Abstract

In this report, we present a method for reducing the inter–coefficient crosstalk problem in optical tomography. The method described is an extension of a previously reported normalized difference method that evaluates relative detector values, and employs a weight matrix scaling technique together with a constrained CGD method for image reconstruction. Results from numerical and experimental studies using DC measurement data demonstrate that the approach can effectively isolate absorption and scattering heterogeneities, even for complex combinations of perturbations in optical properties. The significance of these results in light of recent theoretical findings is discussed.

© Optical Society of America

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References

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  1. T.O. McBride, B. W. Pogue, U.L. �sterberg, and K.D. Paulsen, "Separation of absorption and scattering heterogeneities in NIR tomographic imaging of tissue," in Biomedical Topical Meetings, OSA Technical Digest (Optical Society of America, Washington, D.C., 2000), pp. 339-341.
  2. S. R. Arridge and W. R. B. Lionheart, "Nonuniqueness in diffusion-based optical tomography," Opt. Lett. 23, 882-884 (1998).
    [CrossRef]
  3. J. C. Hebden, S. R. Arridge and M. Schweiger, "Investigation of alterative data types for time-resolved optical tomography," Trends in Optics and Photonics vol. 21, Advances in Optical Imaging and Photon Migration, James G. Fujimoto and Michael S. Patterson, eds. (Optical Society of America, Washington, DC 1998), pp 162-167.
  4. Y. Pei, H. L. Graber and R L. Barbour, "Influence of systematic errors in reference states on image quality and on stability of derived information for DC optical imaging," Appl. Opt., 2001, in press.
    [CrossRef]
  5. Y. Pei, Optical Tomographic Imaging Using the Finite Element Method, Ph. D. Thesis (1999), Polytechnic University.
  6. Y. Pei, F.-B. Lin, R. L. Barbour, "Model-based imaging of scattering media using relative detector values," presented at 1999 OSA Annual Meeting & Exhibit: Optics in High-Tech Industries (Santa Clara, CA, September 26-30).
  7. J. Chang, H.L. Graber, R.L. Barbour and R. Aronson, "Recovery of optical cross-section perturbations in dense-scattering media by transport-theory-based imaging operators and steady-state simulated data," Appl. Opt. 35, 3963-3978 (1996)
    [CrossRef] [PubMed]
  8. P.E. Gill, W. Murray and M. H. Wright, Practical Optimization, Academic Press, New York (1981).
  9. R. Aronson and N. Corngold, "Photon diffusion coefficient in an absorbing medium," J. Opt. Soc. Am. A 14, 262-266 (1997).
  10. C. H. Schmitz, M. L�cker, J. Lasker, A. H. Hielscher, and R. L. Barbour, " Performance characteristics of silicon photodiode (SiPD) based instrument for fast function optical tomography," Proc. SPIE 4250, San Jose, CA, in press, (2001).
  11. S. Fantini, M.A. Franceschini, G. Gaida, H. Jess, H. Erdl, W.W. Mantulin, E. Gratton, K.T. Moesta, P.M. Schlag and M. Kaschke, "Contrast enhancement by edge effect corrections in frequency-domain optical mammography," in OSA Trends in Optics and Photonics on Advances in Optical Imaging and Photon.Migration, R.R. Alfano and J.G. Fujimoto, eds., (Optical Society of America, Washington DC, 1996) Vol. 2, pp. 160-163.
  12. S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. van Gemert, "Optical Properties of Intralipid: A phantom medium for light propagation studies," Lasers Surg. Med., Vol. 12, 510-519 (1992).
    [CrossRef]
  13. H. Dehghani, D. T. Delpy and S. R. Arridge, "Photon migration in non-scattering tissue and the effects on image reconstruction," Phys. Med. Biol. 44, 2897-2906 (1999).
    [CrossRef]
  14. R. L. Barbour, H.L. Graber, Y. Pei, S. Zhong, and C.H. Schmitz, "Optical tomographic imaging of dynamic features of dense scattering media," J. Opt. Soc. Am. A, in press (2001).
    [CrossRef]
  15. H. L. Graber, Y. Pei and R. L. Barbour, "Imaging of spatiotemporal coincident states by dynamic optical tomography," Proc. SPIE 4250, San Jose, CA, in press, (2001).
  16. G. Landis, S. Blattman, T. Panetta, C. H. Schmitz, H. L. Graber. Y. Pei, and R. L. Barbour, "Clinical applications of dynamic optical tomography in vascular disease," Proc. SPIE 4250, San Jose, CA, in press, (2001).
  17. 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]
  18. Y. Xu, N. Iftimia, H. Jiang, L. Key, M. Bolster, "Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography," Opt. Express 8, 447-451 (2001), http://www.opticsexpress.org/oearchive/source/30565.htm
    [CrossRef] [PubMed]
  19. B.J. Hoenders, "Existence of invisible nonscattering objects and nonradiating sources," J. Opt. Soc. Am. A 14, 262-266, (1997).
    [CrossRef]
  20. A.H. Hielscher, R.E. Alcouffe, and R.L. Barbour, 'Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-1302 (1998).
    [CrossRef] [PubMed]

Other

T.O. McBride, B. W. Pogue, U.L. �sterberg, and K.D. Paulsen, "Separation of absorption and scattering heterogeneities in NIR tomographic imaging of tissue," in Biomedical Topical Meetings, OSA Technical Digest (Optical Society of America, Washington, D.C., 2000), pp. 339-341.

S. R. Arridge and W. R. B. Lionheart, "Nonuniqueness in diffusion-based optical tomography," Opt. Lett. 23, 882-884 (1998).
[CrossRef]

J. C. Hebden, S. R. Arridge and M. Schweiger, "Investigation of alterative data types for time-resolved optical tomography," Trends in Optics and Photonics vol. 21, Advances in Optical Imaging and Photon Migration, James G. Fujimoto and Michael S. Patterson, eds. (Optical Society of America, Washington, DC 1998), pp 162-167.

Y. Pei, H. L. Graber and R L. Barbour, "Influence of systematic errors in reference states on image quality and on stability of derived information for DC optical imaging," Appl. Opt., 2001, in press.
[CrossRef]

Y. Pei, Optical Tomographic Imaging Using the Finite Element Method, Ph. D. Thesis (1999), Polytechnic University.

Y. Pei, F.-B. Lin, R. L. Barbour, "Model-based imaging of scattering media using relative detector values," presented at 1999 OSA Annual Meeting & Exhibit: Optics in High-Tech Industries (Santa Clara, CA, September 26-30).

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

P.E. Gill, W. Murray and M. H. Wright, Practical Optimization, Academic Press, New York (1981).

R. Aronson and N. Corngold, "Photon diffusion coefficient in an absorbing medium," J. Opt. Soc. Am. A 14, 262-266 (1997).

C. H. Schmitz, M. L�cker, J. Lasker, A. H. Hielscher, and R. L. Barbour, " Performance characteristics of silicon photodiode (SiPD) based instrument for fast function optical tomography," Proc. SPIE 4250, San Jose, CA, in press, (2001).

S. Fantini, M.A. Franceschini, G. Gaida, H. Jess, H. Erdl, W.W. Mantulin, E. Gratton, K.T. Moesta, P.M. Schlag and M. Kaschke, "Contrast enhancement by edge effect corrections in frequency-domain optical mammography," in OSA Trends in Optics and Photonics on Advances in Optical Imaging and Photon.Migration, R.R. Alfano and J.G. Fujimoto, eds., (Optical Society of America, Washington DC, 1996) Vol. 2, pp. 160-163.

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, and M. J. C. van Gemert, "Optical Properties of Intralipid: A phantom medium for light propagation studies," Lasers Surg. Med., Vol. 12, 510-519 (1992).
[CrossRef]

H. Dehghani, D. T. Delpy and S. R. Arridge, "Photon migration in non-scattering tissue and the effects on image reconstruction," Phys. Med. Biol. 44, 2897-2906 (1999).
[CrossRef]

R. L. Barbour, H.L. Graber, Y. Pei, S. Zhong, and C.H. Schmitz, "Optical tomographic imaging of dynamic features of dense scattering media," J. Opt. Soc. Am. A, in press (2001).
[CrossRef]

H. L. Graber, Y. Pei and R. L. Barbour, "Imaging of spatiotemporal coincident states by dynamic optical tomography," Proc. SPIE 4250, San Jose, CA, in press, (2001).

G. Landis, S. Blattman, T. Panetta, C. H. Schmitz, H. L. Graber. Y. Pei, and R. L. Barbour, "Clinical applications of dynamic optical tomography in vascular disease," Proc. SPIE 4250, San Jose, CA, in press, (2001).

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]

Y. Xu, N. Iftimia, H. Jiang, L. Key, M. Bolster, "Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography," Opt. Express 8, 447-451 (2001), http://www.opticsexpress.org/oearchive/source/30565.htm
[CrossRef] [PubMed]

B.J. Hoenders, "Existence of invisible nonscattering objects and nonradiating sources," J. Opt. Soc. Am. A 14, 262-266, (1997).
[CrossRef]

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

Supplementary Material (18)

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Figures (6)

Figure 1.
Figure 1.

Target geometry and source–detector configuration for simulation cases.

Figure 2.
Figure 2.

Original and reconstructed profiles for the target medium considered (7 types). Rows one and two are the original and reconstructed profiles for δµa , respectively; rows three and four are the corresponding original and reconstructed D profiles, respectively. Color scale indicates amplitude of perturbation.

Figure 3.
Figure 3.

Experimental phantom cases 1, 2, 3, and 4.

Figure 4.
Figure 4.

The reconstructed diffusion (top row) and absorption (bottom row) profiles for (left to right) cases one through four. Click on figure with mouse to see movie (<1.2 Mb for each). [Media 1] [Media 2] [Media 3] [Media 4] [Media 5] [Media 6] [Media 7] [Media 8]

Figure 5.
Figure 5.

Reconstructed diffusion (top row) and absorption (bottom row) profiles for experimental case one using standard CGD method only (column one), CGD method with range constraints (column two), CGD method with weight matrix scaling (column three) and CGD method with range constraints and matrix scaling (column four). Click on figure with mouse to see movie (<1.2 Mb for each). [Media 9] [Media 10] [Media 11] [Media 12] [Media 13] [Media 14] [Media 15] [Media 16]

Figure 6.
Figure 6.

Weight functions corresponding to source–detector pairs with source 1 and detectors 1 to 16 for absorption (A and B) and diffusion (C and D) coefficients, before (A and C) and after (B and D) applying matrix scaling. Click on figure with mouse to see movie (<0.5 Mb for each). [Media 17] [Media 18]

Equations (10)

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

· [ D ( r ) u ( r ) ] μ a ( r ) u ( r ) = δ ( r r s ) , r Λ
W r ( μ a ) · δ μ a + W r ( D ) · δ D = δ u r ,
( δ u r ) i = ( ( u 1 ) i ( u 2 ) i ( u 2 ) i ) ( u r ) i , i = 1 , 2 , , M .
W ˜ r ( k ) = W r ( k ) · R ( k ) ,
( R ( k ) ) i j = { 1 1 M Σ m = 1 M ( W r ( k ) ) m j j = i , 0 j i , i , j = 1 , 2 , , N ,
W ˜ r ( μ a ) · δ μ ˜ a + W ˜ r ( D ) · δ D ˜ = δ u r ,
E = 1 2 ( W ˜ r · δ x ˜ δ u r ) T ( W ˜ r · δ x ˜ δ u r ) = 1 2 δ x ˜ T · A · δ x ˜ b T · δ x ˜ + 1 2 δ u r T · δ u r ,
g ( δ x ˜ ) = E ( δ x ˜ ) = A · δ x ˜ b = 0
δ x ˜ ( n ) = δ x ˜ ( n 1 ) α ( n ) d ( n ) .
δ μ a = R ( μ a ) · δ μ ˜ a , δ D = R ( D ) · δ D ˜ .

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