Abstract

What we believe to be a novel 3D diffuse optical tomography scheme is developed to reconstruct images of both absorption and scattering coefficients of finger joint systems. Compared with our previous reconstruction method, the improved 3D algorithm employs both modified Newton methods and an enhanced initial value optimization scheme to recover the optical properties of highly heterogeneous media. The developed approach is tested using simulated, phantom, and in vivo measurement data. The recovered results suggest that the improved approach is able to provide quantitatively better images than our previous algorithm for optical tomography reconstruction.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Yodh and B. Chance, "Spectroscopy and imaging with diffusing light," Phys. Today 48(3), 34-40 (1995).
    [CrossRef]
  2. A. Pifferi, A. Torricelli, P. Taroni, A. Bassi, E. Chikoidze, E. Giambattistelli, and R. Cubeddu, "Optical biopsy of bone tissue: a step toward the diagnosis of bone pathologies," J. Biomed. Opt. 9, 474-480 (2004).
    [CrossRef] [PubMed]
  3. Y. Xu, N. Iftimia, and H. Jiang, "Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography," Opt. Express 8, 447-451 (2001).
    [CrossRef] [PubMed]
  4. Y. Xu, N. Iftimia, H. Jiang, L. Key, and M. Bolster, "Three-dimensional diffuse optical tomography of bones and joints," J. Biomed. Opt. 7, 88-92 (2002).
    [CrossRef] [PubMed]
  5. A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
    [CrossRef] [PubMed]
  6. A. H. Hielscher, A. D. Klose, and J. Beuthan, "Near-infrared diffuse optical tomography," Opt. Express 7, 507-518 (2000).
    [CrossRef] [PubMed]
  7. R. Roy and E. M. Sevick-Muraca, "Truncated Newton's optimization scheme for absorption and fluorescence optical tomography: Part I theory and formulation," Opt. Express 4, 353-371 (1999).
    [CrossRef] [PubMed]
  8. D. K. Alexander and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
    [CrossRef]
  9. A. H. Hielscher and S. Bartel, "Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography," J. Biomed. Opt. 6, 183-192 (2001).
    [CrossRef] [PubMed]
  10. K. D. Paulsen and H. Jiang, "Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization," Appl. Opt. 35, 3447-3458 (1996).
    [CrossRef] [PubMed]
  11. N. Iftimia and H. Jiang, "Quantitative optical image reconstruction of turbid media by use of direct-current measurements," Appl. Opt. 39, 5256-5261 (2000).
    [CrossRef]
  12. H. Jiang, K. Paulsen, U. Osterberg, B. Pogue, and M. Patterson, "Optical image reconstruction using frequency-domain data: simulations and experiments," J. Opt. Soc. Am. A 13, 253-266 (1996).
    [CrossRef]
  13. K. D. Paulsen and H. Jiang, "Spatially-varying optical property reconstruction using a finite element diffusion equation approximation," Med. Phys. 22, 691-701 (1995).
    [CrossRef] [PubMed]
  14. H. Jiang, Y. Xu, and N. Iftimia, "Experimental three-dimensional optical image reconstruction of heterogeneous turbid media," Opt. Express 7, 204-209 (2000).
    [CrossRef] [PubMed]
  15. H. Jiang, Y. Xu, N. Iftimia, J. Eggert, K. Klove, L. Lisa Barron, and L. Fajardo, "Three-dimensional optical tomographic imaging of breast in a human subject," IEEE Trans. Med. Imaging 20, 1334-1340 (2001).
    [CrossRef]
  16. M. Michael, H. P. William, A. T. Saul, T. V. William, and P. F. Brian, Numerical Recipes in Fortran 77 (Cambridge U. Press, 1992).
  17. Z. Yuan, C. Wu, and H. Li, "Homogenized-based topology design for pure torsion of composite shaft," Acta Mech. Sin. 19, 241-246 (2003).
    [CrossRef]
  18. Q. Zhang and H. Jiang, "Three-dimensional diffuse optical tomography of simulated hand joints with a 64 × 64-channel photodiodes-based optical system," J. Opt. A 7, 224-231 (2005).
    [CrossRef]

2005

Q. Zhang and H. Jiang, "Three-dimensional diffuse optical tomography of simulated hand joints with a 64 × 64-channel photodiodes-based optical system," J. Opt. A 7, 224-231 (2005).
[CrossRef]

2004

A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

A. Pifferi, A. Torricelli, P. Taroni, A. Bassi, E. Chikoidze, E. Giambattistelli, and R. Cubeddu, "Optical biopsy of bone tissue: a step toward the diagnosis of bone pathologies," J. Biomed. Opt. 9, 474-480 (2004).
[CrossRef] [PubMed]

2003

D. K. Alexander and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

Z. Yuan, C. Wu, and H. Li, "Homogenized-based topology design for pure torsion of composite shaft," Acta Mech. Sin. 19, 241-246 (2003).
[CrossRef]

2002

Y. Xu, N. Iftimia, H. Jiang, L. Key, and M. Bolster, "Three-dimensional diffuse optical tomography of bones and joints," J. Biomed. Opt. 7, 88-92 (2002).
[CrossRef] [PubMed]

2001

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

A. H. Hielscher and S. Bartel, "Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography," J. Biomed. Opt. 6, 183-192 (2001).
[CrossRef] [PubMed]

Y. Xu, N. Iftimia, and H. Jiang, "Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography," Opt. Express 8, 447-451 (2001).
[CrossRef] [PubMed]

2000

1999

1996

1995

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

A. Yodh and B. Chance, "Spectroscopy and imaging with diffusing light," Phys. Today 48(3), 34-40 (1995).
[CrossRef]

Alexander, D. K.

D. K. Alexander and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

Backhaus, M.

A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

Barron, L. Lisa

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

Bartel, S.

A. H. Hielscher and S. Bartel, "Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography," J. Biomed. Opt. 6, 183-192 (2001).
[CrossRef] [PubMed]

Bassi, A.

A. Pifferi, A. Torricelli, P. Taroni, A. Bassi, E. Chikoidze, E. Giambattistelli, and R. Cubeddu, "Optical biopsy of bone tissue: a step toward the diagnosis of bone pathologies," J. Biomed. Opt. 9, 474-480 (2004).
[CrossRef] [PubMed]

Beuthan, J.

A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

A. H. Hielscher, A. D. Klose, and J. Beuthan, "Near-infrared diffuse optical tomography," Opt. Express 7, 507-518 (2000).
[CrossRef] [PubMed]

Bolster, M.

Y. Xu, N. Iftimia, H. Jiang, L. Key, and M. Bolster, "Three-dimensional diffuse optical tomography of bones and joints," J. Biomed. Opt. 7, 88-92 (2002).
[CrossRef] [PubMed]

Brian, P. F.

M. Michael, H. P. William, A. T. Saul, T. V. William, and P. F. Brian, Numerical Recipes in Fortran 77 (Cambridge U. Press, 1992).

Chance, B.

A. Yodh and B. Chance, "Spectroscopy and imaging with diffusing light," Phys. Today 48(3), 34-40 (1995).
[CrossRef]

Chikoidze, E.

A. Pifferi, A. Torricelli, P. Taroni, A. Bassi, E. Chikoidze, E. Giambattistelli, and R. Cubeddu, "Optical biopsy of bone tissue: a step toward the diagnosis of bone pathologies," J. Biomed. Opt. 9, 474-480 (2004).
[CrossRef] [PubMed]

Cubeddu, R.

A. Pifferi, A. Torricelli, P. Taroni, A. Bassi, E. Chikoidze, E. Giambattistelli, and R. Cubeddu, "Optical biopsy of bone tissue: a step toward the diagnosis of bone pathologies," J. Biomed. Opt. 9, 474-480 (2004).
[CrossRef] [PubMed]

Eggert, J.

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

Giambattistelli, E.

A. Pifferi, A. Torricelli, P. Taroni, A. Bassi, E. Chikoidze, E. Giambattistelli, and R. Cubeddu, "Optical biopsy of bone tissue: a step toward the diagnosis of bone pathologies," J. Biomed. Opt. 9, 474-480 (2004).
[CrossRef] [PubMed]

Hielscher, A. H.

A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

D. K. Alexander and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

A. H. Hielscher and S. Bartel, "Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography," J. Biomed. Opt. 6, 183-192 (2001).
[CrossRef] [PubMed]

A. H. Hielscher, A. D. Klose, and J. Beuthan, "Near-infrared diffuse optical tomography," Opt. Express 7, 507-518 (2000).
[CrossRef] [PubMed]

Iftimia, N.

Jiang, H.

Q. Zhang and H. Jiang, "Three-dimensional diffuse optical tomography of simulated hand joints with a 64 × 64-channel photodiodes-based optical system," J. Opt. A 7, 224-231 (2005).
[CrossRef]

Y. Xu, N. Iftimia, H. Jiang, L. Key, and M. Bolster, "Three-dimensional diffuse optical tomography of bones and joints," J. Biomed. Opt. 7, 88-92 (2002).
[CrossRef] [PubMed]

Y. Xu, N. Iftimia, and H. Jiang, "Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography," Opt. Express 8, 447-451 (2001).
[CrossRef] [PubMed]

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

N. Iftimia and H. Jiang, "Quantitative optical image reconstruction of turbid media by use of direct-current measurements," Appl. Opt. 39, 5256-5261 (2000).
[CrossRef]

H. Jiang, Y. Xu, and N. Iftimia, "Experimental three-dimensional optical image reconstruction of heterogeneous turbid media," Opt. Express 7, 204-209 (2000).
[CrossRef] [PubMed]

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

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

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

Key, L.

Y. Xu, N. Iftimia, H. Jiang, L. Key, and M. Bolster, "Three-dimensional diffuse optical tomography of bones and joints," J. Biomed. Opt. 7, 88-92 (2002).
[CrossRef] [PubMed]

Klose, A. D.

A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

A. H. Hielscher, A. D. Klose, and J. Beuthan, "Near-infrared diffuse optical tomography," Opt. Express 7, 507-518 (2000).
[CrossRef] [PubMed]

Klove, K.

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

Li, H.

Z. Yuan, C. Wu, and H. Li, "Homogenized-based topology design for pure torsion of composite shaft," Acta Mech. Sin. 19, 241-246 (2003).
[CrossRef]

Michael, M.

M. Michael, H. P. William, A. T. Saul, T. V. William, and P. F. Brian, Numerical Recipes in Fortran 77 (Cambridge U. Press, 1992).

Moa-Anderson, B.

A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

Netz, U.

A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

Osterberg, U.

Patterson, M.

Paulsen, K.

Paulsen, K. D.

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

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

Pifferi, A.

A. Pifferi, A. Torricelli, P. Taroni, A. Bassi, E. Chikoidze, E. Giambattistelli, and R. Cubeddu, "Optical biopsy of bone tissue: a step toward the diagnosis of bone pathologies," J. Biomed. Opt. 9, 474-480 (2004).
[CrossRef] [PubMed]

Pogue, B.

Roy, R.

Saul, A. T.

M. Michael, H. P. William, A. T. Saul, T. V. William, and P. F. Brian, Numerical Recipes in Fortran 77 (Cambridge U. Press, 1992).

Scheel, A. K.

A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

Sevick-Muraca, E. M.

Taroni, P.

A. Pifferi, A. Torricelli, P. Taroni, A. Bassi, E. Chikoidze, E. Giambattistelli, and R. Cubeddu, "Optical biopsy of bone tissue: a step toward the diagnosis of bone pathologies," J. Biomed. Opt. 9, 474-480 (2004).
[CrossRef] [PubMed]

Torricelli, A.

A. Pifferi, A. Torricelli, P. Taroni, A. Bassi, E. Chikoidze, E. Giambattistelli, and R. Cubeddu, "Optical biopsy of bone tissue: a step toward the diagnosis of bone pathologies," J. Biomed. Opt. 9, 474-480 (2004).
[CrossRef] [PubMed]

William, H. P.

M. Michael, H. P. William, A. T. Saul, T. V. William, and P. F. Brian, Numerical Recipes in Fortran 77 (Cambridge U. Press, 1992).

William, T. V.

M. Michael, H. P. William, A. T. Saul, T. V. William, and P. F. Brian, Numerical Recipes in Fortran 77 (Cambridge U. Press, 1992).

Wu, C.

Z. Yuan, C. Wu, and H. Li, "Homogenized-based topology design for pure torsion of composite shaft," Acta Mech. Sin. 19, 241-246 (2003).
[CrossRef]

Xu, Y.

Y. Xu, N. Iftimia, H. Jiang, L. Key, and M. Bolster, "Three-dimensional diffuse optical tomography of bones and joints," J. Biomed. Opt. 7, 88-92 (2002).
[CrossRef] [PubMed]

Y. Xu, N. Iftimia, and H. Jiang, "Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography," Opt. Express 8, 447-451 (2001).
[CrossRef] [PubMed]

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

H. Jiang, Y. Xu, and N. Iftimia, "Experimental three-dimensional optical image reconstruction of heterogeneous turbid media," Opt. Express 7, 204-209 (2000).
[CrossRef] [PubMed]

Yodh, A.

A. Yodh and B. Chance, "Spectroscopy and imaging with diffusing light," Phys. Today 48(3), 34-40 (1995).
[CrossRef]

Yuan, Z.

Z. Yuan, C. Wu, and H. Li, "Homogenized-based topology design for pure torsion of composite shaft," Acta Mech. Sin. 19, 241-246 (2003).
[CrossRef]

Zhang, Q.

Q. Zhang and H. Jiang, "Three-dimensional diffuse optical tomography of simulated hand joints with a 64 × 64-channel photodiodes-based optical system," J. Opt. A 7, 224-231 (2005).
[CrossRef]

Acta Mech. Sin.

Z. Yuan, C. Wu, and H. Li, "Homogenized-based topology design for pure torsion of composite shaft," Acta Mech. Sin. 19, 241-246 (2003).
[CrossRef]

Appl. Opt.

IEEE Trans. Med. Imaging

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

Inverse Probl.

D. K. Alexander and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

J. Biomed. Opt.

A. H. Hielscher and S. Bartel, "Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography," J. Biomed. Opt. 6, 183-192 (2001).
[CrossRef] [PubMed]

A. Pifferi, A. Torricelli, P. Taroni, A. Bassi, E. Chikoidze, E. Giambattistelli, and R. Cubeddu, "Optical biopsy of bone tissue: a step toward the diagnosis of bone pathologies," J. Biomed. Opt. 9, 474-480 (2004).
[CrossRef] [PubMed]

Y. Xu, N. Iftimia, H. Jiang, L. Key, and M. Bolster, "Three-dimensional diffuse optical tomography of bones and joints," J. Biomed. Opt. 7, 88-92 (2002).
[CrossRef] [PubMed]

J. Opt. A

Q. Zhang and H. Jiang, "Three-dimensional diffuse optical tomography of simulated hand joints with a 64 × 64-channel photodiodes-based optical system," J. Opt. A 7, 224-231 (2005).
[CrossRef]

J. Opt. Soc. Am. A

Med. Phys.

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

Opt. Express

Phys. Med. Biol.

A. H. Hielscher, A. D. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

Phys. Today

A. Yodh and B. Chance, "Spectroscopy and imaging with diffusing light," Phys. Today 48(3), 34-40 (1995).
[CrossRef]

Other

M. Michael, H. P. William, A. T. Saul, T. V. William, and P. F. Brian, Numerical Recipes in Fortran 77 (Cambridge U. Press, 1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Flow chart of the new initial value optimization scheme.

Fig. 2
Fig. 2

Test geometry for (a) simulation cases and phantom experiments and (b) an in vivo digital interphalangeal (DIP) finger joint experiment. The dimension units are millimeters.

Fig. 3
Fig. 3

Reconstructed absorption (left column) and scattering images (right column) at y = 0   mm plane for a simulation test of a large-size target using (a) the existing reconstruction method and the previous initial value optimization scheme, (b) the existing reconstruction method with the new initial value optimization scheme, and (c) the improved reconstruction method with the new initial value optimization scheme.

Fig. 4
Fig. 4

Reconstructed images at a selected longitudinal plane x = 0   mm from simulated data. (a) Absorption images from the existing algorithm, (b) scattering images from the existing algorithm, (c) absorption images from the improved algorithm, (d) scattering images from the improved algorithm.

Fig. 5
Fig. 5

Reconstructed images at a selected longitudinal plane y = 0   mm from the simulated data using the improved algorithm with different initial values. (a), (b), Case 1: μ a = 0.04 mm 1 , μ s = 0.9 mm 1 . (c), (d), Case 2: μ a = 0.03 mm 1 , μ s = 0.9 mm 1 . (e), (f), Case 3: μ a = 0.03 mm 1 , μ s = 0.8 mm 1 (left column, absorption images; right column, scattering images).

Fig. 6
Fig. 6

Comparison of exact and reconstructed optical property profiles along transect AB [see Fig. 1(a)] for the images shown in Fig. 5. (a) Absorption coefficient distribution, (b) scattering coefficient distribution.

Fig. 7
Fig. 7

Reconstructed images at selected longitudinal or transverse planes from phantom test 1 using the improved (right column) and existing (left column) algorithm. (a) Absorption images at plane x = 3   mm , (b) absorption images at plane z = 5   mm , (c) scattering images at plane x = 3   mm , (d) scattering images at plane y = 0   mm .

Fig. 8
Fig. 8

Reconstructed images at selected longitudinal planes from phantom test 2 using the improved (right column) and existing (left column) algorithm. (a) Absorption images at plane x = 3   mm , (b) absorption images at plane y=0 mm, (c) scattering images at plane x = 3   mm , (d) scattering images at plane y = 0   mm .

Fig. 9
Fig. 9

Reconstructed images at selected longitudinal planes from phantom test 3 using the improved (right column) and existing (left column) algorithm. (a) Absorption images at plane x = 3   mm , (b) absorption images at plane y = 0   mm , (c) scattering images at plane x = 3   mm , (d) scattering images at plane y = 0   mm .

Fig. 10
Fig. 10

Reconstructed images at selected longitudinal planes from the in vivo measurement using the improved (left column) and existing (right column) algorithm. (a) Scattering images at plane y = 0   mm , (b) scattering images at plane x = 2   mm , (c) absorption images at plane y = 0   mm , (d) absorption images at plane x = 2   mm . Arrows indicate the bones.

Tables (2)

Tables Icon

Table 1 Initial Optical Properties for Reconstruction and Corresponding Relative Error in Equation (15)

Tables Icon

Table 2 Averaged Absorption and Scattering Coefficients of the Bone and Cartilage from the Three Phantom Tests Using the Improved (New) and Existing (Old) Algorithms

Equations (15)

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

D ( r ) Φ ( r ) μ a ( r ) Φ ( r ) = S ( r ) ,
D Φ n = α Φ ,
Φ = i = 1 N Φ i ϕ i , D = i = 1 N D i ϕ i , μ a = i = 1 N ( μ a ) i ϕ i ,
[ A ] { Φ } = { b } ,
[ A ] { Φ / χ } = { b / χ } [ A / χ ] { Φ } ,
( T + λ I ) Δ χ = T ( Φ o Φ c ) ,
χ new = χ old + λ Δ χ ( 0 < λ 1 ) ,
f = 1 2   g g .
f ( χ new ) = f ( χ old ) + f ( χ old ) Δ χ + 1 2 Δ χ T 2 f ( ξ ) Δ χ .
f ( χ new ) f ( χ old ) + f ( χ old ) Δ χ + m 2 Δ χ 2 2 .
Δ χ = 1 m f ( χ old ) .
f ( χ new ) f ( χ old ) 1 2 m f ( χ old ) 2 2 .
f Δ χ = g g < 0.
f ( χ new ) f ( χ old ) + θ λ f Δ χ .
Min:   F = i = 1 M ( Φ i m Φ i c ) 2 ,

Metrics