Abstract

A general framework for incorporating single and multiple priors in diffuse optical tomography is described. We explore the use of this framework for simultaneously utilizing spatial and spectral priors in the context of imaging breast cancer. The utilization of magnetic resonance images of water and lipid content as a statistical spatial prior for the diffuse optical image reconstructions is also discussed. Simulations are performed to demonstrate the significant improvement in image quality afforded by combining spatial and spectral priors.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
  28. A. Dale, M. Sereno, “Improved localization of cortical activity by combining EEG and MEG with MRI cortical surface reconstruction—a linear approach,” J. Cogn. Neurosci. 5, 162–176 (1993).
    [CrossRef] [PubMed]
  29. A. Liu, A. Dale, J. Belliveau, “Monte Carlo simulation studies of EEG and MEG localization accuracy,” Hum. Brain Mapp. 16, 47–62 (2002).
    [CrossRef] [PubMed]
  30. 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]
  31. M. Schweiger, S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori region boundary information,” Phys. Med. Biol. 44, 2703–2721 (1999).
    [CrossRef] [PubMed]
  32. B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38, 2950–2961 (1999).
    [CrossRef]
  33. D. J. Hawrysz, E. M. Sevick-Muraca, “Developments toward diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2, 388–417 (2000).
    [CrossRef]
  34. S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
    [PubMed]
  35. 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]

2004 (4)

M. A. Franceschini, D. A. Boas, “Noninvasive measurement of neuronal activity with near-infrared optical imaging,” Neuroimage 21, 372–386 (2004).

X. Intes, C. Maloux, M. Guven, B. Yazici, B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef] [PubMed]

A. Corlu, T. Durduran, R. Choe, M. Schweiger, E. M. C. Hillman, S. R. Arridge, A. G. Yodh, “Uniqueness and wavelength optimization in continuous-wave multispectral diffuse optical tomography,” Opt. Lett. 28, 2339–2341 (2004).
[CrossRef]

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29, 256–258 (2004).
[CrossRef] [PubMed]

2003 (3)

B. A. Brooksby, H. Dehghani, B. W. Pogue, K. D. Paulsen, “Near-infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (2003).
[CrossRef]

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[CrossRef] [PubMed]

S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
[PubMed]

2002 (2)

A. Liu, A. Dale, J. Belliveau, “Monte Carlo simulation studies of EEG and MEG localization accuracy,” Hum. Brain Mapp. 16, 47–62 (2002).
[CrossRef] [PubMed]

A. Hielscher, A. Bluestone, G. Abdoulaev, A. Klose, J. Lasker, M. Stewart, U. Netz, J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18, 313–337 (2002).
[CrossRef]

2001 (8)

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[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]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[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]

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

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

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]

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 (3)

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

V. Ntziachristos, A. G. 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)

Q. Zhu, T. Durduran, V. Ntziachristos, M. Holboke, A. G. Yodh, “Imager that combines near-infrared diffusive light and ultrasound,” Opt. Lett. 24, 1050–1052 (1999).
[CrossRef]

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

M. Schweiger, S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori region boundary information,” Phys. Med. Biol. 44, 2703–2721 (1999).
[CrossRef] [PubMed]

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

1997 (1)

1995 (1)

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

1994 (1)

B. W. Pogue, M. S. Patterson, “Frequency-domain optical-absorption spectroscopy of finite tissue volumes using diffusion-theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[CrossRef] [PubMed]

1993 (1)

A. Dale, M. Sereno, “Improved localization of cortical activity by combining EEG and MEG with MRI cortical surface reconstruction—a linear approach,” J. Cogn. Neurosci. 5, 162–176 (1993).
[CrossRef] [PubMed]

1991 (1)

G. Glover, E. Schneider, “3-point Dixon technique for true water fat decomposition with BO inhomogeneity correction,” Magn. Reson. Med. 18, 373–381 (1991).
[CrossRef]

1989 (1)

Abdoulaev, G.

A. Hielscher, A. Bluestone, G. Abdoulaev, A. Klose, J. Lasker, M. Stewart, U. Netz, J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18, 313–337 (2002).
[CrossRef]

Arridge, S. R.

Barbour, R.

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]

Belliveau, J.

A. Liu, A. Dale, J. Belliveau, “Monte Carlo simulation studies of EEG and MEG localization accuracy,” Hum. Brain Mapp. 16, 47–62 (2002).
[CrossRef] [PubMed]

Berger, A. J.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef] [PubMed]

Beuthan, J.

A. Hielscher, A. Bluestone, G. Abdoulaev, A. Klose, J. Lasker, M. Stewart, U. Netz, J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18, 313–337 (2002).
[CrossRef]

Bevilacqua, F.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef] [PubMed]

Bluestone, A.

A. Hielscher, A. Bluestone, G. Abdoulaev, A. Klose, J. Lasker, M. Stewart, U. Netz, J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18, 313–337 (2002).
[CrossRef]

Boas, D. A.

M. A. Franceschini, D. A. Boas, “Noninvasive measurement of neuronal activity with near-infrared optical imaging,” Neuroimage 21, 372–386 (2004).

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29, 256–258 (2004).
[CrossRef] [PubMed]

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[CrossRef] [PubMed]

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]

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]

Brooksby, B. A.

B. A. Brooksby, H. Dehghani, B. W. Pogue, K. D. Paulsen, “Near-infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (2003).
[CrossRef]

Brukilacchio, T. J.

Butler, J.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef] [PubMed]

Cerussi, A.

S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
[PubMed]

Cerussi, A. E.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef] [PubMed]

Chance, B.

X. Intes, C. Maloux, M. Guven, B. Yazici, B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef] [PubMed]

V. Ntziachristos, A. G. 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).

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[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]

Chaves, T.

Chiou, G.

S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
[PubMed]

Choe, R.

Chorlton, M.

Chu, Y.

S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
[PubMed]

Cope, M.

Corlu, A.

Culver, J. P.

Dale, A.

A. Liu, A. Dale, J. Belliveau, “Monte Carlo simulation studies of EEG and MEG localization accuracy,” Hum. Brain Mapp. 16, 47–62 (2002).
[CrossRef] [PubMed]

A. Dale, M. Sereno, “Improved localization of cortical activity by combining EEG and MEG with MRI cortical surface reconstruction—a linear approach,” J. Cogn. Neurosci. 5, 162–176 (1993).
[CrossRef] [PubMed]

Dehghani, H.

B. A. Brooksby, H. Dehghani, B. W. Pogue, K. D. Paulsen, “Near-infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (2003).
[CrossRef]

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[CrossRef]

Delpy, D. T.

Deng, C.

S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
[PubMed]

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]

Durduran, T.

Durkin, A.

S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
[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]

Firbank, M.

Franceschini, M. A.

M. A. Franceschini, D. A. Boas, “Noninvasive measurement of neuronal activity with near-infrared optical imaging,” Neuroimage 21, 372–386 (2004).

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]

Glover, G.

G. Glover, E. Schneider, “3-point Dixon technique for true water fat decomposition with BO inhomogeneity correction,” Magn. Reson. Med. 18, 373–381 (1991).
[CrossRef]

Graber, H.

Gulsen, G.

S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
[PubMed]

Guven, M.

X. Intes, C. Maloux, M. Guven, B. Yazici, B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef] [PubMed]

Hawrysz, D. J.

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

Hebden, J. C.

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[CrossRef]

Hielscher, A.

A. Hielscher, A. Bluestone, G. Abdoulaev, A. Klose, J. Lasker, M. Stewart, U. Netz, J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18, 313–337 (2002).
[CrossRef]

Hillman, E. M. C.

A. Corlu, T. Durduran, R. Choe, M. Schweiger, E. M. C. Hillman, S. R. Arridge, A. G. Yodh, “Uniqueness and wavelength optimization in continuous-wave multispectral diffuse optical tomography,” Opt. Lett. 28, 2339–2341 (2004).
[CrossRef]

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt. 40, 3278–3287 (2001).
[CrossRef]

E. M. C. Hillman, “Experimental and theoretical investigations of near infrared tomographic imaging methods and clinical applications,” Ph.D. dissertation (University of London, London, UK, 2002).

Holboke, M.

Holboke, M. J.

Holcombe, R. F.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef] [PubMed]

Iftimia, N.

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]

Intes, X.

X. Intes, C. Maloux, M. Guven, B. Yazici, B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef] [PubMed]

Jakubowski, D.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef] [PubMed]

Jiang, H.

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]

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.

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[CrossRef] [PubMed]

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.

A. Hielscher, A. Bluestone, G. Abdoulaev, A. Klose, J. Lasker, M. Stewart, U. Netz, J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18, 313–337 (2002).
[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]

Kopans, D. B.

Lasker, J.

A. Hielscher, A. Bluestone, G. Abdoulaev, A. Klose, J. Lasker, M. Stewart, U. Netz, J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18, 313–337 (2002).
[CrossRef]

Li, A.

Liu, A.

A. Liu, A. Dale, J. Belliveau, “Monte Carlo simulation studies of EEG and MEG localization accuracy,” Hum. Brain Mapp. 16, 47–62 (2002).
[CrossRef] [PubMed]

Maloux, C.

X. Intes, C. Maloux, M. Guven, B. Yazici, B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef] [PubMed]

McBride, T. O.

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

Merritt, S.

S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
[PubMed]

Miller, E. L.

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29, 256–258 (2004).
[CrossRef] [PubMed]

A. Li, E. L. Miller, M. E. Kilmer, T. J. Brukilacchio, T. Chaves, J. Stott, Q. Zhang, T. Wu, M. Chorlton, R. H. Moore, D. B. Kopans, D. A. Boas, “Tomographic optical breast imaging guided by three-dimensional mammography,” Appl. Opt. 42, 5181–5190 (2003).
[CrossRef] [PubMed]

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]

Moore, R. H.

Nalcioglu, O.

S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
[PubMed]

Netz, U.

A. Hielscher, A. Bluestone, G. Abdoulaev, A. Klose, J. Lasker, M. Stewart, U. Netz, J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18, 313–337 (2002).
[CrossRef]

Ntziachristos, V.

O’Leary, M. A.

M. A. O’Leary, “Imaging with diffuse photon density waves,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1996).

Okada, E.

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

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]

Patterson, M. S.

B. W. Pogue, M. S. Patterson, “Frequency-domain optical-absorption spectroscopy of finite tissue volumes using diffusion-theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[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]

Paulsen, K. D.

B. A. Brooksby, H. Dehghani, B. W. Pogue, K. D. Paulsen, “Near-infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (2003).
[CrossRef]

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

Pei, Y.

Pogue, B. W.

B. A. Brooksby, H. Dehghani, B. W. Pogue, K. D. Paulsen, “Near-infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (2003).
[CrossRef]

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

B. W. Pogue, M. S. Patterson, “Frequency-domain optical-absorption spectroscopy of finite tissue volumes using diffusion-theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[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.

Schmidt, F. E. W.

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

Schmitz, C.

Schnall, M.

V. Ntziachristos, A. G. 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).

Schneider, E.

G. Glover, E. Schneider, “3-point Dixon technique for true water fat decomposition with BO inhomogeneity correction,” Magn. Reson. Med. 18, 373–381 (1991).
[CrossRef]

Schweiger, M.

Sereno, M.

A. Dale, M. Sereno, “Improved localization of cortical activity by combining EEG and MEG with MRI cortical surface reconstruction—a linear approach,” J. Cogn. Neurosci. 5, 162–176 (1993).
[CrossRef] [PubMed]

Sevick-Muraca, E. M.

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

Shah, N.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef] [PubMed]

Stewart, M.

A. Hielscher, A. Bluestone, G. Abdoulaev, A. Klose, J. Lasker, M. Stewart, U. Netz, J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18, 313–337 (2002).
[CrossRef]

Stott, J.

Tromberg, B.

S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
[PubMed]

Tromberg, B. J.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef] [PubMed]

Veenstra, H.

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]

Wilson, B. C.

Wu, T.

Xu, Y.

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]

Yazici, B.

X. Intes, C. Maloux, M. Guven, B. Yazici, B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef] [PubMed]

Yodh, A.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

Yodh, A. G.

Zhang, Q.

Zhong, S.

Zhu, Q.

Acad. Radiol. (1)

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef] [PubMed]

Appl. Opt. (5)

Dis. Markers (1)

A. Hielscher, A. Bluestone, G. Abdoulaev, A. Klose, J. Lasker, M. Stewart, U. Netz, J. Beuthan, “Near-infrared diffuse optical tomography,” Dis. Markers 18, 313–337 (2002).
[CrossRef]

Hum. Brain Mapp. (1)

A. Liu, A. Dale, J. Belliveau, “Monte Carlo simulation studies of EEG and MEG localization accuracy,” Hum. Brain Mapp. 16, 47–62 (2002).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

B. A. Brooksby, H. Dehghani, B. W. Pogue, K. D. Paulsen, “Near-infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. Sel. Top. Quantum Electron. 9, 199–209 (2003).
[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 (1)

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]

Inverse Probl. (1)

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

J. Cogn. Neurosci. (1)

A. Dale, M. Sereno, “Improved localization of cortical activity by combining EEG and MEG with MRI cortical surface reconstruction—a linear approach,” J. Cogn. Neurosci. 5, 162–176 (1993).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Magn. Reson. Med. (1)

G. Glover, E. Schneider, “3-point Dixon technique for true water fat decomposition with BO inhomogeneity correction,” Magn. Reson. Med. 18, 373–381 (1991).
[CrossRef]

Neoplasia (1)

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

Neuroimage (1)

M. A. Franceschini, D. A. Boas, “Noninvasive measurement of neuronal activity with near-infrared optical imaging,” Neuroimage 21, 372–386 (2004).

Opt. Lett. (4)

Phys. Med. Biol. (5)

B. W. Pogue, M. S. Patterson, “Frequency-domain optical-absorption spectroscopy of finite tissue volumes using diffusion-theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori region boundary information,” Phys. Med. Biol. 44, 2703–2721 (1999).
[CrossRef] [PubMed]

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]

X. Intes, C. Maloux, M. Guven, B. Yazici, B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef] [PubMed]

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

Phys. Today (1)

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

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

V. Ntziachristos, A. G. 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).

Radiology (1)

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]

Technol. Cancer Res. Treat. (1)

S. Merritt, G. Gulsen, G. Chiou, Y. Chu, C. Deng, A. Cerussi, A. Durkin, B. Tromberg, O. Nalcioglu, “Comparison of water and lipid content measurements using diffuse optical spectroscopy and MRI in emulsion phantoms,” Technol. Cancer Res. Treat. 2, 563–569 (2003).
[PubMed]

Other (5)

M. A. O’Leary, “Imaging with diffuse photon density waves,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1996).

E. M. C. Hillman, “Experimental and theoretical investigations of near infrared tomographic imaging methods and clinical applications,” Ph.D. dissertation (University of London, London, UK, 2002).

B. Chance, E. Anday, S. Nioka, S. Zhou, L. Hong, K. Worden, L. C. T. Murray, Y. Ovetsky, D. Pidikiti, R. Thomas, “A novel method for fast imaging of brain function, non-invasively, with light,” Opt. Express2, 411–423 (1998), http://wwwopticsexpress.org .
[CrossRef]

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

Y. Xu, N. Iftimia, H. B. Jiang, L. L. Key, M. B. Bolster, “Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography,” Opt. Express8, 447–451 (2001), http://www.opticsexpress.org .
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Four targets are embedded in the homogeneous background in the simulations. All targets have a diameter of 2 cm. Targets 1, 2, 3, and 4 are HbO2, HbR, water, and lipid perturbations, respectively.

Fig. 2
Fig. 2

Physiological image reconstruction without any prior information, using simulated data. The images are shown for the slice at a depth of 4 cm where the true objects are centered. βr is set to 0.0005. The field of view of the image is 8 cm × 10 cm.

Fig. 3
Fig. 3

Physiological image reconstruction with a spectral prior, using simulated data. The images are shown for the slice at a depth of 4 cm where the true objects are centered. βr is set to 0.0001. The FWHM of the reconstructed HbO2 object is the same as the one in the reconstruction without a prior, which is shown in Fig. 2. The field of view of the image is 8 cm × 10 cm.

Fig. 4
Fig. 4

Plot of the CNR versus the FWHM of the reconstructed images without and with spectral priors, using simulated data. Dashed arrow, CNR and FWHM in the reconstruction shown in Fig. 2; solid arrow, values in the reconstruction shown in Fig. 3.

Fig. 5
Fig. 5

Physiological image reconstruction with both spectral and spatial priors for water and lipid content, using simulated data. The images are shown for the slice at a depth of 4 cm where the true objects are centered. βr is set to 0.0001. The FWHM of the reconstructed HbO2 object is same as that in the reconstruction without a prior, which is shown in Fig. 2. The field of view of the image is 8 cm × 10 cm.

Fig. 6
Fig. 6

(a) The 3-D display of water and lipid image reconstruction with the spectral prior, using simulated data. (b) The 3-D display of water and lipid image reconstruction with both spectral and spatial priors, using simulated data.

Tables (2)

Tables Icon

Table 1 Chromophore Content of the Background Medium and the Absorbing Objects

Tables Icon

Table 2 Range of SNR Measurements at Each Wavelength

Equations (17)

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

Φ 1 ( r s ,     r d ,     λ ) = V - δ μ a ( r ,     λ ) ν D - 1 G ( r s ,     r ,     λ ) × G ( r ,     r d ,     λ ) d 3 r ,
Φ 1 = Ax + n ,
W = R A T ( ARA T + β C ) - 1
W = ( A T C - 1 A + β R - 1 ) - 1 A T C - 1 ,
x ^ = W Φ m ,
f ( x ) = Φ m - Ax 2 + β 1 ( I - S ) x 2 + β 2 Sx 2 ,
μ a ( λ ) = ɛ HbO 2 ( λ ) [ HbO 2 ] + ɛ HbR ( λ ) [ HbR ] ,
[ Φ 1 ( λ 1 ) Φ 1 ( λ 2 ) ] = [ A ( λ 1 ) 0 0 A ( λ 2 ) ] [ δ μ a ( λ 1 ) δ μ a ( λ 2 ) ]
= AE [ δ [ HbO 2 ] δ [ HbR ] ]
= [ ɛ HbO 2 ( λ 1 ) A ( λ 1 ) ɛ HbR 1 ( λ 1 ) A ( λ 1 ) ɛ HbO 2 ( λ 2 ) A ( λ 2 ) ɛ HbO ( λ 2 ) A ( λ 2 ) ] [ δ [ HbO 2 ] δ [ HbR ] ] , E = ɛ I ,             A = [ A ( λ 1 ) 0 0 A ( λ 2 ) ] , [ ɛ HbO 2 , λ 1 ɛ HbR , λ 1 ɛ HbO 2 , λ 2 ɛ HbR , λ 2 ] .
[ δ HbO 2 δ HbR ] = E T A T ( AEE T A T + β C ) - 1 Φ m .
R = E E T .
R = Ω E E T Ω T ,
R = E Ω Ω T E T
Ω = [ R HbO 2 0 0 R HbR ]
μ a ( λ ) = ɛ HbO 2 ( λ ) [ HbO 2 ] + ɛ HbR ( λ ) [ HbR ] + ɛ H 2 O ( λ ) [ H 2 O ] + ɛ lipid ( λ ) [ Lipid ] .
Ω = [ R HbO 2 0 0 0 0 R HbR 0 0 0 0 R H 2 O 0 0 0 0 R lipid ] .

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