Abstract

Systematic characterization studies are presented, relating to a previously reported spatial deconvolution operation that seeks to compensate for the information-blurring property of first-order perturbation algorithms for diffuse optical tomography (DOT) image reconstruction. In simulation results that are presented, this deconvolution operation has been applied to two-dimensional DOT images reconstructed by solving a first-order perturbation equation. Under study was the effect on algorithm performance of control parameters in the measurement (number and spatial distribution of sources and detectors, presence of noise, and presence of systematic error), target (medium shape; and number, location, size, and contrast of inclusions), and computational (number of finite-element-method mesh nodes, length of filter-generating linear system, among others) parameter spaces associated with computation and the use of the deconvolution operators. Substantial improvements in reconstructed image quality, in terms of recovered inclusion location, size, and contrast, are found in all cases. A finding of practical importance is that the method is robust to appreciable differences between the optical coefficients of the media used for filter generation and those of the target media to which the filters are subsequently applied.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  19. It is recognized that techniques for experimental estimation of the bulk or background properties of target media will not yield perfectly accurate results. Consequently, a full characterization of the spatial deconvolution method will require consideration of cases in which the properties of the media used for the computations of I and I0 differ. For reasons of space limitations, the influence of disparities between the media on the accuracy of the deconvolved image is deferred to future publications in this series.
  20. When images are reconstructed from experimental or clinical data, typically there is an appreciable difference between I0and Ir. But as shown in Ref. 18, the normalized-difference method is highly robust to disparities between the media that yield these measurement vectors. Then it is expected that introducing a difference between I0 and Ir will not affect the performance of the spatial deconvolution algorithm. Direct tests of this hypothesis will be another subject presented in future publications.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2005 (1)

2004 (1)

R. L. Barbour, H. L. Graber, Y. Xu, Y. Pei, R. Aronson, “Strategies for imaging diffusing media,” Transp. Theory Stat. Phys. 33, 361–371 (2004).
[CrossRef]

2003 (8)

D. A. Boas, G. Strangman, J. P. Culver, R. D. Hoge, G. Jasdzewski, R. A. Poldrack, B. R. Rosen, J. B. Mandeville, “Can the cerebral metabolic rate of oxygen be estimated with near-infrared spectroscopy?” Phys. Med. Biol. 48, 2405–2418 (2003).
[CrossRef] [PubMed]

H. Obrig, A. Villringer, “Beyond the visible—imaging the human brain with light,” J. Cereb. Blood Flow Metab. 23, 1–18 (2003).
[CrossRef]

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

V. Kolehmainen, S. Prince, S. R. Arridge, J. P. Kaipio, “State-estimation approach to the nonstationary optical tomography problem,” J. Opt. Soc. Am. A 20, 876–889 (2003).
[CrossRef]

J. C. Hebden, “Advances in optical imaging of the newborn infant brain,” Psychophysiology 40, 501–510 (2003).
[CrossRef] [PubMed]

J. Zhou, J. Bai, P. He, “Spatial location weighted optimization scheme for DC optical tomography,” Opt. Express 11, 141–150 (2003), http://www.opticsexpress.org .
[CrossRef] [PubMed]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

V. E. Pera, E. L. Heffer, H. Siebold, O. Schütz, S. Heywang-Köbrunner, A. Götz, A. Heinig, S. Fantini, “Spatial second-derivative image processing: an application to optical mammography to enhance the detection of breast tumors,” J. Biomed. Opt. 8, 517–524 (2003).
[CrossRef] [PubMed]

2002 (3)

H. L. Graber, Y. Pei, R. L. Barbour, “Imaging of spatiotemporal coincident states by DC optical tomography,” IEEE Trans. Med. Imaging 21, 852–866 (2002).
[CrossRef] [PubMed]

R. Archibald, A. Gelb, “A method to reduce the Gibbs ringing artifact in MRI scans while keeping tissue boundary integrity,” IEEE Trans. Med. Imaging 21, 305–319 (2002).
[CrossRef] [PubMed]

V. A. Markel, J. C. Schotland, “Effects of sampling and limited data in optical tomography,” Appl. Phys. Lett. 81, 1180–1182 (2002).
[CrossRef]

2001 (7)

Y. Pei, H. L. Graber, R. L. Barbour, “Normalized-constraint algorithm for minimizing inter-parameter crosstalk in DC optical tomography,” Opt. Express 9, 97–109 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Y. Pei, H. L. Graber, R. L. Barbour, “Influence of systematic errors in reference states on image quality and on stability of derived information for dc optical imaging,” Appl. Opt. 40, 5755–5769 (2001).
[CrossRef]

A. Y. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express 9, 272–286 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A 18, 3018–3036 (2001).
[CrossRef]

J. P. Culver, V. Ntziachristos, M. J. Holboke, A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
[CrossRef]

2000 (1)

V. Ntziachristos, A. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after Indocyanine Green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).

1999 (4)

1998 (1)

J. Chang, H. L. Graber, R. L. Barbour, “Dependence of image quality on image operator and noise for optical diffusion tomography,” J. Biomed. Opt. 3, 137–144 (1998).
[CrossRef] [PubMed]

1996 (2)

1995 (1)

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–702 (1995).
[CrossRef] [PubMed]

1988 (1)

Abdoulaev, G.

Archibald, R.

R. Archibald, A. Gelb, “A method to reduce the Gibbs ringing artifact in MRI scans while keeping tissue boundary integrity,” IEEE Trans. Med. Imaging 21, 305–319 (2002).
[CrossRef] [PubMed]

Aronson, R.

Arridge, S. R.

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

V. Kolehmainen, S. Prince, S. R. Arridge, J. P. Kaipio, “State-estimation approach to the nonstationary optical tomography problem,” J. Opt. Soc. Am. A 20, 876–889 (2003).
[CrossRef]

Bai, J.

Barbour, R. L.

H. L. Graber, Y. Xu, Y. Pei, R. L. Barbour, “Qualitative and quantitative improvement of optical tomographic reconstructed images via spatial deconvolution: three-dimensional case,” Appl. Opt. 44, 941–953 (2005).
[CrossRef] [PubMed]

R. L. Barbour, H. L. Graber, Y. Xu, Y. Pei, R. Aronson, “Strategies for imaging diffusing media,” Transp. Theory Stat. Phys. 33, 361–371 (2004).
[CrossRef]

H. L. Graber, Y. Pei, R. L. Barbour, “Imaging of spatiotemporal coincident states by DC optical tomography,” IEEE Trans. Med. Imaging 21, 852–866 (2002).
[CrossRef] [PubMed]

A. Y. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express 9, 272–286 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Y. Pei, H. L. Graber, R. L. Barbour, “Normalized-constraint algorithm for minimizing inter-parameter crosstalk in DC optical tomography,” Opt. Express 9, 97–109 (2001), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Y. Pei, H. L. Graber, R. L. Barbour, “Influence of systematic errors in reference states on image quality and on stability of derived information for dc optical imaging,” Appl. Opt. 40, 5755–5769 (2001).
[CrossRef]

R. L. Barbour, H. L. Graber, Y. Pei, S. Zhong, C. H. Schmitz, “Optical tomographic imaging of dynamic features of dense-scattering media,” J. Opt. Soc. Am. A 18, 3018–3036 (2001).
[CrossRef]

Y. Pei, F.-B. Lin, R. L. Barbour, “Modeling of sensitivity and resolution to an included object in homogeneous scattering media and in MRI-derived breast maps,” Opt. Express 5, 203–219 (1999), http://www.opticsexpress.org .
[CrossRef] [PubMed]

J. Chang, H. L. Graber, R. L. Barbour, “Dependence of image quality on image operator and noise for optical diffusion tomography,” J. Biomed. Opt. 3, 137–144 (1998).
[CrossRef] [PubMed]

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

Baron, L.

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
[CrossRef]

Bishop, C. M.

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford U. Press, Oxford, UK, 1995).

Bluestone, A. Y.

Blumenfeld, S. M.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Boas, D.

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

Boas, D. A.

D. A. Boas, G. Strangman, J. P. Culver, R. D. Hoge, G. Jasdzewski, R. A. Poldrack, B. R. Rosen, J. B. Mandeville, “Can the cerebral metabolic rate of oxygen be estimated with near-infrared spectroscopy?” Phys. Med. Biol. 48, 2405–2418 (2003).
[CrossRef] [PubMed]

Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

Boverman, G.

Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

Brukilacchio, T. J.

Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

Budinger, T.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Chance, B.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

V. Ntziachristos, A. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after Indocyanine Green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).

Chang, J.

Chaves, T.

Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

Cho, Z. H.

Z. H. Cho, J. P. Jones, M. Singh, Foundation of Medical Imaging (Wiley, New York, 1993), p. 80.

Choe, R.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

Chorlton, M.

Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

Colak, S.

S. Colak, M. van der Mark, G. W.'t Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Contini, D.

Culver, J. P.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

D. A. Boas, G. Strangman, J. P. Culver, R. D. Hoge, G. Jasdzewski, R. A. Poldrack, B. R. Rosen, J. B. Mandeville, “Can the cerebral metabolic rate of oxygen be estimated with near-infrared spectroscopy?” Phys. Med. Biol. 48, 2405–2418 (2003).
[CrossRef] [PubMed]

J. P. Culver, V. Ntziachristos, M. J. Holboke, A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
[CrossRef]

Durduran, T.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

Eggert, J.

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
[CrossRef]

Fajardo, L.

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
[CrossRef]

Fantini, S.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schütz, S. Heywang-Köbrunner, A. Götz, A. Heinig, S. Fantini, “Spatial second-derivative image processing: an application to optical mammography to enhance the detection of breast tumors,” J. Biomed. Opt. 8, 517–524 (2003).
[CrossRef] [PubMed]

Franceschini, M. A.

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

Gelb, A.

R. Archibald, A. Gelb, “A method to reduce the Gibbs ringing artifact in MRI scans while keeping tissue boundary integrity,” IEEE Trans. Med. Imaging 21, 305–319 (2002).
[CrossRef] [PubMed]

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H. L. Graber, Y. Xu, Y. Pei, R. L. Barbour, “Qualitative and quantitative improvement of optical tomographic reconstructed images via spatial deconvolution: three-dimensional case,” Appl. Opt. 44, 941–953 (2005).
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T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

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V. E. Pera, E. L. Heffer, H. Siebold, O. Schütz, S. Heywang-Köbrunner, A. Götz, A. Heinig, S. Fantini, “Spatial second-derivative image processing: an application to optical mammography to enhance the detection of breast tumors,” J. Biomed. Opt. 8, 517–524 (2003).
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V. E. Pera, E. L. Heffer, H. Siebold, O. Schütz, S. Heywang-Köbrunner, A. Götz, A. Heinig, S. Fantini, “Spatial second-derivative image processing: an application to optical mammography to enhance the detection of breast tumors,” J. Biomed. Opt. 8, 517–524 (2003).
[CrossRef] [PubMed]

Henkelman, R. M.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

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V. E. Pera, E. L. Heffer, H. Siebold, O. Schütz, S. Heywang-Köbrunner, A. Götz, A. Heinig, S. Fantini, “Spatial second-derivative image processing: an application to optical mammography to enhance the detection of breast tumors,” J. Biomed. Opt. 8, 517–524 (2003).
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Hoge, R. D.

D. A. Boas, G. Strangman, J. P. Culver, R. D. Hoge, G. Jasdzewski, R. A. Poldrack, B. R. Rosen, J. B. Mandeville, “Can the cerebral metabolic rate of oxygen be estimated with near-infrared spectroscopy?” Phys. Med. Biol. 48, 2405–2418 (2003).
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J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
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J. P. Culver, V. Ntziachristos, M. J. Holboke, A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
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S. Colak, M. van der Mark, G. W.'t Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
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Hoogenraad, J.

S. Colak, M. van der Mark, G. W.'t Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
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H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
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D. A. Boas, G. Strangman, J. P. Culver, R. D. Hoge, G. Jasdzewski, R. A. Poldrack, B. R. Rosen, J. B. Mandeville, “Can the cerebral metabolic rate of oxygen be estimated with near-infrared spectroscopy?” Phys. Med. Biol. 48, 2405–2418 (2003).
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H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
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K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–702 (1995).
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Z. H. Cho, J. P. Jones, M. Singh, Foundation of Medical Imaging (Wiley, New York, 1993), p. 80.

Kaipio, J. P.

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

V. Kolehmainen, S. Prince, S. R. Arridge, J. P. Kaipio, “State-estimation approach to the nonstationary optical tomography problem,” J. Opt. Soc. Am. A 20, 876–889 (2003).
[CrossRef]

Klove, K.

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
[CrossRef]

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S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

V. Kolehmainen, S. Prince, S. R. Arridge, J. P. Kaipio, “State-estimation approach to the nonstationary optical tomography problem,” J. Opt. Soc. Am. A 20, 876–889 (2003).
[CrossRef]

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Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

Kuijpers, F.

S. Colak, M. van der Mark, G. W.'t Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Lauterbur, P. C.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Li, A.

Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

Lin, F.-B.

Liszka, H.

Loeffler, W.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Mandeville, J. B.

D. A. Boas, G. Strangman, J. P. Culver, R. D. Hoge, G. Jasdzewski, R. A. Poldrack, B. R. Rosen, J. B. Mandeville, “Can the cerebral metabolic rate of oxygen be estimated with near-infrared spectroscopy?” Phys. Med. Biol. 48, 2405–2418 (2003).
[CrossRef] [PubMed]

Markel, V. A.

V. A. Markel, J. C. Schotland, “Effects of sampling and limited data in optical tomography,” Appl. Phys. Lett. 81, 1180–1182 (2002).
[CrossRef]

McBride, T. O.

Moore, R. H.

Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

Natterer, F.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Nelson, S. J.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Ntziachristos, V.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

J. P. Culver, V. Ntziachristos, M. J. Holboke, A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
[CrossRef]

V. Ntziachristos, A. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after Indocyanine Green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).

Obrig, H.

H. Obrig, A. Villringer, “Beyond the visible—imaging the human brain with light,” J. Cereb. Blood Flow Metab. 23, 1–18 (2003).
[CrossRef]

Osterberg, U. L.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

B. W. Pogue, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270–286 (1999), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Österberg, U. L.

Osterman, K. S.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

Paulsen, K. D.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

B. W. Pogue, T. O. McBride, U. L. Osterberg, K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270–286 (1999), http://www.opticsexpress.org .
[CrossRef] [PubMed]

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

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–702 (1995).
[CrossRef] [PubMed]

Pechura, C. M.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Pei, Y.

Pera, V. E.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schütz, S. Heywang-Köbrunner, A. Götz, A. Heinig, S. Fantini, “Spatial second-derivative image processing: an application to optical mammography to enhance the detection of breast tumors,” J. Biomed. Opt. 8, 517–524 (2003).
[CrossRef] [PubMed]

Pogue, B. W.

Poldrack, R. A.

D. A. Boas, G. Strangman, J. P. Culver, R. D. Hoge, G. Jasdzewski, R. A. Poldrack, B. R. Rosen, J. B. Mandeville, “Can the cerebral metabolic rate of oxygen be estimated with near-infrared spectroscopy?” Phys. Med. Biol. 48, 2405–2418 (2003).
[CrossRef] [PubMed]

Poplack, S. P.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

Prewitt, J.

Prince, S.

V. Kolehmainen, S. Prince, S. R. Arridge, J. P. Kaipio, “State-estimation approach to the nonstationary optical tomography problem,” J. Opt. Soc. Am. A 20, 876–889 (2003).
[CrossRef]

S. Prince, V. Kolehmainen, J. P. Kaipio, M. A. Franceschini, D. Boas, S. R. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003).
[CrossRef] [PubMed]

Rafferty, T.

Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

Riemer, R. L.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Rosen, B. R.

D. A. Boas, G. Strangman, J. P. Culver, R. D. Hoge, G. Jasdzewski, R. A. Poldrack, B. R. Rosen, J. B. Mandeville, “Can the cerebral metabolic rate of oxygen be estimated with near-infrared spectroscopy?” Phys. Med. Biol. 48, 2405–2418 (2003).
[CrossRef] [PubMed]

Sassaroli, A.

Schmitz, C. H.

Schnall, M.

V. Ntziachristos, A. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after Indocyanine Green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).

Schotland, J. C.

V. A. Markel, J. C. Schotland, “Effects of sampling and limited data in optical tomography,” Appl. Phys. Lett. 81, 1180–1182 (2002).
[CrossRef]

Schütz, O.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schütz, S. Heywang-Köbrunner, A. Götz, A. Heinig, S. Fantini, “Spatial second-derivative image processing: an application to optical mammography to enhance the detection of breast tumors,” J. Biomed. Opt. 8, 517–524 (2003).
[CrossRef] [PubMed]

Shepp, L.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Shulman, R. G.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Siebold, H.

V. E. Pera, E. L. Heffer, H. Siebold, O. Schütz, S. Heywang-Köbrunner, A. Götz, A. Heinig, S. Fantini, “Spatial second-derivative image processing: an application to optical mammography to enhance the detection of breast tumors,” J. Biomed. Opt. 8, 517–524 (2003).
[CrossRef] [PubMed]

Singh, M.

Z. H. Cho, J. P. Jones, M. Singh, Foundation of Medical Imaging (Wiley, New York, 1993), p. 80.

Slemp, A.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef] [PubMed]

Stott, J. J.

Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

Strangman, G.

D. A. Boas, G. Strangman, J. P. Culver, R. D. Hoge, G. Jasdzewski, R. A. Poldrack, B. R. Rosen, J. B. Mandeville, “Can the cerebral metabolic rate of oxygen be estimated with near-infrared spectroscopy?” Phys. Med. Biol. 48, 2405–2418 (2003).
[CrossRef] [PubMed]

Suzuki, S.

Tsui, B. M. W.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

van der Linden, E.

S. Colak, M. van der Mark, G. W.'t Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

van der Mark, M.

S. Colak, M. van der Mark, G. W.'t Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143–1158 (1999).
[CrossRef]

Villringer, A.

H. Obrig, A. Villringer, “Beyond the visible—imaging the human brain with light,” J. Cereb. Blood Flow Metab. 23, 1–18 (2003).
[CrossRef]

Wehrli, F.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Weidman, S. T.

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

Wells, W. A.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).
[CrossRef] [PubMed]

Wu, T.

Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

Xu, Y.

H. L. Graber, Y. Xu, Y. Pei, R. L. Barbour, “Qualitative and quantitative improvement of optical tomographic reconstructed images via spatial deconvolution: three-dimensional case,” Appl. Opt. 44, 941–953 (2005).
[CrossRef] [PubMed]

R. L. Barbour, H. L. Graber, Y. Xu, Y. Pei, R. Aronson, “Strategies for imaging diffusing media,” Transp. Theory Stat. Phys. 33, 361–371 (2004).
[CrossRef]

H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Baron, L. Fajardo, “Three-dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
[CrossRef]

Yamaguchi, S.

Yodh, A.

V. Ntziachristos, A. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after Indocyanine Green enhancement,” Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000).

Yodh, A. G.

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Zubkov, L.

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Other (6)

T. Budinger, F. Wehrli, S. M. Blumenfeld, F. A. Grunbaum, R. M. Henkelman, P. C. Lauterbur, W. Loeffler, F. Natterer, S. J. Nelson, L. Shepp, R. G. Shulman, B. M. W. Tsui, S. T. Weidman, R. L. Riemer, C. M. Pechura, Mathematics and Physics of Emerging Biomedical Imaging (National Academy Press, Washington, D.C., 1996), p. 138.

It is recognized that techniques for experimental estimation of the bulk or background properties of target media will not yield perfectly accurate results. Consequently, a full characterization of the spatial deconvolution method will require consideration of cases in which the properties of the media used for the computations of I and I0 differ. For reasons of space limitations, the influence of disparities between the media on the accuracy of the deconvolved image is deferred to future publications in this series.

When images are reconstructed from experimental or clinical data, typically there is an appreciable difference between I0and Ir. But as shown in Ref. 18, the normalized-difference method is highly robust to disparities between the media that yield these measurement vectors. Then it is expected that introducing a difference between I0 and Ir will not affect the performance of the spatial deconvolution algorithm. Direct tests of this hypothesis will be another subject presented in future publications.

Z. H. Cho, J. P. Jones, M. Singh, Foundation of Medical Imaging (Wiley, New York, 1993), p. 80.

C. M. Bishop, Neural Networks for Pattern Recognition (Oxford U. Press, Oxford, UK, 1995).

Q. Zhang, J. J. Stott, T. J. Brukilacchio, A. Li, T. Chaves, G. Boverman, T. Wu, M. Chorlton, T. Rafferty, R. H. Moore, D. B. Kopans, D. A. Boas, “Preliminary study of the breast's bulk optical properties using a co-registered tomographic x-ray and optical breast imaging system,” presented at OSA Biomedical Topical Meetings and Tabletop Exhibit, Miami Beach, Fla., 14–17 April 2004.

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Figures (18)

Fig. 1
Fig. 1

Schematic illustration of the process of assigning a unique temporal modulation to the absorption or scattering coefficient of each medium pixel. The functional form shown is a set of sinusoids with incommensurate frequencies. For presentation purposes they are drawn as if in phase at time t = 0, but in practice a random initial phase shift is assigned to each one.

Fig. 2
Fig. 2

Medium geometries and S–D configurations used for forward-problem computations, in the filter-generating and filter-testing phases of the reported studies: (a) circular disk, full tomographic measurement (256-channel S–D configuration shown); (b) circular disk, limited-view (backscattering) measurement; (c) rectangular medium, limited-view (backscattering) measurement; (d) rectangular medium, limited-view (transmission) measurement. Indicated S–D locations are only suggestive; see Table 2 for exact numbers and patterning.

Fig. 3
Fig. 3

Study 1: definitions of spatial resolution and of inclusion center coordinates for reconstructed images. (a) Point-like inclusion located at (20, 0) mm; (b) image before deconvolution; (c) image after deconvolution; (d) 1D recovered μa distribution along y = 0 before (dashed curve) and after (solid) deconvolution; (e) μa distribution along x = 20 mm. Gray-scale [(a)–(c)] and ordinate axis [(d), (e)] values are 1000 × μa.

Fig. 4
Fig. 4

Study 1: position dependence of spatial resolution and absolute location error of recovered images. (a) Image resolution, in which curves with + and □ markers are the FWHMX and FWHMY, respectively, before deconvolution, and curves with * and ○ symbols are the FWHMX and FWHMY, respectively, after deconvolution; (b) inclusion's absolute location error EX before (+) and after (*) deconvolution; (c) absolute location error EY before (□) and after (○) deconvolution. The mesh and S–D geometry are the same as in Fig. 3.

Fig. 5
Fig. 5

Study 1: resolution and absolute location error of recovered inclusion for three different meshes. (a) FWHMX; (b) FWHMY; (c) EX; (d) EY. All results shown are for deconvolved images; *, ○, and □ labels denote results for 717-, 1019-, and 1610-node meshes, respectively. The same medium and S–D geometry used in Fig. 3 were also used here.

Fig. 6
Fig. 6

Study 2: FWHMs for finite-diameter inclusions. (a) FWHMX versus true diameter and (b) FWHMY versus true diameter. Results shown are for corrected images; curves with □ and ○ symbols are the results for inclusion centered at (30, 0) mm and at (10, 0) mm, respectively; solid lines are ideal results. The same mesh and S–D geometry used in Fig. 3 were also used here.

Fig. 7
Fig. 7

Study 3: deconvolved images for two FEM meshes and three different interinclusion separation distances. (a) 717-node mesh, 10-mm center-to-center separation; (b) 1019 nodes, 10 mm; (c) 717 nodes, 14 mm; (d) 1019 nodes, 14 mm; (e) 717 nodes, 20 mm; (f) 1019 nodes, 20 mm. All inclusions have 6-mm diameter and μ a incl / μ a bkgr = 2. Gray-scale values are 1000 × μa.

Fig. 8
Fig. 8

Study 4: images for different numbers of S–D channels, Nc. (a)–(c) Corrected images for Nc = 256, 768, and 1024, respectively. (d) Uncorrected image, Nc = 1024. Inclusion center-to-center distance is 20 mm. A 717-node mesh was used for all reconstructions. The inclusion diameter, absorption contrast, and FEM mesh are the same as in study 3 (Fig. 7). Gray-scale values are 1000 × μa.

Fig. 9
Fig. 9

Study 5: images for different inclusion depths. (a), (b) Images before and after deconvolution, with inclusions at y = 0. (c), (d) Inclusions at y = 15 mm. (e), (f) Inclusions at y = 25 mm. Inclusion diameter, absorption contrast, and FEM mesh are the same as in study 4 (Fig. 8), and the center-to-center distance is 14 mm. Gray-scale values are 1000 × μa.

Fig. 10
Fig. 10

Study 6: images and 1D μa distributions for different inclusion contrasts. (a) Uncorrected image, μ a incl / μ a bkgr = 1.5. (b)–(d) Corrected images, μ a incl / μ a bkgr = 1.5, 2, and 3, respectively. (e)–(g) μa distributions along y = 15 mm, μ a incl / μ a bkgr = 1.5, 2, and 3, respectively. The solid curve is ideal values; dotted and dashed curves are sections through the uncorrected and corrected images, respectively. Each inclusion diameter is 10 mm; inclusions are located at y = 15 mm, with center-to-center distance of 20 mm. The FEM mesh is the same as in study 5 (Fig. 9). Gray-scale [(a)–(d)] and ordinate axis [(e)–(g)] values are 1000 × μa.

Fig. 11
Fig. 11

Study 7: application of a filter generated for a medium with one set of optical coefficients to target media with different background properties. The filter-generating medium had μa = 0.002 mm−1 and μs = 1.0 mm−1. For the 56 test media, the background μa and μs ranges were 0.0005–0.02 and 0.3-3.0 mm−1, respectively. Also shown is the uncorrected image for the target medium with μa = 0.002 mm−1 and μs = 1.0 mm−1; the remaining 55 are qualitatively similar. In every case μs was spatially homogeneous and μ a incl / μ a bkgr = 2.

Fig. 12
Fig. 12

Study 8: images and 1D sections for a 20-mm-diameter inclusion with and without multiplicative noise in detector data. (a), (b) Uncorrected and corrected images from noise-free data. (c), (d) Images from noisy data. (e), (f) 1D sections along y = 0 for noise-free and noisy cases, respectively. Solid curves are ideal profiles; dotted and dashed curves are uncorrected and corrected results, respectively. The inclusion is centered at (15, 0) mm, μ a incl / μ a bkgr = 2. The reconstruction mesh had 1019 nodes. Gray-scale [(a)–(d)] and ordinate axis [(e), (f)] values are 1000 × μa.

Fig. 13
Fig. 13

Study 9: images and corresponding 1D sections with a two-inclusion target medium for different inclusion-background contrasts and the limited-view S–D configurations shown in Fig. 2(b). (a) Uncorrected image, μ a incl / μ a bkgr = 1.2. (b)–(e) Deconvolved images, μ a incl / μ a bkgr = 1.2, 2, 4, and 8, respectively. (f) 1D sections along x = 0 through images in (b)–(e), for μ a incl / μ a bkgr = 1.2 (dotted curve), 2 (dashed–dotted curve), 4 (dashed curve), and 8 (solid curve). The 6-mm-diameter inclusions are located at (0, 15) and (0, 15). The reconstruction mesh had 717 nodes. Gray-scale [(a)–(e)] and ordinate axis [(f)] values are 1000 × μa.

Fig. 14
Fig. 14

Study 10: images produced by spatial deconvolution and by a LM method, for the limited-view S–D configurations shown in Fig. 2(b). (a)–(d) One-inclusion target, uncorrected image, deconvolved image, and image produced by 50 LM iterations, respectively. (e)–(h) The same as in (a)–(d), but for a two-inclusion target. The inclusion diameter and FEM mesh are the same as in study 9 (Fig. 13), and μ a incl / μ a bkgr = 2. Gray-scale values are 1000 × μa.

Fig. 15
Fig. 15

Study 11: images of rectangular target media, using the limited view (backreflection) S–D configurations shown in Fig. 2(c). (a)–(c) Target with inclusion located at (0, 20) mm, the uncorrected image, and the deconvolved image, respectively. (d)–(f) Target with inclusion at (0, −10) mm, the uncorrected image, and the deconvolved image, respectively. The inclusion area is 10 × 10 mm, μ a incl / μ a bkgr = 2. The reconstruction mesh had 1025 nodes. Gray-scale values are 1000 × μa.

Fig. 16
Fig. 16

Study 11: 1D sections through images in Fig. 15, for four inclusion locations. (a) Section along the line y = 20 mm, inclusion centered at (0, 20) mm; (b) x = 0, (0, 20) mm; (c) y = 10, (0, 10) mm; (d) x = 0, (0, 10) mm; (e) y = 0, (0, 0) mm; (f) x = 0, (0, 0); (g) y = −10, (0, −10) mm; (h) x = 0, (0, −10) mm. The solid curve is ideal values; dotted and dashed curves are sections through the uncorrected and corrected images, respectively. Ordinate axis values are 1000 × μa.

Fig. 17
Fig. 17

Study 12: images of rectangular target media, using the limited-view (transmission) S–D configuration shown in Fig. 2(d). (a) Target with one point-like inclusion located at (0, 0). (b) Uncorrected image, Nc = 81. (c)–(e) Deconvolved images, Nc = 81, 289, and 1089, respectively. The FEM mesh is the same as that in study 11 (Fig. 15). Gray-scale values are 1000 × μa.

Fig. 18
Fig. 18

Study 12: 1D sections through images shown in Fig. 17. (a), (b) Distributions along y = 0 and x = 0, Nc = 81. (c), (d) Nc = 289. (e), (f) Nc = 1089. Dashed and solid curves are sections through the uncorrected and corrected images, respectively. Ordinate axis values are 1000 ×μa.

Tables (5)

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Table 1 Control Parameters Considered in the Reported Simulation Experiments

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Table 2 Properties of Media and S–D Configurations for Which Deconvolution Operators Were Computeda

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Table 3 Properties of Inclusions Used in Deconvolution Procedure Characterization Simulations

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Table 4 Quantitative Accuracy Indices for Study 7 (Systematic Error Study)

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Table 5 Accuracy of Recovered Inclusion Properties for Study 8 and Ref. 12

Equations (10)

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

F = YX T W + T ( W + XX T W + T ) 1 ,
= [ YX T W + T ( W + XX T W + T ) 1 W + W ] z ,
· [ D ( r ) ϕ ( r ) ] μ a ( r ) ϕ ( r ) = δ ( r r s ) , r Λ ,
δ x = W r T ( W r W r T + λ I ) 1 δ I r ,
δ x = ( W r T W r + λ I ) 1 W r T δ I r ,
( δ I r ) i = ( I I 0 ) i ( I 0 ) i ( I r ) i .
r s = i = 1 N p ( μ a , img i μ ¯ a , img ) ( μ a , tgt i μ ¯ a , tgt ) [ i = 1 N p ( μ a , img i μ ¯ a , img ) 2 · i = 1 N p ( μ a , tgt i μ ¯ a , tgt ) 2 ] 1 / 2 ,
ε = [ 1 N p i = 1 N p ( μ a , img i μ a , tgt i ) 2 ] 1 / 2 ,
F = YX T ( XX T ) 1 ,
= [ YX T ( XX T ) 1 ] v .

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