., 1996), pp. 126–129.

Fantini, S.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. A. Franceschini, M. Kaschke, P. M. Schlag, “Contrast features ofbreast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
[CrossRef] [PubMed]

H. Jess, H. Erdl, K. T. Moesta, S. Fantini, M. A. Franceschini, E. Gratton, “Intensity modulated breast imaging: technology and clinical pilot study results,” 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., 1996), pp. 126–129.

Finander, M.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Flor, H.

C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).

Franceschini, M. A.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. A. Franceschini, M. Kaschke, P. M. Schlag, “Contrast features ofbreast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
[CrossRef] [PubMed]

H. Jess, H. Erdl, K. T. Moesta, S. Fantini, M. A. Franceschini, E. Gratton, “Intensity modulated breast imaging: technology and clinical pilot study results,” 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., 1996), pp. 126–129.

Fry, M. E.

F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, S. R. Arridge, “Multiple-slice imaging of a tissue-equivalent phantom by use of time-resolved optical tomography,” Appl. Opt. 39, 3380–3387 (2000).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delby, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Gaida, G.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
[CrossRef] [PubMed]

Gaudette, R. J.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

Gaudette, T.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

Ghesquiere, S.

G. Jarry, S. Ghesquiere, J. M. Maarek, S. Debray, Bui-Mong-Hung, D. Laurent, “Imaging mammalian tissues and organs using laser collimated transillumination,” J. Biomed. Eng. 6, 70–74 (1984).
[CrossRef] [PubMed]

Goble, J.

M. Cheney, D. Isaacson, J. C. Newell, S. Simske, J. Goble, “NOSER: an algorithm for solving the inverse conductivity problem,” Int. J. Imaging Syst. Technol. 2, 66–75 (1990).
[CrossRef]

Graber, H. L.

C. H. Schmitz, H. L. Graber, H. Lou, I. Arif, J. Ira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, D.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6485 (2000).
[CrossRef]

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

J. Chang, H. L. Graber, R. L. Barbour, R. Aronson, “Recovery of optical cross-section perturbations in dense-scattering media by transport theory based imaging operators and steady state simulated data,” Appl. Opt. 35, 3963–3978 (1996).
[CrossRef] [PubMed]

B. B. Das, J. Dolne, R. L. Barbour, H. L. Graber, J. Chang, M. Zevallos, F. Liu, R. R. Alfano, “Analysis of time-resolved data for tomographical image reconstruction of opaque phantoms and finite absorbers in diffusive media,” 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, 16–28 (1995).
[CrossRef]

Gratton, E.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
[CrossRef] [PubMed]

H. Jess, H. Erdl, K. T. Moesta, S. Fantini, M. A. Franceschini, E. Gratton, “Intensity modulated breast imaging: technology and clinical pilot study results,” 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., 1996), pp. 126–129.

Greenfield, R.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[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]

Hawysz, D.

D. Hawysz, E. M. Sevick-Muraca, “Developments towards diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2, 388–417 (2000).
[CrossRef]

Hawysz, D. J.

M. J. Eppstein, D. E. Dougherty, D. J. Hawysz, E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef] [PubMed]

Hebden, J. C.

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delby, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, S. R. Arridge, “Multiple-slice imaging of a tissue-equivalent phantom by use of time-resolved optical tomography,” Appl. Opt. 39, 3380–3387 (2000).
[CrossRef]

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

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

Heereken, K. R.

K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997).
[CrossRef]

Hibst, R.

Hielscher, A. H.

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, R. E. Alcouffe, R. L. Barbour, “Comparison of finite difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

Hillman, E. M. C.

F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, S. R. Arridge, “Multiple-slice imaging of a tissue-equivalent phantom by use of time-resolved optical tomography,” Appl. Opt. 39, 3380–3387 (2000).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delby, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Hiraoka, M.

S. R. Arridge, M. Hiraoka, M. Schweiger, “Statistical basis for the determination of optical pathlength in tissue,” Phys. Med. Biol. 40, 1539–1558 (1995).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

S. R. Arridge, M. Hiraoka, M. Schweiger, “Modeling of noise for near-infrared transillumination imaging,” 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, 389–399 (1995).
[CrossRef]

Hirth, C.

C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).

Ira, J.

Isaacson, D.

M. Cheney, D. Isaacson, J. C. Newell, S. Simske, J. Goble, “NOSER: an algorithm for solving the inverse conductivity problem,” Int. J. Imaging Syst. Technol. 2, 66–75 (1990).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

Jarry, G.

G. Jarry, S. Ghesquiere, J. M. Maarek, S. Debray, Bui-Mong-Hung, D. Laurent, “Imaging mammalian tissues and organs using laser collimated transillumination,” J. Biomed. Eng. 6, 70–74 (1984).
[CrossRef] [PubMed]

Jess, H.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. A. Franceschini, M. Kaschke, P. M. Schlag, “Contrast features ofbreast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
[CrossRef] [PubMed]

H. Jess, H. Erdl, K. T. Moesta, S. Fantini, M. A. Franceschini, E. Gratton, “Intensity modulated breast imaging: technology and clinical pilot study results,” 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., 1996), pp. 126–129.

Jiang, H.

Jöbsis, J. J.

J. J. Jöbsis, “Noninvasive infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
[CrossRef]

Jöbsis van der Vliet, F. F.

J. E. Brazy, D. V. Lewis, M. H. Mitnick, F. F. Jöbsis van der Vliet, “Noninvasive monitoring of cerebral oxygenation in preterm infants: preliminary observations,” Pediatrics 75, 217–225 (1985).
[PubMed]

Kaipio, J. P.

A. Seppänen, M. Vauhkonen, P. J. Vauhkonen, E. Somersalo, J. P. Kaipio, “State estimation with fluid dynamical evolution models in process tomography—an application to impedance tomography,” Inverse Probl. 17, 467–484 (2001).
[CrossRef]

V. Kolehmainen, A. Voutilainen, J. P. Kaipio, “Estimation of non-stationary region boundaries in EIT—state estimation approach,” Inverse Probl. 17, 1937–1956 (2001).
[CrossRef]

A. Seppänen, M. Vauhkonen, E. Somersalo, J. P. Kaipio, “State space models in process tomography—approximation of state noise covariance,” Inverse Probl. Eng. 9, 561–585 (2001).
[CrossRef]

J. P. Kaipio, V. Kolehmainen, E. Somersalo, M. Vauhkonen, “Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography,” Inverse Probl. 16, 1487–1522 (2000).
[CrossRef]

J. P. Kaipio, E. Somersalo, “Nonstationary inverse problems and state estimation,” J. Inverse Ill-Posed Probl. 7, 273–282 (1999).
[CrossRef]

Kalman, R. E.

R. E. Kalman, R. S. Bucy, “New results in linear filter ing and prediction theory,” Trans. ASME J. Basic Eng. 83, 95–108 (1961).
[CrossRef]

Kaltenbach, J. P.

J. P. Kaltenbach, M. Kaschke, “Frequency- and time-domain modelling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (Society at Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 65–86.

Kaschke, M.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. A. Franceschini, M. Kaschke, P. M. Schlag, “Contrast features ofbreast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
[CrossRef] [PubMed]

J. P. Kaltenbach, M. Kaschke, “Frequency- and time-domain modelling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (Society at Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 65–86.

Kaufman, K.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Kienle, A.

Kilmer, M.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Kilmer, M. E.

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

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]

Kohl, M.

Kolehmainen, V.

V. Kolehmainen, A. Voutilainen, J. P. Kaipio, “Estimation of non-stationary region boundaries in EIT—state estimation approach,” Inverse Probl. 17, 1937–1956 (2001).
[CrossRef]

J. P. Kaipio, V. Kolehmainen, E. Somersalo, M. Vauhkonen, “Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography,” Inverse Probl. 16, 1487–1522 (2000).
[CrossRef]

Koo, P. C.

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

Kurth, R.

K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997).
[CrossRef]

Laurent, D.

G. Jarry, S. Ghesquiere, J. M. Maarek, S. Debray, Bui-Mong-Hung, D. Laurent, “Imaging mammalian tissues and organs using laser collimated transillumination,” J. Biomed. Eng. 6, 70–74 (1984).
[CrossRef] [PubMed]

Leigh, J. S.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Levy, W.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Lewis, D. V.

J. E. Brazy, D. V. Lewis, M. H. Mitnick, F. F. Jöbsis van der Vliet, “Noninvasive monitoring of cerebral oxygenation in preterm infants: preliminary observations,” Pediatrics 75, 217–225 (1985).
[PubMed]

Lilge, L.

Lionheart, W. R. B.

Liu, F.

B. B. Das, J. Dolne, R. L. Barbour, H. L. Graber, J. Chang, M. Zevallos, F. Liu, R. R. Alfano, “Analysis of time-resolved data for tomographical image reconstruction of opaque phantoms and finite absorbers in diffusive media,” 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, 16–28 (1995).
[CrossRef]

Lou, H.

Maarek, J. M.

G. Jarry, S. Ghesquiere, J. M. Maarek, S. Debray, Bui-Mong-Hung, D. Laurent, “Imaging mammalian tissues and organs using laser collimated transillumination,” J. Biomed. Eng. 6, 70–74 (1984).
[CrossRef] [PubMed]

Mantulin, W. W.

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
[CrossRef] [PubMed]

Martelli, F.

McBride, T. O.

Melsa, J. L.

J. L. Melsa, D. L. Cohn, Decision and Estimation Theory (McGraw-Hill, New York, 1978).

Millane, R. P.

Miller, E. L.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

Mitnick, M. H.

J. E. Brazy, D. V. Lewis, M. H. Mitnick, F. F. Jöbsis van der Vliet, “Noninvasive monitoring of cerebral oxygenation in preterm infants: preliminary observations,” Pediatrics 75, 217–225 (1985).
[PubMed]

Miyake, H.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Moesta, K. T.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. A. Franceschini, M. Kaschke, P. M. Schlag, “Contrast features ofbreast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
[CrossRef] [PubMed]

H. Jess, H. Erdl, K. T. Moesta, S. Fantini, M. A. Franceschini, E. Gratton, “Intensity modulated breast imaging: technology and clinical pilot study results,” 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., 1996), pp. 126–129.

Moore, J. B.

B. D. O. Anderson, J. B. Moore, Optimal Filtering (Prentice-Hall, Englewood Cliffs, N.J., 1979).

Muhhlnickel, W.

C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).

Newell, J. C.

M. Cheney, D. Isaacson, J. C. Newell, S. Simske, J. Goble, “NOSER: an algorithm for solving the inverse conductivity problem,” Int. J. Imaging Syst. Technol. 2, 66–75 (1990).
[CrossRef]

Nioka, S.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

O’Leary, M. A.

Obrig, H.

K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997).
[CrossRef]

R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).
[CrossRef] [PubMed]

C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).

Okada, E.

S. R. Arridge, H. Dehghani, M. Schweiger, E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with non-scattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

Östeberg, U. L.

Osterberg, U. L.

Patterson, M. S.

Paulsen, K. D.

Pei, Y.

Pogue, B. W.

Prewitt, J.

Ramirez, N.

Reynolds, E. O. R.

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).

Richardson, C. E.

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).

Ruben, J.

K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997).
[CrossRef]

R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).
[CrossRef] [PubMed]

Schlag, P. M.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. A. Franceschini, M. Kaschke, P. M. Schlag, “Contrast features ofbreast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
[CrossRef] [PubMed]

Schmidt, F. E. W.

F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, S. R. Arridge, “Multiple-slice imaging of a tissue-equivalent phantom by use of time-resolved optical tomography,” Appl. Opt. 39, 3380–3387 (2000).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delby, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Schmitz, C. H.

Schweiger, M.

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delby, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

S. R. Arridge, H. Dehghani, M. Schweiger, E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with non-scattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, S. R. Arridge, “Multiple-slice imaging of a tissue-equivalent phantom by use of time-resolved optical tomography,” Appl. Opt. 39, 3380–3387 (2000).
[CrossRef]

M. Schweiger, S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

S. R. Arridge, M. Hiraoka, M. Schweiger, “Statistical basis for the determination of optical pathlength in tissue,” Phys. Med. Biol. 40, 1539–1558 (1995).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “A general framework for iterative reconstruction algorithms in optical tomography, using a finite element method,” in Computational Radiology and Imaging: Therapy and Diagnosis, C. Borgers, F. Natteres, eds., Vol. 110 of IMA Volumes in Mathematics and Its Applications (Springer-Verlag, Berlin, 1998), pp. 45–70.
[CrossRef]

S. R. Arridge, M. Hiraoka, M. Schweiger, “Modeling of noise for near-infrared transillumination imaging,” 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, 389–399 (1995).
[CrossRef]

Seppänen, A.

A. Seppänen, M. Vauhkonen, P. J. Vauhkonen, E. Somersalo, J. P. Kaipio, “State estimation with fluid dynamical evolution models in process tomography—an application to impedance tomography,” Inverse Probl. 17, 467–484 (2001).
[CrossRef]

A. Seppänen, M. Vauhkonen, E. Somersalo, J. P. Kaipio, “State space models in process tomography—approximation of state noise covariance,” Inverse Probl. Eng. 9, 561–585 (2001).
[CrossRef]

Sevick-Muraca, E. M.

M. J. Eppstein, D. E. Dougherty, D. J. Hawysz, E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef] [PubMed]

D. Hawysz, E. M. Sevick-Muraca, “Developments towards diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2, 388–417 (2000).
[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]

Simske, S.

M. Cheney, D. Isaacson, J. C. Newell, S. Simske, J. Goble, “NOSER: an algorithm for solving the inverse conductivity problem,” Int. J. Imaging Syst. Technol. 2, 66–75 (1990).
[CrossRef]

Smith, D. S.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Soller, I.

Somersalo, E.

A. Seppänen, M. Vauhkonen, E. Somersalo, J. P. Kaipio, “State space models in process tomography—approximation of state noise covariance,” Inverse Probl. Eng. 9, 561–585 (2001).
[CrossRef]

A. Seppänen, M. Vauhkonen, P. J. Vauhkonen, E. Somersalo, J. P. Kaipio, “State estimation with fluid dynamical evolution models in process tomography—an application to impedance tomography,” Inverse Probl. 17, 467–484 (2001).
[CrossRef]

J. P. Kaipio, V. Kolehmainen, E. Somersalo, M. Vauhkonen, “Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography,” Inverse Probl. 16, 1487–1522 (2000).
[CrossRef]

J. P. Kaipio, E. Somersalo, “Nonstationary inverse problems and state estimation,” J. Inverse Ill-Posed Probl. 7, 273–282 (1999).
[CrossRef]

Splilman, S.

J. P. van Houten, D. A. Benaron, S. Splilman, D. K. Stevenson, “Imaging brain injury using time-resolved near infrared light scanning,” Pediatr. Res. 39, 470–476 (1996).
[CrossRef] [PubMed]

Steiner, R.

Stevenson, D. K.

J. P. van Houten, D. A. Benaron, S. Splilman, D. K. Stevenson, “Imaging brain injury using time-resolved near infrared light scanning,” Pediatr. Res. 39, 470–476 (1996).
[CrossRef] [PubMed]

Taddeucci, A.

Thiel, A.

C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).

R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).
[CrossRef] [PubMed]

Totkas, S.

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. A. Franceschini, M. Kaschke, P. M. Schlag, “Contrast features ofbreast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

Troy, T. L.

van Houten, J. P.

J. P. van Houten, D. A. Benaron, S. Splilman, D. K. Stevenson, “Imaging brain injury using time-resolved near infrared light scanning,” Pediatr. Res. 39, 470–476 (1996).
[CrossRef] [PubMed]

Vauhkonen, M.

A. Seppänen, M. Vauhkonen, E. Somersalo, J. P. Kaipio, “State space models in process tomography—approximation of state noise covariance,” Inverse Probl. Eng. 9, 561–585 (2001).
[CrossRef]

A. Seppänen, M. Vauhkonen, P. J. Vauhkonen, E. Somersalo, J. P. Kaipio, “State estimation with fluid dynamical evolution models in process tomography—an application to impedance tomography,” Inverse Probl. 17, 467–484 (2001).
[CrossRef]

J. P. Kaipio, V. Kolehmainen, E. Somersalo, M. Vauhkonen, “Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography,” Inverse Probl. 16, 1487–1522 (2000).
[CrossRef]

Vauhkonen, P. J.

A. Seppänen, M. Vauhkonen, P. J. Vauhkonen, E. Somersalo, J. P. Kaipio, “State estimation with fluid dynamical evolution models in process tomography—an application to impedance tomography,” Inverse Probl. 17, 467–484 (2001).
[CrossRef]

Villringer, A.

A. Villringer, B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435–442 (1997).
[CrossRef] [PubMed]

K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997).
[CrossRef]

R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).
[CrossRef] [PubMed]

C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).

Villringer, K.

K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997).
[CrossRef]

C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).

R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).
[CrossRef] [PubMed]

Voutilainen, A.

V. Kolehmainen, A. Voutilainen, J. P. Kaipio, “Estimation of non-stationary region boundaries in EIT—state estimation approach,” Inverse Probl. 17, 1937–1956 (2001).
[CrossRef]

Watson, R.

Webb, K. J.

Wenzel, R.

K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997).
[CrossRef]

R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).
[CrossRef] [PubMed]

Wilson, B. C.

Wray, S. C.

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).

Wyatt, J. S.

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).

Ye, J. C.

Yodh, A.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 38–40 (1995).
[CrossRef]

Yodh, A. G.

Yoshioka, H.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Young, M.

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Zaccanti, G.

Zevallos, M.

B. B. Das, J. Dolne, R. L. Barbour, H. L. Graber, J. Chang, M. Zevallos, F. Liu, R. R. Alfano, “Analysis of time-resolved data for tomographical image reconstruction of opaque phantoms and finite absorbers in diffusive media,” 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, 16–28 (1995).
[CrossRef]

Zhang, Q.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Zhong, S.

Zweifel, P. F.

M. C. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, New York, 1967).

Appl. Opt. (9)

F. Martelli, D. Contini, A. Taddeucci, G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. 2. Comparison with Monte Carlo results,” Appl. Opt. 36, 4600–4612 (1997).
[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]

B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Östeberg, K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38, 2950–2960 (1999).
[CrossRef]

S. R. Arridge, “Photon measurement density functions. Part 1: analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
[CrossRef] [PubMed]

J. Chang, H. L. Graber, R. L. Barbour, R. Aronson, “Recovery of optical cross-section perturbations in dense-scattering media by transport theory based imaging operators and steady state simulated data,” Appl. Opt. 35, 3963–3978 (1996).
[CrossRef] [PubMed]

A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, B. C. Wilson, “Spatially resolved absolute diffusive reflectance measurements for noninvasive determination of the optical scattering and absorption coefficients of biological tissue,” Appl. Opt. 35, 2304–2314 (1996).
[CrossRef] [PubMed]

K. D. Paulsen, H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total variation minimization,” Appl. Opt. 35, 3447–3458 (1996).
[CrossRef] [PubMed]

F. E. W. Schmidt, J. C. Hebden, E. M. C. Hillman, M. E. Fry, M. Schweiger, H. Dehghani, D. T. Delpy, S. R. Arridge, “Multiple-slice imaging of a tissue-equivalent phantom by use of time-resolved optical tomography,” Appl. Opt. 39, 3380–3387 (2000).
[CrossRef]

C. H. Schmitz, H. L. Graber, H. Lou, I. Arif, J. Ira, Y. Pei, A. Bluestone, S. Zhong, R. Andronica, I. Soller, N. Ramirez, D.-L. S. Barbour, R. L. Barbour, “Instrumentation and calibration protocol for imaging dynamic features in dense-scattering media by optical tomography,” Appl. Opt. 39, 6466–6485 (2000).
[CrossRef]

IEEE Signal Process. Mag. (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

IEEE Trans. Med. Imaging (3)

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]

M. J. Eppstein, D. E. Dougherty, D. J. Hawysz, E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef] [PubMed]

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

Int. J. Imaging Syst. Technol. (2)

M. Cheney, D. Isaacson, J. C. Newell, S. Simske, J. Goble, “NOSER: an algorithm for solving the inverse conductivity problem,” Int. J. Imaging Syst. Technol. 2, 66–75 (1990).
[CrossRef]

S. R. Arridge, J. C. Hebden, M. Schweiger, F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, H. Dehghani, D. T. Delby, “A method for three-dimensional time-resolved optical tomography,” Int. J. Imaging Syst. Technol. 11, 2–11 (2000).
[CrossRef]

Inverse Probl. (5)

J. P. Kaipio, V. Kolehmainen, E. Somersalo, M. Vauhkonen, “Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography,” Inverse Probl. 16, 1487–1522 (2000).
[CrossRef]

O. Dorn, “A transport–backtransport method for optical tomography,” Inverse Probl. 14, 1107–1130 (1998).
[CrossRef]

A. Seppänen, M. Vauhkonen, P. J. Vauhkonen, E. Somersalo, J. P. Kaipio, “State estimation with fluid dynamical evolution models in process tomography—an application to impedance tomography,” Inverse Probl. 17, 467–484 (2001).
[CrossRef]

V. Kolehmainen, A. Voutilainen, J. P. Kaipio, “Estimation of non-stationary region boundaries in EIT—state estimation approach,” Inverse Probl. 17, 1937–1956 (2001).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

Inverse Probl. Eng. (1)

A. Seppänen, M. Vauhkonen, E. Somersalo, J. P. Kaipio, “State space models in process tomography—approximation of state noise covariance,” Inverse Probl. Eng. 9, 561–585 (2001).
[CrossRef]

J. Appl. Physiol. (1)

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).

J. Biomed. Eng. (1)

G. Jarry, S. Ghesquiere, J. M. Maarek, S. Debray, Bui-Mong-Hung, D. Laurent, “Imaging mammalian tissues and organs using laser collimated transillumination,” J. Biomed. Eng. 6, 70–74 (1984).
[CrossRef] [PubMed]

J. Biomed. Opt. (2)

K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. A. Franceschini, M. Kaschke, P. M. Schlag, “Contrast features ofbreast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998).
[CrossRef] [PubMed]

R. Wenzel, H. Obrig, J. Ruben, K. Villringer, A. Thiel, J. Bernarding, U. Dirnagl, A. Villringer, “Cerebral blood oxygenation changes induced by visual stimulation humans,” J. Biomed. Opt. 1, 399–404 (1996).
[CrossRef] [PubMed]

J. Inverse Ill-Posed Probl. (1)

J. P. Kaipio, E. Somersalo, “Nonstationary inverse problems and state estimation,” J. Inverse Ill-Posed Probl. 7, 273–282 (1999).
[CrossRef]

J. Opt. Soc. Am. A (3)

Med. Phys. (4)

S. R. Arridge, H. Dehghani, M. Schweiger, E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with non-scattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, K. T. Moesta, P. M. Schlag, M. Kaschke, “Frequency-domain optical mammography: edge effect corrections,” Med. Phys. 23, 149–157 (1996).
[CrossRef] [PubMed]

Neoplasia (1)

D. Hawysz, E. M. Sevick-Muraca, “Developments towards diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2, 388–417 (2000).
[CrossRef]

Neuro. Report (1)

C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Non-invasive functional mapping of the human motor cortex using near-infrared spectroscopy,” Neuro. Report 7, 1977–1981 (1996).

Opt. Lett. (3)

Pediatr. Res. (1)

J. P. van Houten, D. A. Benaron, S. Splilman, D. K. Stevenson, “Imaging brain injury using time-resolved near infrared light scanning,” Pediatr. Res. 39, 470–476 (1996).
[CrossRef] [PubMed]

Pediatrics (1)

J. E. Brazy, D. V. Lewis, M. H. Mitnick, F. F. Jöbsis van der Vliet, “Noninvasive monitoring of cerebral oxygenation in preterm infants: preliminary observations,” Pediatrics 75, 217–225 (1985).
[PubMed]

Philos. Trans. R. Soc. London Ser. B (2)

D. T. Delpy, M. Cope, “Quantitation in tissue near infra-red spectroscopy,” Philos. Trans. R. Soc. London Ser. B 352, 649–659 (1997).
[CrossRef]

K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997).
[CrossRef]

Phys. Med. Biol. (6)

R. J. Gaudette, D. H. Brooks, C. A. DiMarzio, M. E. Kilmer, E. L. Miller, T. Gaudette, D. A. Boas, “A comparison study of linear reconstruction techniques for diffuse optical tomographic imaging of absorption coefficient,” Phys. Med. Biol. 45, 1051–1070 (2000).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging 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. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Hiraoka, M. Schweiger, “Statistical basis for the determination of optical pathlength in tissue,” Phys. Med. Biol. 40, 1539–1558 (1995).
[CrossRef] [PubMed]

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

Phys. Today (1)

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 38–40 (1995).
[CrossRef]

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

B. Chance, J. S. Leigh, H. Miyake, D. S. Smith, S. Nioka, R. Greenfield, M. Finander, K. Kaufman, W. Levy, M. Young, P. Cohne, H. Yoshioka, R. Boretsky, “Comparison of time-resolved and unresolved measurements of deoxyhemoglobin in brain,” Proc. Natl. Acad. Sci. USA 85, 4971–4975 (1988).
[CrossRef]

Science (1)

J. J. Jöbsis, “Noninvasive infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
[CrossRef]

Surg. Gynecol. Obstet. (1)

M. Cutler, “Transillumination as an aid in the diagnosis of breast lesions,” Surg. Gynecol. Obstet. 48, 721–729 (1929).

Trans. ASME J. Basic Eng. (1)

R. E. Kalman, R. S. Bucy, “New results in linear filter ing and prediction theory,” Trans. ASME J. Basic Eng. 83, 95–108 (1961).
[CrossRef]

Trends Neurosci. (1)

A. Villringer, B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435–442 (1997).
[CrossRef] [PubMed]

Other (18)

H. Jess, H. Erdl, K. T. Moesta, S. Fantini, M. A. Franceschini, E. Gratton, “Intensity modulated breast imaging: technology and clinical pilot study results,” 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., 1996), pp. 126–129.

S. R. Arridge, M. Schweiger, “A general framework for iterative reconstruction algorithms in optical tomography, using a finite element method,” in Computational Radiology and Imaging: Therapy and Diagnosis, C. Borgers, F. Natteres, eds., Vol. 110 of IMA Volumes in Mathematics and Its Applications (Springer-Verlag, Berlin, 1998), pp. 45–70.
[CrossRef]

S. R. Arridge, “The 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. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE, Institute Series (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 35–64.

R. A. Williams, M. S. Beck, eds., Process Tomography, Principles, Techniques and Applications (Butterworth-Heinemann, Oxford, UK, 1995).

V. Kolehmainen, M. Vauhkonen, J. P. Kaipio, S. R. Arridge, “Recovery of piecewise constant coefficients in optical diffusion tomography,” Opt. Express7, 468–480 (2000); http://www.opticsexpress.org .
[CrossRef] [PubMed]

A. V. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express9, 272–286 (2001); http://www.opticsexpress.org .
[CrossRef] [PubMed]

B. B. Das, J. Dolne, R. L. Barbour, H. L. Graber, J. Chang, M. Zevallos, F. Liu, R. R. Alfano, “Analysis of time-resolved data for tomographical image reconstruction of opaque phantoms and finite absorbers in diffusive media,” 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, 16–28 (1995).
[CrossRef]

J. P. Kaltenbach, M. Kaschke, “Frequency- and time-domain modelling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Mueller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Vol. IS11 of SPIE Institute Series (Society at Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 65–86.

M. C. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, New York, 1967).

J. L. Melsa, D. L. Cohn, Decision and Estimation Theory (McGraw-Hill, New York, 1978).

C. K. Chui, G. Chen, Kalman Filtering with Practical Applications (Springer-Verlag, Berlin, 1987).

B. D. O. Anderson, J. B. Moore, Optimal Filtering (Prentice-Hall, Englewood Cliffs, N.J., 1979).

H. W. Sorenson, ed., Kalman Filtering: Theory and Applications (IEEE Press, Piscataway, N.J., 1985).

A. Gelb, ed., Applied Optimal Estimation (MIT Press, Cambridge, Mass., 1974).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

V. Kolehmainen, “Novel approaches to image reconstruction in diffusion tomography,” Ph.D. thesis (University of Kuopio, Kuopio, Finland, 2001); http://venda.uku.fi/~vkolehma/ .

S. R. Arridge, M. Hiraoka, M. Schweiger, “Modeling of noise for near-infrared transillumination imaging,” 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, 389–399 (1995).
[CrossRef]

J. Riley, M. Schweiger, S. R. Arridge, J. Ripoll, M. Nieto-Vesperinas, “3D optical tomography in the presence of void regions,” Opt. Express7, 462–467 (2000); http://www.opticsexpress.org .
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Illustration of the source configurations for the data-acquisition protocols: (a) traditional 16 × 16 protocol, (b) 4 × 16 protocol. Thick tick marks denote the locations of the source fibers k , and shorter thin marks denote the locations of the detector fibers. For both protocols, the indices of the sources are in accordance with the sequence in which they are fired.

Fig. 2
Fig. 2

True absorption images are shown in the first column at eight time instants t i , i = 1 ,   3 ,   5 ,   7 ,   9 ,   11 ,   13 ,   15 . The data-acquisition protocol was the 16 × 16 system. The red markers on the boundary of the phantom domains denote the source that is fired at time t i . The Kalman filter estimates f t | t are shown in the second column, and the Kalman smoother estimates f t | T are shown in the third column. The current value of the Kalman predictor was used as linearization point of the observation model at each time instant; i.e., f t * = f t | t - 1 . The fourth column shows stationary reconstructions that are based on the 16 detector readings for the single source that is fired at time t i (i.e., z R 16 ). The fifth column shows stationary reconstruction that is based on the traditional 16 × 16 frame (i.e., z R 256 ) that is acquired during the instants { t i ,   i = 1 ,   2 ,   3 , ,   16 } .

Fig. 3
Fig. 3

True absorption images are shown in the first column at eight time instants t i , i = 1 ,   3 ,   5 ,   7 ,   9 ,   11 , 13 ,   15 . The data-acquisition protocol was the 4 × 16 system. The red markers on the boundary of the phantom domains denote the source that is fired at time t i . The Kalman filter estimates f t | t are shown in the second column, and the Kalman smoother estimates f t | T are shown in the third column. The current value of the Kalman predictor was used as linearization point of the observation model at each time instant; i.e., f t * = f t | t - 1 . The fourth column shows (stationary) reconstructions that are based on the detector readings for the single source that is fired at time t i (i.e., z R 16 ). The fifth column shows stationary reconstructions based on the 4 × 16 frame (i.e., z R 64 ) that is acquired during instants { t i - 3 ,   t i - 2 ,   t i - 1 ,   t i } .

Fig. 4
Fig. 4

True absorption images are shown in the first column at eight time instants t i , i = 1 ,   3 ,   5 ,   7 ,   9 ,   11 ,   13 ,   15 . The data-acquisition protocol was the 4 × 16 system. The red markers on the boundary of the phantom domains denote the source that is fired at time t i . The Kalman filter estimates f t | t are shown in the second column, and the Kalman smoother estimates f t | T are shown in the third column. The current value of the Kalman predictor was used as linearization point of the observation model at each time instant, i.e., f t * = f t | t - 1 . The fourth column shows (stationary) reconstructions that are based on the detector readings for the single source that is fired at time t i (i.e., z R 16 ). The fifth column shows (stationary) reconstructions that are based on the traditional 4 × 16 frame (i.e., z R 64 ) that is acquired during instants { t i - 3 ,   t i - 2 ,   t i - 1 ,   t i } .

Fig. 5
Fig. 5

True absorption images are shown in the first column at four consecutive time instants t i , i = 5 ,   6 ,   7 ,   8 . The data-acquisition protocol was the 4 × 16 system. The red markers on the boundary of the phantom domains denote the source that is fired at time t i . The Kalman filter estimates f t | t are shown in the second column, and the Kalman smoother estimates f t | T are shown in the third column. The current value of the Kalman predictor was used as linearization point of the observation model at each time instant; i.e., f t * = f t | t - 1 . The fourth column shows (stationary) reconstructions that are based on the traditional 4 × 16 frame (i.e., z R 64 ) that is acquired during instants { t i - 3 ,   t i - 2 ,   t i - 1 ,   t i } .

Fig. 6
Fig. 6

Time-varying contrast of absorption within the inclusion in Fig. 5 at time instants t i , i = 1 ,   2 , ,   16 . The true value is shown as the thick solid curve. The mean value of the reconstructed absorption within the inclusion for the Kalman filter estimates f t | t is shown as the thin solid curve and for the Kalman smother estimates f t | T is shown as the dashed curve. The dotted curve shows the respective value for the stationary reconstructions with the 4 × 16 frame (i.e., z R 64 ) at time instants t i , i = 4 ,   5 , ,   16 . The vertical lines denote the part of the time series that is shown in Fig. 5.  

Equations (34)

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- κ ( r ) Φ k ( r ,   ω ) + μ a ( r ) Φ k ( r ,   ω ) + i ω c   Φ k ( r ,   ω )
= q 0 , k ( r ,   ω ) , r Ω ,
Φ k ( r ,   ω ) + 2 κ ( r ) θ   Φ k ( r ,   ω ) n ˆ = g k ( r ,   ω ) , r Ω ,
g k ( r ,   ω ) = - 4 Γ s ( r ,   ω ) , r k 0 , r Ω \ k .
Γ i , k ( r ,   ω ) = - κ ( r ) n ˆ Φ k ( r ,   ω ) , r ζ i Ω .
μ a ( r ) = j = 1 M μ μ a , j χ j ( μ ) ( r ) ,
κ ( r ) = j = 1 M κ κ j χ j ( κ ) ( r ) ,
μ a = ( μ a , 1 , ,   μ a , M μ ) T R M μ ,
κ = ( κ 1 , ,   κ M κ ) T R M κ .
f = μ a κ R M μ + M κ .
z ( k ) = ( z 1 , k , ,   z M , k ) T ,
z ( k ) = F ( k ) ( f ) .
z = z ( 1 ) z ( S ) , F ( f ) = F ( 1 ) ( f ) F ( S ) ( f ) .
z = F ( f ) + n ,
Ξ ( f ) = z - F ( f ) 2 .
Ξ ( f ) = z - F ( f ) 2 + β A ( f ) ,
A ( f ) = Rf 2 ,
f t + 1 = K t f t + w t , t I = { 1 ,   2 , ,   T } ,
w t N ( 0 ,   C w , t ) ,
z t = F t ( f t ) + n t , n t N ( 0 ,   C n , t ) ,
f t | I k = E ( f t | z k ,   k I k ) ,
z t = F t ( f t * ) + J t ( f t * ) ( f t - f t * ) + n t , t I ,
G t = C t | t - 1 J t T ( f t * ) [ J t ( f t * ) C t | t - 1 J t T ( f t * ) + C n , t ] - 1 ,
f t | t = f t | t - 1 + G t [ z t - F t ( f t * ) - J t ( f t * ) ( f t | t - 1 - f t * ) ] ,
 
C t | t = C t | t - 1 - G t J t ( f t * ) C t | t - 1 ,
f t + 1 | t = K t f t | t ,
C t + 1 | t = K t C t | t K t T + C w , t ,
f t | t = f t | t - 1 + G t [ z t - F t ( f t | t - 1 ) ] .
X t - 1 = C t - 1 | t - 1 K t - 1 T C t | t - 1 - 1 ,
f t - 1 | T = f t - 1 | t - 1 + X t - 1 ( f t | T - f t | t - 1 ) .
z t - F t ( f t * ) + J t ( f t * ) f t * 0 = J t ( f t * ) β R f t + n t n ^ t ,
Lz t = LF t ( f t * ) + LJ t ( f t * ) ( f t - f t * ) + Ln t ,
C n , t = C n , t 0 0 I

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