Abstract

Diffuse tomography with near-infrared light has biomedical application for imaging hemoglobin, water, lipids, cytochromes, or exogenous contrast agents and is being investigated for breast cancer diagnosis. A Newton–Raphson inversion algorithm is used for image reconstruction of tissue optical absorption and transport scattering coefficients from frequency-domain measurements of modulated phase shift and light intensity. A variant of Tikhonov regularization is examined in which radial variation is allowed in the value of the regularization parameter. This method minimizes high-frequency noise in the reconstructed image near the source–detector locations and can produce constant image resolution and contrast across the image field.

© 1999 Optical Society of America

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    [CrossRef] [PubMed]
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1998 (3)

A. Neumaier, “Solving ill-conditioned and singular linear systems: a tutorial on regularization,” SIAM Rev. 40, 636–666 (1998).
[CrossRef]

H.-S. Wong, L. Guan, “Adaptive regularization in image restoration by unsupervised learning,” J. Electr. Imag. 7, 211–221 (1998).
[CrossRef]

W. Freeden, F. Schneider, “Regularization wavelets and multiresolution,” Inverse Probl. 14, 225–243 (1998).
[CrossRef]

1997 (9)

B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction for breast imaging: initial evaluation in multi-target tissue-like phantoms,” Med. Phys. 25, 183–193 (1997).
[CrossRef]

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[CrossRef]

B. Chance, Q. Luo, S. Nioka, D. C. Alsop, J. A. Detre, “Optical investigations of physiology: a study of intrinsic and extrinsic biomedical contrast,” Phil. Trans. R. Soc. Lond. B 352, 707–716 (1997).
[CrossRef]

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

L. W. Lo, W. T. Jenkins, S. A. Vinogradov, S. M. Evans, D. F. Wilson, “Oxygen distribution in the vasculature of mouse tissue in vivo measured using a near-infrared phosphor,” Adv. Exp. Med. Biol. 411, 577–583 (1997).
[CrossRef]

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

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

H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction in turbid media: an experimental study of single-target detectability,” Appl. Opt. 36, 52–63 (1997).
[CrossRef] [PubMed]

1996 (2)

1995 (2)

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

K. D. Paulsen, H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef] [PubMed]

1994 (2)

M. M. Nioka, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” Adv. Exp. Med. Biol. 361, 171–179 (1994).
[CrossRef] [PubMed]

H. W. Engl, W. Grever, “Using the L-curve for determining optimal regularization parameters,” Numer. Math. 69, 25–31 (1994).
[CrossRef]

1992 (1)

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

1991 (2)

H. Miyake, S. Nioka, A. Zaman, D. S. Smith, B. Chance, “The detection of cytochrome oxidase heme iron and copper absorption in the blood-perfused and blood-free brain in normoxia and hypoxia,” Anal. Biochem. 192, 149–155 (1991).
[CrossRef] [PubMed]

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

1990 (2)

J. R. Singer, F. A. Grunbaum, P. D. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1990).
[CrossRef]

1989 (3)

1988 (1)

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “Light dosimetry in optical phantoms and in tissues. I. Multiple flux and transport theory,” Phys. Med. Biol. 33, 437–454 (1988).
[CrossRef] [PubMed]

Alsop, D. C.

B. Chance, Q. Luo, S. Nioka, D. C. Alsop, J. A. Detre, “Optical investigations of physiology: a study of intrinsic and extrinsic biomedical contrast,” Phil. Trans. R. Soc. Lond. B 352, 707–716 (1997).
[CrossRef]

Anderson, E. R.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[CrossRef]

Arridge, S. R.

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

S. R. Arridge, M. Schweiger, “Inverse methods for optical tomography,” in Information Processing in Medical Imaging, Thirteenth Information Processing and Medical Imaging Conference (Springer-Verlag, Flagstaff, Ariz., 1993), pp. 259–277.
[CrossRef]

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

Barbour, R. L.

Berndt, K. W.

Butler, J.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[CrossRef]

Cahn, M.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[CrossRef]

Chance, B.

B. Chance, Q. Luo, S. Nioka, D. C. Alsop, J. A. Detre, “Optical investigations of physiology: a study of intrinsic and extrinsic biomedical contrast,” Phil. Trans. R. Soc. Lond. B 352, 707–716 (1997).
[CrossRef]

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

M. M. Nioka, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” Adv. Exp. Med. Biol. 361, 171–179 (1994).
[CrossRef] [PubMed]

H. Miyake, S. Nioka, A. Zaman, D. S. Smith, B. Chance, “The detection of cytochrome oxidase heme iron and copper absorption in the blood-perfused and blood-free brain in normoxia and hypoxia,” Anal. Biochem. 192, 149–155 (1991).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

Chang, J.

Cope, M.

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

Coquoz, O.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[CrossRef]

Delpy, D. T.

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

Detre, J. A.

B. Chance, Q. Luo, S. Nioka, D. C. Alsop, J. A. Detre, “Optical investigations of physiology: a study of intrinsic and extrinsic biomedical contrast,” Phil. Trans. R. Soc. Lond. B 352, 707–716 (1997).
[CrossRef]

Engl, H. W.

H. W. Engl, W. Grever, “Using the L-curve for determining optimal regularization parameters,” Numer. Math. 69, 25–31 (1994).
[CrossRef]

Evans, S. M.

L. W. Lo, W. T. Jenkins, S. A. Vinogradov, S. M. Evans, D. F. Wilson, “Oxygen distribution in the vasculature of mouse tissue in vivo measured using a near-infrared phosphor,” Adv. Exp. Med. Biol. 411, 577–583 (1997).
[CrossRef]

Farrell, T. J.

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

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” 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, 328–339 (1995).
[CrossRef]

Fishkin, J.

J. Fishkin, E. Gratton, M. J. van de Ven, W. W. Mantulin, “Diffusion of intensity modulated near infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

Fishkin, J. B.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[CrossRef]

Freeden, W.

W. Freeden, F. Schneider, “Regularization wavelets and multiresolution,” Inverse Probl. 14, 225–243 (1998).
[CrossRef]

Gerety, E.

T. O. McBride, B. W. Pogue, E. Gerety, S. Poplack, U. L. Osterberg, K. D. Paulsen, “Spectroscopic diffuse optical tomography for quantitatively assessing hemoglobin concentration and oxygen saturation in tissue,” (submitted to Appl. Opt.).

Graber, H. L.

Gratton, E.

J. Fishkin, E. Gratton, M. J. van de Ven, W. W. Mantulin, “Diffusion of intensity modulated near infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

Grever, W.

H. W. Engl, W. Grever, “Using the L-curve for determining optimal regularization parameters,” Numer. Math. 69, 25–31 (1994).
[CrossRef]

Gross, J. D.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[CrossRef]

Grunbaum, F. A.

J. R. Singer, F. A. Grunbaum, P. D. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

Guan, L.

H.-S. Wong, L. Guan, “Adaptive regularization in image restoration by unsupervised learning,” J. Electr. Imag. 7, 211–221 (1998).
[CrossRef]

Haida, M.

M. M. Nioka, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” Adv. Exp. Med. Biol. 361, 171–179 (1994).
[CrossRef] [PubMed]

Ishimaru, A.

Jenkins, W. T.

L. W. Lo, W. T. Jenkins, S. A. Vinogradov, S. M. Evans, D. F. Wilson, “Oxygen distribution in the vasculature of mouse tissue in vivo measured using a near-infrared phosphor,” Adv. Exp. Med. Biol. 411, 577–583 (1997).
[CrossRef]

Jiang, H.

H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction in turbid media: an experimental study of single-target detectability,” Appl. Opt. 36, 52–63 (1997).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction for breast imaging: initial evaluation in multi-target tissue-like phantoms,” Med. Phys. 25, 183–193 (1997).
[CrossRef]

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]

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

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

K. D. Paulsen, H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef] [PubMed]

Kohn, P. D.

J. R. Singer, F. A. Grunbaum, P. D. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

Lakowicz, J. R.

Lo, L. W.

L. W. Lo, W. T. Jenkins, S. A. Vinogradov, S. M. Evans, D. F. Wilson, “Oxygen distribution in the vasculature of mouse tissue in vivo measured using a near-infrared phosphor,” Adv. Exp. Med. Biol. 411, 577–583 (1997).
[CrossRef]

Luo, Q.

B. Chance, Q. Luo, S. Nioka, D. C. Alsop, J. A. Detre, “Optical investigations of physiology: a study of intrinsic and extrinsic biomedical contrast,” Phil. Trans. R. Soc. Lond. B 352, 707–716 (1997).
[CrossRef]

Mantulin, W. W.

J. Fishkin, E. Gratton, M. J. van de Ven, W. W. Mantulin, “Diffusion of intensity modulated near infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

Marijnissen, J. P. A.

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “Light dosimetry in optical phantoms and in tissues. I. Multiple flux and transport theory,” Phys. Med. Biol. 33, 437–454 (1988).
[CrossRef] [PubMed]

McBride, T.

B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

McBride, T. O.

T. O. McBride, B. W. Pogue, E. Gerety, S. Poplack, U. L. Osterberg, K. D. Paulsen, “Spectroscopic diffuse optical tomography for quantitatively assessing hemoglobin concentration and oxygen saturation in tissue,” (submitted to Appl. Opt.).

Miyake, H.

H. Miyake, S. Nioka, A. Zaman, D. S. Smith, B. Chance, “The detection of cytochrome oxidase heme iron and copper absorption in the blood-perfused and blood-free brain in normoxia and hypoxia,” Anal. Biochem. 192, 149–155 (1991).
[CrossRef] [PubMed]

Moulton, J. D.

Navarro, G. A.

A. E. Profio, G. A. Navarro, “Scientific basis of breast diaphanography,” Med. Phys. 16, 60–65 (1989).
[CrossRef] [PubMed]

Neumaier, A.

A. Neumaier, “Solving ill-conditioned and singular linear systems: a tutorial on regularization,” SIAM Rev. 40, 636–666 (1998).
[CrossRef]

Nioka, M. M.

M. M. Nioka, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” Adv. Exp. Med. Biol. 361, 171–179 (1994).
[CrossRef] [PubMed]

Nioka, S.

B. Chance, Q. Luo, S. Nioka, D. C. Alsop, J. A. Detre, “Optical investigations of physiology: a study of intrinsic and extrinsic biomedical contrast,” Phil. Trans. R. Soc. Lond. B 352, 707–716 (1997).
[CrossRef]

H. Miyake, S. Nioka, A. Zaman, D. S. Smith, B. Chance, “The detection of cytochrome oxidase heme iron and copper absorption in the blood-perfused and blood-free brain in normoxia and hypoxia,” Anal. Biochem. 192, 149–155 (1991).
[CrossRef] [PubMed]

Orel, S.

M. M. Nioka, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” Adv. Exp. Med. Biol. 361, 171–179 (1994).
[CrossRef] [PubMed]

Osterberg, U.

B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

Osterberg, U. L.

H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction for breast imaging: initial evaluation in multi-target tissue-like phantoms,” Med. Phys. 25, 183–193 (1997).
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction in turbid media: an experimental study of single-target detectability,” Appl. Opt. 36, 52–63 (1997).
[CrossRef] [PubMed]

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

T. O. McBride, B. W. Pogue, E. Gerety, S. Poplack, U. L. Osterberg, K. D. Paulsen, “Spectroscopic diffuse optical tomography for quantitatively assessing hemoglobin concentration and oxygen saturation in tissue,” (submitted to Appl. Opt.).

Patterson, M. S.

H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction in turbid media: an experimental study of single-target detectability,” Appl. Opt. 36, 52–63 (1997).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction for breast imaging: initial evaluation in multi-target tissue-like phantoms,” Med. Phys. 25, 183–193 (1997).
[CrossRef]

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

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

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

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1990).
[CrossRef]

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” 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, 328–339 (1995).
[CrossRef]

Paulsen, K.

B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

Paulsen, K. D.

H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction for breast imaging: initial evaluation in multi-target tissue-like phantoms,” Med. Phys. 25, 183–193 (1997).
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction in turbid media: an experimental study of single-target detectability,” Appl. Opt. 36, 52–63 (1997).
[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]

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

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

K. D. Paulsen, H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef] [PubMed]

T. O. McBride, B. W. Pogue, E. Gerety, S. Poplack, U. L. Osterberg, K. D. Paulsen, “Spectroscopic diffuse optical tomography for quantitatively assessing hemoglobin concentration and oxygen saturation in tissue,” (submitted to Appl. Opt.).

Pham, D.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[CrossRef]

Pham, T.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[CrossRef]

Pogue, B. W.

B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

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

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

T. O. McBride, B. W. Pogue, E. Gerety, S. Poplack, U. L. Osterberg, K. D. Paulsen, “Spectroscopic diffuse optical tomography for quantitatively assessing hemoglobin concentration and oxygen saturation in tissue,” (submitted to Appl. Opt.).

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” 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, 328–339 (1995).
[CrossRef]

Poplack, S.

T. O. McBride, B. W. Pogue, E. Gerety, S. Poplack, U. L. Osterberg, K. D. Paulsen, “Spectroscopic diffuse optical tomography for quantitatively assessing hemoglobin concentration and oxygen saturation in tissue,” (submitted to Appl. Opt.).

Profio, A. E.

A. E. Profio, G. A. Navarro, “Scientific basis of breast diaphanography,” Med. Phys. 16, 60–65 (1989).
[CrossRef] [PubMed]

Schneider, F.

W. Freeden, F. Schneider, “Regularization wavelets and multiresolution,” Inverse Probl. 14, 225–243 (1998).
[CrossRef]

Schweiger, M.

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

S. R. Arridge, M. Schweiger, “Inverse methods for optical tomography,” in Information Processing in Medical Imaging, Thirteenth Information Processing and Medical Imaging Conference (Springer-Verlag, Flagstaff, Ariz., 1993), pp. 259–277.
[CrossRef]

Shnall, M.

M. M. Nioka, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” Adv. Exp. Med. Biol. 361, 171–179 (1994).
[CrossRef] [PubMed]

Singer, J. R.

J. R. Singer, F. A. Grunbaum, P. D. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

Smith, D. S.

H. Miyake, S. Nioka, A. Zaman, D. S. Smith, B. Chance, “The detection of cytochrome oxidase heme iron and copper absorption in the blood-perfused and blood-free brain in normoxia and hypoxia,” Anal. Biochem. 192, 149–155 (1991).
[CrossRef] [PubMed]

Star, W. M.

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “Light dosimetry in optical phantoms and in tissues. I. Multiple flux and transport theory,” Phys. Med. Biol. 33, 437–454 (1988).
[CrossRef] [PubMed]

Testorf, M.

B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

Tromberg, B. J.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[CrossRef]

van de Ven, M. J.

J. Fishkin, E. Gratton, M. J. van de Ven, W. W. Mantulin, “Diffusion of intensity modulated near infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

van der Zee, P.

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

van Gemert, M. J. C.

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “Light dosimetry in optical phantoms and in tissues. I. Multiple flux and transport theory,” Phys. Med. Biol. 33, 437–454 (1988).
[CrossRef] [PubMed]

Venugopalan, V.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[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]

Vinogradov, S. A.

L. W. Lo, W. T. Jenkins, S. A. Vinogradov, S. M. Evans, D. F. Wilson, “Oxygen distribution in the vasculature of mouse tissue in vivo measured using a near-infrared phosphor,” Adv. Exp. Med. Biol. 411, 577–583 (1997).
[CrossRef]

Wilson, B. C.

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

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[CrossRef] [PubMed]

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1990).
[CrossRef]

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

Wilson, D. F.

L. W. Lo, W. T. Jenkins, S. A. Vinogradov, S. M. Evans, D. F. Wilson, “Oxygen distribution in the vasculature of mouse tissue in vivo measured using a near-infrared phosphor,” Adv. Exp. Med. Biol. 411, 577–583 (1997).
[CrossRef]

Wong, H.-S.

H.-S. Wong, L. Guan, “Adaptive regularization in image restoration by unsupervised learning,” J. Electr. Imag. 7, 211–221 (1998).
[CrossRef]

Wyman, D. R.

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1990).
[CrossRef]

Zaman, A.

H. Miyake, S. Nioka, A. Zaman, D. S. Smith, B. Chance, “The detection of cytochrome oxidase heme iron and copper absorption in the blood-perfused and blood-free brain in normoxia and hypoxia,” Anal. Biochem. 192, 149–155 (1991).
[CrossRef] [PubMed]

Zhao, S.

M. M. Nioka, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” Adv. Exp. Med. Biol. 361, 171–179 (1994).
[CrossRef] [PubMed]

Zubelli, J. P.

J. R. Singer, F. A. Grunbaum, P. D. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

Adv. Exp. Med. Biol. (2)

M. M. Nioka, S. Orel, M. Shnall, M. Haida, S. Zhao, B. Chance, “Optical imaging of human breast cancer,” Adv. Exp. Med. Biol. 361, 171–179 (1994).
[CrossRef] [PubMed]

L. W. Lo, W. T. Jenkins, S. A. Vinogradov, S. M. Evans, D. F. Wilson, “Oxygen distribution in the vasculature of mouse tissue in vivo measured using a near-infrared phosphor,” Adv. Exp. Med. Biol. 411, 577–583 (1997).
[CrossRef]

Anal. Biochem. (1)

H. Miyake, S. Nioka, A. Zaman, D. S. Smith, B. Chance, “The detection of cytochrome oxidase heme iron and copper absorption in the blood-perfused and blood-free brain in normoxia and hypoxia,” Anal. Biochem. 192, 149–155 (1991).
[CrossRef] [PubMed]

Appl. Opt. (5)

Inverse Probl. (1)

W. Freeden, F. Schneider, “Regularization wavelets and multiresolution,” Inverse Probl. 14, 225–243 (1998).
[CrossRef]

J. Electr. Imag. (1)

H.-S. Wong, L. Guan, “Adaptive regularization in image restoration by unsupervised learning,” J. Electr. Imag. 7, 211–221 (1998).
[CrossRef]

J. Opt. Soc. Am. A (2)

Lasers Med. Sci. (1)

M. S. Patterson, B. C. Wilson, D. R. Wyman, “The propagation of optical radiation in tissue. I. Models of radiation transport and their application,” Lasers Med. Sci. 6, 155–168 (1990).
[CrossRef]

Med. Phys. (4)

H. Jiang, K. D. Paulsen, U. L. Osterberg, M. S. Patterson, “Frequency-domain optical image reconstruction for breast imaging: initial evaluation in multi-target tissue-like phantoms,” Med. Phys. 25, 183–193 (1997).
[CrossRef]

A. E. Profio, G. A. Navarro, “Scientific basis of breast diaphanography,” Med. Phys. 16, 60–65 (1989).
[CrossRef] [PubMed]

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

K. D. Paulsen, H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef] [PubMed]

Numer. Math. (1)

H. W. Engl, W. Grever, “Using the L-curve for determining optimal regularization parameters,” Numer. Math. 69, 25–31 (1994).
[CrossRef]

Opt. Exp. (1)

B. W. Pogue, M. Testorf, T. McBride, U. Osterberg, K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Exp. 1, 391–403 (1997).
[CrossRef]

Phil. Trans. R. Soc. Lond. B (3)

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. D. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Phil. Trans. R. Soc. Lond. B 352, 661–668 (1997).
[CrossRef]

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

B. Chance, Q. Luo, S. Nioka, D. C. Alsop, J. A. Detre, “Optical investigations of physiology: a study of intrinsic and extrinsic biomedical contrast,” Phil. Trans. R. Soc. Lond. B 352, 707–716 (1997).
[CrossRef]

Phys. Med. Biol. (2)

W. M. Star, J. P. A. Marijnissen, M. J. C. van Gemert, “Light dosimetry in optical phantoms and in tissues. I. Multiple flux and transport theory,” Phys. Med. Biol. 33, 437–454 (1988).
[CrossRef] [PubMed]

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

Science (1)

J. R. Singer, F. A. Grunbaum, P. D. Kohn, J. P. Zubelli, “Image reconstruction of the interior of bodies that diffuse radiation,” Science 248, 990–993 (1990).
[CrossRef] [PubMed]

SIAM Rev. (1)

A. Neumaier, “Solving ill-conditioned and singular linear systems: a tutorial on regularization,” SIAM Rev. 40, 636–666 (1998).
[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 (6)

T. O. McBride, B. W. Pogue, E. Gerety, S. Poplack, U. L. Osterberg, K. D. Paulsen, “Spectroscopic diffuse optical tomography for quantitatively assessing hemoglobin concentration and oxygen saturation in tissue,” (submitted to Appl. Opt.).

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

J. Fishkin, E. Gratton, M. J. van de Ven, W. W. Mantulin, “Diffusion of intensity modulated near infrared light in turbid media,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 122–135 (1991).
[CrossRef]

B. W. Pogue, M. S. Patterson, T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” 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, 328–339 (1995).
[CrossRef]

S. R. Arridge, M. Schweiger, “Inverse methods for optical tomography,” in Information Processing in Medical Imaging, Thirteenth Information Processing and Medical Imaging Conference (Springer-Verlag, Flagstaff, Ariz., 1993), pp. 259–277.
[CrossRef]

M. M. Ter-Pogossian, M. E. Phelps, G. L. Brownell, J. R. Cox, D. O. Davis, R. G. Evens, eds., Reconstruction Tomography in Diagnostic Radiology and Nuclear Medicine (University Park Press, Baltimore, 1977).

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Figures (9)

Fig. 1
Fig. 1

Schematic of imaging geometry (left), including the laser source and the photomultiplier tube, along with the fiber optics used to multiplex these into all 16 × 16 locations, for 256 measurements of transmission through the tissue. An image of the tissue contact device is shown (right) where the fibers are held in an array that allows variation of the circular diameter between 5 and 10 cm.

Fig. 2
Fig. 2

Two test objects (A) and (E) were generated and used with 1% noise added to the observed projections with the first test object (A) having a localized absorber in the center of the image, and the second test object (E) having the same absorber on the edge. Image reconstructions for both objects are shown to the right; the three images for each target location use decreasing values of the regularization parameter λ. For (B), (C), and (D), the regularization parameters were 100, 10, and 1 respectively, and for (F), (G), and (H) the regularization parameters were 100, 10 and 1, respectively. Note that the scale bars for the first test object (A) and for the second test object (E) do not show the full height of the targets since they are effectively infinitely absorbing. Scale bars are in units of absorption coefficient, inverse millimeters.

Fig. 3
Fig. 3

(A) Profiles of the central horizontal line through the images in Figs. 2(B)2(D). (B) Profiles of the central horizontal line through the images in Figs. 2(F)2(H). In both graphs, the true size of the target simulated is also shown (small dashed curve).

Fig. 4
Fig. 4

(A) Test object with three point absorbers, which was used to simulate data with 1% noise added. (B), (C), (D) Reconstructions of this object for which the scalar regularization parameter was used with regularization parameters λ = 3 × 104, 3 × 103, and 3 × 102, respectively. (E)–(H) Reconstructions of the object with radial variation in the regularization parameter where λ e = 104 on the radial edge of the image, with decreasing levels of regularization at the center. The regularization parameter at a radius of zero, for images (E), (F), (G), and (H) was λ c = 3000, 1000, 300, and 100, respectively. In each image, the regularization was varied exponentially according to Eq. (8). Scale bars are in units of absorption coefficient, inverse millimeters.

Fig. 5
Fig. 5

(A) Line profiles through the center of the images in Figs. 4(B)4(D) show the locations of the two targets within the reconstructed images. (B) Line profiles through the center of images in Figs. 4(E)4(H) show the absorption coefficient values of the two reconstructed targets. The real size of each absorber was 1 cm in diameter, with μ a = 0.015 mm-1.

Fig. 6
Fig. 6

(A) Test object simulated with 1% noise added to all the projection measurements and with absorption coefficients of 0.006 mm-1 on the left and 0.003 mm-1 on the right. (B), (C), (D) Reconstructions of the absorption distribution with a constant scalar regularization parameter with λ = 104, 103, 102, respectively. (E) Reconstruction with a radially variant regularization parameter with λ e = 3 × 104 and λ c = 103. Scale bars are in units of absorption coefficient, inverse millimeters.

Fig. 7
Fig. 7

(A) Profiles of the images in Figs. 6(A)6(D) along the horizontal line through the center to show the edge-spread function as it depends on the regularization parameter used. (B) Profiles of the image in Fig. 6(B) as a function of the vertical position in the image, where y = 0 is a horizontal line through the center of the image, and y = 2 and y = 3 are horizontal lines 2 and 3 cm below the center, respectively. (C) Profiles of the Fig. 6(E) as a function of vertical position in the image, where the vertical locations are the same as those in (B).

Fig. 8
Fig. 8

Experimental images of a 16-mm-diameter black ball bearing located (A) and (B) in the center and (C) and (D) on the edge of a tissue-simulating phantom. (A) and (C) Images reconstructed with a scalar regularization parameter that could vary between 1000 and 10. (B) and (D) Images in which the radially variant reconstruction was used with λ e = 300 and λ c = 10. The background liquid was 0.5% Intralipid in a 92-mm diameter cylinder, with optical properties of μ s ′ = 0.5 mm-1 and μ a = 0.003 mm-1 at 800 nm. Scale bars are in units of absorption coefficient, inverse millimeters.

Fig. 9
Fig. 9

Experimental images of a 92-mm tissue-simulating phantom containing 0.5% Intralipid mixed with 5 ml/L of human blood. On the left side of the phantom (indicated by a black dotted circle, a 25-mm cylinder was positioned, with the blood concentration increased to 10 ml/L. (A), (B), and (C) were reconstructed with constant scalar regularization parameters of 100, 10 and 1, whereas (D) was reconstructed with the radially variant regularization parameter that scaled exponentially from 300 on the edge to 10 in the center. Background optical properties were μ a = 0.0052 mm-1 and μ s ′ = 0.5 mm-1, whereas the target has the same μ s ′ with μ a = 0.0074 mm-1. Scale bars are in units of absorption coefficient, inverse millimeters.

Tables (1)

Tables Icon

Table 1 Tabulated Values for Comparison of Scalar Regularization Parametera Reconstructions with Radially Variant Regularization Parameterb Reconstructions

Equations (9)

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

-·DrΦr, ω+μar+iω/cΦr, ω=s0r, ω,
D=3μs+μa-1.
χμ=ΦCq, μ-ΦoqΦCq, μ-Φoq.
0χμ0+Δμχ"μ0+Δμ2χμ0/2+ ,
0=-ΦCq, μ0-ΦoqJq, μ0+ΔμJq, μ0Jq, μ0,
Δμ=ΦCq, μ0-ΦoqJq, μ0Jq, μ0Jq, μ0-1.
Δμ=ΦCq, μ0-ΦoqJq, μ0Jq, μ0Jq, μ0+λI-1.
Δμ=ΦCq, μ0-ΦoqJq, μ0Jq, μ0Jq, μ0+λrI-1.
λρj=λe expρj/R+λc,

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