## Improvement of absorption and scattering discrimination by selection of sensitive points on temporal profile in diffuse optical tomography |

Optics Express, Vol. 19, Issue 13, pp. 12843-12854 (2011)

http://dx.doi.org/10.1364/OE.19.012843

Acrobat PDF (1233 KB)

### Abstract

We present a new method allowing the reconstruction of 3D time-domain diffuse optical tomography images, based on the time-dependent diffusion equation and an iterative algorithm (ART) using specific points on the temporal profiles. The first advantage of our method versus the full time-resolved scheme consists in considerably reducing the inverse problem resolution time. Secondly, in the presence of scattering heterogeneities, our method provides images of better quality comparatively to classical methods using full-time data or the first moments of the profiles.

© 2011 OSA

## 1. Introduction

1. B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. **35**(6), 2443–2451 (2008). [CrossRef] [PubMed]

2. J. C. Hebden, “Advances in optical imaging of the newborn infant brain,” Psychophysiology **40**(4), 501–510 (2003). [CrossRef] [PubMed]

3. V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. **23**(3), 313–320 (2005). [CrossRef] [PubMed]

5. A. G. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today **48**(3), 34–40 (1995). [CrossRef]

6. X. Intes and B. Chance, “Non-PET functional imaging techniques: optical,” Radiol. Clin. North Am. **43**(1), 221–234 (2005). [CrossRef] [PubMed]

8. Y. Lin, G. Lech, S. Nioka, X. Intes, and B. Chance, “Noninvasive, low-noise, fast imaging of blood volume and deoxygenation changes in muscles using light-emitting diode continuous-wave imager,” Rev. Sci. Instrum. **73**(8), 3065–3074 (2002). [CrossRef]

9. S. B. Colak, D. G. Papaioannou, G. W. ’t Hooft, M. B. van der Mark, H. Schomberg, J. C. Paasschens, J. B. Melissen, and N. A. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. **36**(1), 180–213 (1997). [CrossRef] [PubMed]

12. H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. **70**(9), 3595–3602 (1999). [CrossRef]

13. S. R. Arridge, M. Schweiger, and D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” Proc. SPIE **1767**, 372–383 (1992). [CrossRef]

17. M. Torregrossa, C. V. Zint, and P. Poulet, “Effects of prior MRI information on image reconstruction in diffuse optical tomography,” Proc. SPIE **5143**, 29–40 (2003). [CrossRef]

14. M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. **44**(7), 1699–1717 (1999). [CrossRef] [PubMed]

14. M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. **44**(7), 1699–1717 (1999). [CrossRef] [PubMed]

18. H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. **25**(6), 711–732 (2009). [CrossRef]

14. M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. **44**(7), 1699–1717 (1999). [CrossRef] [PubMed]

15. F. Gao, P. Poulet, and Y. Yamada, “Simultaneous mapping of absorption and scattering coefficients from a three-dimensional model of time-resolved optical tomography,” Appl. Opt. **39**(31), 5898–5910 (2000). [CrossRef]

23. V. Venugopal, J. Chen, and X. Intes, “Development of an optical imaging platform for functional imaging of small animals using widefield excitation,” Biomed. Opt. Express **1**(1), 143–156 (2010). [CrossRef]

## 2. Method - the studied phantom

24. F. Nouizi, R. Chabrier, M. Torregrossa, and P. Poulet, “3D modeling for solving forward model of no-contact fluorescence diffuse optical tomography method,” Proc. SPIE **7369**, 73690C (2009). [CrossRef]

_{a}= 0.005 mm

^{−1}, µ

_{s}’ = 0.6 mm

^{−1}. The cylinder contained 2 rods, 5 mm in diameter and centered on:

## 3. DOT forward model

### 3.1 Photon transport model

*P*1 approximation to the radiative transfer equation, is an efficient model of light transport in scattering media [20

20. A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging **18**(3), 262–271 (1999). [CrossRef] [PubMed]

25. S. R. Arridge, “Photon-measurement density functions. Part I: analytical forms,” Appl. Opt. **34**(31), 7395–7409 (1995). [CrossRef] [PubMed]

27. F. Gao, H. Zhao, L. Zhang, Y. Tanikawa, A. Marjono, and Y. Yamada, “A self-normalized, full time-resolved method for fluorescence diffuse optical tomography,” Opt. Express **16**(17), 13104–13121 (2008). [CrossRef] [PubMed]

_{a}, the absorption coefficient and κ the diffusion coefficient, κ = c/3(μ

_{a}+ μ

_{s}’) with µ

_{s}’ being the reduced scattering coefficient and c the speed of light in the medium. δ(t, r

_{0}) is the Dirac pulse modeling the isotropic sources positioned under the irradiated surface of the studied object, at a distance from the surface imposed by the approximation to DE and equal to 1/µ

_{s}’.

27. F. Gao, H. Zhao, L. Zhang, Y. Tanikawa, A. Marjono, and Y. Yamada, “A self-normalized, full time-resolved method for fluorescence diffuse optical tomography,” Opt. Express **16**(17), 13104–13121 (2008). [CrossRef] [PubMed]

24. F. Nouizi, R. Chabrier, M. Torregrossa, and P. Poulet, “3D modeling for solving forward model of no-contact fluorescence diffuse optical tomography method,” Proc. SPIE **7369**, 73690C (2009). [CrossRef]

### 3.2 Generation of simulated measurement data sets

_{a},μ’

_{s}} and using a mesh finer than the one described in section 2 (23242 nodes, 149545 tetrahedral elements). The data set consisted of the theoretical temporal profiles Γ

_{s,d}(t) obtained using the Comsol Multiphysics

^{®}time-dependent solver for the 112 source-detector pairs obtained with 16 sources and 7 detectors per source at the model surface.

## 4. DOT inverse problem

_{a},μ

_{s}’} from the measured TPSF, for a given distribution of light sources and detectors.

_{a},μ’

_{s}] were iteratively updated using:with

*J*being the Jacobian matrix corresponding to the data type

^{(D)}*D,*and λ the relaxation parameter proven in the range {0,2} [15

15. F. Gao, P. Poulet, and Y. Yamada, “Simultaneous mapping of absorption and scattering coefficients from a three-dimensional model of time-resolved optical tomography,” Appl. Opt. **39**(31), 5898–5910 (2000). [CrossRef]

*D*are presented below:

### 4.1 Method 1: optimization using the time-weighted moments

*Arridge et al*[13

13. S. R. Arridge, M. Schweiger, and D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” Proc. SPIE **1767**, 372–383 (1992). [CrossRef]

**44**(7), 1699–1717 (1999). [CrossRef] [PubMed]

### 4.2 Method 2: optimization using a large number of points of the TPSF

### 4.3 Method 3: optimization using a reduced number of points of the TPSF

_{a_new}= μ

_{a_old}+ ∆μ

_{a}) or the reduced scattering coefficient (μ

_{s}’

_{_new}= μ

_{s}’

_{_old}+ ∆μ

_{s}’). This method is inspired from the idea that the contrast obtained by late gating of the TPSF is more sensitive to absorption heterogeneities than early gating contrast [30

30. A. H. Gandjbakhche, R. F. Bonner, R. Nossal, and G. H. Weiss, “Absorptivity contrast in transillumination imaging of tissue abnormalities,” Appl. Opt. **35**(10), 1767–1774 (1996). [CrossRef] [PubMed]

33. R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Imaging with diffusing light: an experimental study of the effect of background optical properties,” Appl. Opt. **37**(16), 3564–3573 (1998). [CrossRef]

23. V. Venugopal, J. Chen, and X. Intes, “Development of an optical imaging platform for functional imaging of small animals using widefield excitation,” Biomed. Opt. Express **1**(1), 143–156 (2010). [CrossRef]

_{i}(i = 1, 2, 3) computed using different {µ

_{ai},µ

_{si}’} with µ

_{a2}≠ µ

_{a1}= µ

_{a3}, and µ

_{s3}’ ≠ µ

_{s1}’ = µ

_{s2}’, enable point-to-point comparisons. Figure 2 (left) shows the influence of the TPSF due to an increase of 50% of μ

_{a}or μ

_{s}’. Indeed, using TPSF

_{1}as a reference, one can observe that varying μ

_{s}’ causes the rising edge of TPSF

_{3}to shift more than that of TPSF

_{2}. Information about a change in µ

_{a}in the medium is better extracted from the tail of the TPSF, since presented with logarithm scale, the slope of this tail is independent from µ

_{s}’ and proportional to µ

_{a}only.

_{s}’ or Δμ

_{a}, respectively. This method reduces the number of considered points by 81% compared to method 2. In fact, the inverse problem is solved by using only 3 points chosen on the rising edge at 20%, 50% and 80% of the maximum amplitude of the profile when reconstructing µ

_{s}’ images, and only 4 points on the profile tail, selected at 10%, 20%, 50% and 80% of the maximum amplitude, when reconstructing µ

_{a}images, as shown in Fig. 2 (right).

_{s}’, and points on the tail of the TPSF when reconstructing µ

_{a}can also be justified with a theoretical model of light propagation. We used the Patterson equation R(t,µ

_{a},µ

_{s}’) for an infinite medium [34

34. M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. **28**(12), 2331–2336 (1989). [CrossRef] [PubMed]

_{a}, multiplied by µ

_{a}, (∂R/∂µ

_{a}).µ

_{a}, is equal to its partial derivative with respect to µ

_{s}’, multiplied by µ

_{s}’, (∂R/∂µ

_{s}’).µ

_{s}’, at a time which is always very close from that of the maximum of the TPSF. The choice of the amplitude of the individual points was mainly done by considering their time separation and the signal to noise ratio to get valuable information. The optimal number of points was experimentally found to be seven. Using more points did not improve significantly the quality of the reconstructed images but using fewer points degrades it drastically.

## 5. Results and discussion

### 5.1 Simulated data sets

_{0}(x = z = 0 mm, y = −14 mm), corresponding to an isotropic source positioned at 1/µ

_{s}’ under r

_{0}: (x = z = 0 mm and y = −12.33 mm).

^{5}photons.

### 5.2 Reconstruction results

#### 5.2.1 Phantom object_1

22. F. Gao, H. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. **41**(4), 778–791 (2002). [CrossRef] [PubMed]

27. F. Gao, H. Zhao, L. Zhang, Y. Tanikawa, A. Marjono, and Y. Yamada, “A self-normalized, full time-resolved method for fluorescence diffuse optical tomography,” Opt. Express **16**(17), 13104–13121 (2008). [CrossRef] [PubMed]

_{s}’ is usually set to naught and Eq. (8) is used to compute Δµ

_{a}only. However,

*in-vivo*tissues exhibit heterogeneous scattering coefficients so that Δµ

_{s}’ must be computed (Δµ

_{s}’ ≠ 0).

_{s}’ ≠ 0. We can clearly notice that the algorithm diverges. The reconstructed µ

_{a}map is totally false and thus the position of the rods is not localized. The reconstructed µ

_{s}’ presented on Fig. 4 (bottom right) shows that the algorithm is able to detect the position of two rods but is not able to estimate the correct values. However, the attenuation of light traveling through the object is not only interpreted as increased absorption but also as increased scattering (crosstalk) which distorts the absorption map (0,58 mm

^{−1}<µ

_{s}'<0,76 mm

^{−1}). Hence, to obtain acceptable results, Δµ

_{s}’ is set to naught when reconstructing objects which contain only absorbing heterogeneities.

_{a}and µ

_{s}’ maps obtained on the numerical phantom object_1 using the three reconstruction methods. According to the results presented on Fig. 5 (left), we notice that method 1 (0,58<µ

_{s}’<0,61) and method 3 (0,59<µ

_{s}’<0,6) are stable when reconstructing µ

_{s}’ unlike method 2 (µ

_{s}’ has to be null). Figure 5 (right) shows that the three methods yield almost the same result when reconstructing µ

_{a}. As cited in subsection 4.3, method 3 allows to solve the inverse problem by using 7 points on the profiles. This method reduces reconstruction time by approximately 67% compared to method 2.

_{data}to compare reconstructed images and the true data in order to evaluate the three methods, defined by Eq. (9):with

*P*being the number of pixels in the region of interest (ROI). The ROI can be either background, target or bleed-through. In a given image type (µ

_{a}or µ

_{s}’) the target is defined as the region having that coefficient different from the background. The bleed-through is defined as the region with the other coefficient different from the background. The E

_{data}parameter computed either on the background or the target is called error and the E

_{data}computed on the bleed-through is called crosstalk.

_{s}’ images and method 3 is more accurate than method 1. Figure 6 (left,right) shows the profiles along the z-axis of the reconstructed µ

_{a}and μ

_{s}’ presented on Fig. 5, respectively.

_{a}than either method 1 or 3. The reconstructed µ

_{a}using method 1 and 3 look similar but method 3 shows a better stability when reconstructing µ

_{s}’. In fact, the small increase in the reconstructed µ

_{s}’ is centered on the rods (C1,C2) owing to crosstalk.

#### 5.2.2 Phantom object_2

_{s}’ was not set to naught and computed using Eq. (8). The µ

_{a}and µ

_{s}’ maps reconstructed using method 1, 2 and 3 are presented in Fig. 7 .

^{−1}.

_{s}’ images and the bleed-through in the µ

_{a}images. The cylinder C2 is the target in the reconstructed µ

_{a}images and the bleed-through in the µ

_{s}’ images. The background is chosen to be C-(C1 + C2).

_{a}and μ

_{s}’ maps, presented on Fig. 7, respectively. These profiles show clearly that methods 1 and 3 provided more accurate reconstructions than method 2, in both cases owing to the detection of the more scattering rod. In fact, at the first iteration, method 2 fostered absorption in both rods. Thus, light attenuation was interpreted as increased absorption rather than scattering and huge crosstalk between absorption and scattering was observed.

_{a}and µ

_{s}’.

## 6. Conclusion

23. V. Venugopal, J. Chen, and X. Intes, “Development of an optical imaging platform for functional imaging of small animals using widefield excitation,” Biomed. Opt. Express **1**(1), 143–156 (2010). [CrossRef]

35. V. Venugopal, J. Chen, F. Lesage, and X. Intes, “Full-field time-resolved fluorescence tomography of small animals,” Opt. Lett. **35**(19), 3189–3191 (2010). [CrossRef] [PubMed]

24. F. Nouizi, R. Chabrier, M. Torregrossa, and P. Poulet, “3D modeling for solving forward model of no-contact fluorescence diffuse optical tomography method,” Proc. SPIE **7369**, 73690C (2009). [CrossRef]

## Acknowledgments

## References and links

1. | B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. |

2. | J. C. Hebden, “Advances in optical imaging of the newborn infant brain,” Psychophysiology |

3. | V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. |

4. | W. G. Egan and T. W. Hilgeman, |

5. | A. G. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today |

6. | X. Intes and B. Chance, “Non-PET functional imaging techniques: optical,” Radiol. Clin. North Am. |

7. | F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science |

8. | Y. Lin, G. Lech, S. Nioka, X. Intes, and B. Chance, “Noninvasive, low-noise, fast imaging of blood volume and deoxygenation changes in muscles using light-emitting diode continuous-wave imager,” Rev. Sci. Instrum. |

9. | S. B. Colak, D. G. Papaioannou, G. W. ’t Hooft, M. B. van der Mark, H. Schomberg, J. C. Paasschens, J. B. Melissen, and N. A. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. |

10. | H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A |

11. | M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite-element method for the forward and inverse models in optical tomography,” J. Math. Imaging Vis. |

12. | H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. |

13. | S. R. Arridge, M. Schweiger, and D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” Proc. SPIE |

14. | M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. |

15. | F. Gao, P. Poulet, and Y. Yamada, “Simultaneous mapping of absorption and scattering coefficients from a three-dimensional model of time-resolved optical tomography,” Appl. Opt. |

16. | E. M. C. Hillman, J. C. Hebden, F. E. R. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, and D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. |

17. | M. Torregrossa, C. V. Zint, and P. Poulet, “Effects of prior MRI information on image reconstruction in diffuse optical tomography,” Proc. SPIE |

18. | H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. |

19. | R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, and R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” Proc. SPIE |

20. | A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging |

21. | R. Model, M. Orlt, M. Walzel, and R. Hünlich, “Reconstruction algorithm for near-infrared imaging in turbid media by means of timedomain data,” J. Opt. Soc. Am. A |

22. | F. Gao, H. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. |

23. | V. Venugopal, J. Chen, and X. Intes, “Development of an optical imaging platform for functional imaging of small animals using widefield excitation,” Biomed. Opt. Express |

24. | F. Nouizi, R. Chabrier, M. Torregrossa, and P. Poulet, “3D modeling for solving forward model of no-contact fluorescence diffuse optical tomography method,” Proc. SPIE |

25. | S. R. Arridge, “Photon-measurement density functions. Part I: analytical forms,” Appl. Opt. |

26. | S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. |

27. | F. Gao, H. Zhao, L. Zhang, Y. Tanikawa, A. Marjono, and Y. Yamada, “A self-normalized, full time-resolved method for fluorescence diffuse optical tomography,” Opt. Express |

28. | W. Becker, |

29. | G. T. Herman, |

30. | A. H. Gandjbakhche, R. F. Bonner, R. Nossal, and G. H. Weiss, “Absorptivity contrast in transillumination imaging of tissue abnormalities,” Appl. Opt. |

31. | A. H. Gandjbakhche, V. Chernomordik, J. C. Hebden, and R. Nossal, “Time-dependent contrast functions for quantitative imaging in time-resolved transillumination experiments,” Appl. Opt. |

32. | R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Imaging of optical inhomogeneities in highly diffusive media: Discrimination between scattering and absorption contributions,” Appl. Phys. Lett. |

33. | R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Imaging with diffusing light: an experimental study of the effect of background optical properties,” Appl. Opt. |

34. | M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. |

35. | V. Venugopal, J. Chen, F. Lesage, and X. Intes, “Full-field time-resolved fluorescence tomography of small animals,” Opt. Lett. |

**OCIS Codes**

(100.3190) Image processing : Inverse problems

(170.3660) Medical optics and biotechnology : Light propagation in tissues

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(170.6920) Medical optics and biotechnology : Time-resolved imaging

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: May 9, 2011

Revised Manuscript: June 3, 2011

Manuscript Accepted: June 7, 2011

Published: June 17, 2011

**Virtual Issues**

Vol. 6, Iss. 7 *Virtual Journal for Biomedical Optics*

**Citation**

Farouk Nouizi, Murielle Torregrossa, Renee Chabrier, and Patrick Poulet, "Improvement of absorption and scattering discrimination by selection of sensitive points on temporal profile in diffuse optical tomography," Opt. Express **19**, 12843-12854 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-13-12843

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### References

- B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. 35(6), 2443–2451 (2008). [CrossRef] [PubMed]
- J. C. Hebden, “Advances in optical imaging of the newborn infant brain,” Psychophysiology 40(4), 501–510 (2003). [CrossRef] [PubMed]
- V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005). [CrossRef] [PubMed]
- W. G. Egan and T. W. Hilgeman, Optical Properties of Inhomogeneous Materials (Academic, 1979).
- A. G. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995). [CrossRef]
- X. Intes and B. Chance, “Non-PET functional imaging techniques: optical,” Radiol. Clin. North Am. 43(1), 221–234 (2005). [CrossRef] [PubMed]
- F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977). [CrossRef] [PubMed]
- Y. Lin, G. Lech, S. Nioka, X. Intes, and B. Chance, “Noninvasive, low-noise, fast imaging of blood volume and deoxygenation changes in muscles using light-emitting diode continuous-wave imager,” Rev. Sci. Instrum. 73(8), 3065–3074 (2002). [CrossRef]
- S. B. Colak, D. G. Papaioannou, G. W. ’t Hooft, M. B. van der Mark, H. Schomberg, J. C. Paasschens, J. B. Melissen, and N. A. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36(1), 180–213 (1997). [CrossRef] [PubMed]
- H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13(2), 253–266 (1996). [CrossRef]
- M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite-element method for the forward and inverse models in optical tomography,” J. Math. Imaging Vis. 3(3), 263–283 (1993). [CrossRef]
- H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70(9), 3595–3602 (1999). [CrossRef]
- S. R. Arridge, M. Schweiger, and D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” Proc. SPIE 1767, 372–383 (1992). [CrossRef]
- M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44(7), 1699–1717 (1999). [CrossRef] [PubMed]
- F. Gao, P. Poulet, and Y. Yamada, “Simultaneous mapping of absorption and scattering coefficients from a three-dimensional model of time-resolved optical tomography,” Appl. Opt. 39(31), 5898–5910 (2000). [CrossRef]
- E. M. C. Hillman, J. C. Hebden, F. E. R. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, and D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71(9), 3415–3427 (2000). [CrossRef]
- M. Torregrossa, C. V. Zint, and P. Poulet, “Effects of prior MRI information on image reconstruction in diffuse optical tomography,” Proc. SPIE 5143, 29–40 (2003). [CrossRef]
- H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009). [CrossRef]
- R. L. Barbour, H. L. Graber, Y. Wang, J. H. Chang, and R. Aronson, “A perturbation approach for optical diffusion tomography using continuous-wave and time-resolved data,” Proc. SPIE IS11, 87–120 (1993).
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