## Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis

Optics Express, Vol. 14, Issue 13, pp. 6113-6127 (2006)

http://dx.doi.org/10.1364/OE.14.006113

Acrobat PDF (688 KB)

### Abstract

The image resolution and contrast in Near-Infrared (NIR) tomographic image reconstruction are affected by parameters such as the number of boundary measurements, the mesh resolution in the forward calculation and the reconstruction basis. Increasing the number of measurements tends to make the sensitivity of the domain more uniform reducing the hypersensitivity at the boundary. Using singular-value decomposition (SVD) and reconstructed images, it is shown that the numbers of 16 or 24 fibers are sufficient for imaging the 2D circular domain for the case of 1% noise in the data. The number of useful singular values increases as the logarithm of the number of measurements. For this 2D reconstruction problem, given a computational limit of 10 sec per iteration, leads to choice of forward mesh with 1785 nodes and reconstruction basis of 30×30 elements. In a three-dimensional (3D) NIR imaging problem, using a single plane of data can provide useful images if the anomaly to be reconstructed is within the measurement plane. However, if the location of the anomaly is not known, 3D data collection strategies are very important. Further the quantitative accuracy of the reconstructed anomaly increased approximately from 15% to 89% as the anomaly is moved from the centre to boundary, respectively. The data supports the exclusion of out of plane measurements may be valid for 3D NIR imaging.

© 2006 Optical Society of America

## 1. Introduction

1. D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. **18**, 57–75 (2001). [CrossRef]

3. S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. U.S.A. **100**, 12349–12354 (2003). [CrossRef] [PubMed]

1. D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. **18**, 57–75 (2001). [CrossRef]

4. J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. **42**, 4155–4166 (2002). [CrossRef]

5. N. Ramanujam, G. Vishnoi, A. H. Hielscher, M. E. Rode, I. Forouzan, and B. Chance, “Photon migration through fetal head in utero using continuous wave, near infrared spectroscopy: clinical and experimental model studies,” J. Biomed. Opt. **5**, 173–184 (2000). [CrossRef] [PubMed]

6. S. R. Arridge, “Optical tomography in medical imaging,” Inv. Problems **5**, R41–R93 (1999). [CrossRef]

7. N. Polydorides1 and H. McCann, “Electrode configurations for improved spatial resolution in electrical impedance tomography,” Meas. Sci. Technol. **13**, 1862–1870 (2002). [CrossRef]

4. J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. **42**, 4155–4166 (2002). [CrossRef]

12. H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three dimensional near infrared tomography of the breast: Initial simulation, phantom and clinical results,” App. Opt. **42**, 135–145 (2003). [CrossRef]

17. A. Gibson, R. M. Yusof, E. M. C. Hillman, H. Dehghani, J. Riley, N. Everdale, R. Richards, J. C. Hebden, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Optical tomography of a realistic neonatal head phantom,” Appl. Opt. **42**, 3109–3116 (2003). [CrossRef] [PubMed]

18. J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. **30**, 235–247 (2003). [CrossRef] [PubMed]

## 2. Methods

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

*r,ω*) is the photon density at position r and modulation frequency

*ω*(100 MHz in this work), and κ=1/[3(µ

_{a}+µ

^{/}

*)], the diffusion coefficient, where µ*

_{s}_{a}and µ/

_{s}are the probabilities per unit length of absorption and transport scattering, respectively, and

*q*is an isotropic source term. The Robin (Type III) boundary condition is used which best describes the light interaction from a scattering medium to the external air boundary [20

_{0}(r,ω)20. M. Schweiger, S R Arridge, M Hiroaka, and D T Delpy, “The finite element model for the propagation of light in scattering media: Boundary and source Conditions,” Med. Phys. **22**, 1779–1792 (1995). [CrossRef] [PubMed]

*J*section is considered (dimension of (S×D) by N), which maps a small change in the absorption coefficient to a small change in measured log intensity of the signal. Since all kernels of the complete Jacobian show similar results, the discussion is limited to the results of

_{2}*J*, and shall henceforth be referred to as J.

_{2}_{a}, which is an iterative procedure [10

10. H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt. **8**, 102–110 (2003). [CrossRef] [PubMed]

_{a}] is an update vector for the absorption coefficient,

**I**is the identity matrix and λ is a regularization parameter. Also,

**b**=[y-ℱ(µ

_{a})], where y is the measured (or simulated) heterogeneous boundary data and ℱ(µ

_{a}) is the forward data for the current estimate of µ

_{a}. In all of the presented work using simulated data, 1% noise was added to the amplitude, which is a typical noise observed in experimental data [2

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

_{a}=0.01 mm

^{-1}and µ/

*=1.0 mm*

_{s}^{-1}is considered. The light collection/delivery fibers are arranged in a circular equally spaced fashion, where one fiber is used as the source while all other fibers are used as detectors, to give ‘P’ number of measurements (where P=M(M-1), where M is number of fibers). The source is a Gaussian source of Full Width Half Maximum (FWHM) of 3mm, and it is placed one transport scattering length within the external boundary.

_{a}=0.01 mm

^{-1}and µ/s=1 mm

^{-1}is used (Fig. 1). The light collection/delivery fibers are arranged in a circular and equally spaced fashion and are in either a single plane of 16 fibers or 3 planes of 16 fibers per plane, totaling 48 fibers. Specifically three different strategies for data collection are considered:

### 2.1. 2D Mesh Resolution

### 2.2. Singular-Value (SV) analysis

10. H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt. **8**, 102–110 (2003). [CrossRef] [PubMed]

22. B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast”, Rev. Sci. Inst. **75**, 5262–5270 (2004). [CrossRef]

_{a}=0.003 mm

^{-1}and µ/

*=0.95 mm*

_{s}^{-1}and having diameter of 66 mm and fatty layer surrounding it having µ

_{a}=0.006 mm

^{-1}and µ/

*=1.1 mm*

_{s}^{-1}with a thickness of 20mm. The number of useful singular values above the noise level were calculated as the number of measurements was increased. The mesh that was found to have an optimum resolution from the previous analysis of the Jacobian (Sec. 2.1) was used for these analysis. For both these cases, the percentage of useful measurements with respect to total number of measurements was calculated as:

23. M. Schweiger and S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori region boundary information,” Phys. Med. Biol. **44**, 2703–2722 (1999). [CrossRef] [PubMed]

24. H. Jiang, K. D. Paulsen, U. L. Osterberg, and M. Patterson, “Improved continuous light diffusion imaging in single and multiple target tissue-like phantoms,” Phys. Med. Biol. **43**, 675–693 (1998). [CrossRef] [PubMed]

23. M. Schweiger and S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori region boundary information,” Phys. Med. Biol. **44**, 2703–2722 (1999). [CrossRef] [PubMed]

25. Q. Zhu, N. G. Chen, and S. C. Kurtzman, “Imaging tumor angiogenesis by use of combined near-infrared diffusive light and ultrasound,” Opt. Lett. **28**, 337–339 (2003). [CrossRef] [PubMed]

26. M. Molinari, B. H. Blott, S. J. Cox, and G. J. Daniell, “Optimal imaging with adaptive mesh refinement in electrical impedance tomography,” Physiol. Meas. **23**, 121–128 (2002). [CrossRef] [PubMed]

### 2.3. Reconstruction examples

## 3 Results

_{a}distribution, is shown in Fig. 6. The contrast of the inhomogeneity to background is 2:1 and for these reconstructions a pixel basis of 30×30 elements is used, with a forward mesh consisting of 1785 nodes. Figure 7 shows the plot of logarithm of rms error in the horizontal cross-section (as sown by dotted line in Fig. 6) as a function of measurement number. The legend of the figure gives the position of the inhomogeneity (diameter of 10mm).

## 4 Discussion

3. S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. U.S.A. **100**, 12349–12354 (2003). [CrossRef] [PubMed]

*J2*in Eq. (2), has been examined here, images have also been reconstructed for µa using log amplitude data for a 2D forward mesh of 1785 nodes and a reconstruction basis 30 by 30 pixel basis. Noisy simulated data were generated for various radial positions of the absorption inhomogeneity with a contrast of 2, relative to the background and having a diameter of 10 mm. The log of RMS error was calculated as the difference in the original and the reconstructed horizontal cross-sections of each image (Fig. 6) as a function of number of measurements and these were plotted in Fig. 7. The results show that, as evident from Fig. 7, although there is a decrease in the RMS error as the number of measurements is increased, the improvement in the reconstructed images is not significant for measurements greater than 552 (corresponding to 24 fibers). However, for a central anomaly, the RMS error continued to decrease with increasing number of measurements, whereas for an anomaly near the boundary the RMS error does not improve more than 0.5% with respect to 552 measurements.

13. H. Dehghani, B. W. Pogue, J. Shudong, B. Brooksby, and K. D. Paulsen, “Three dimensional optical tomography: Resolution in small object imaging,” App. Opt. **42**, 3117–3128 (2003). [CrossRef]

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

17. A. Gibson, R. M. Yusof, E. M. C. Hillman, H. Dehghani, J. Riley, N. Everdale, R. Richards, J. C. Hebden, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Optical tomography of a realistic neonatal head phantom,” Appl. Opt. **42**, 3109–3116 (2003). [CrossRef] [PubMed]

## 5 Conclusions

## Acknowledgments

## References and links

1. | D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. |

2. | B. W. Pogue, M. Testorf, T. Mcbride, U. L. Osterberg, and K. D. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,”. Opt. Express |

3. | S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography,” Proc. Natl. Acad. Sci. U.S.A. |

4. | J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. |

5. | N. Ramanujam, G. Vishnoi, A. H. Hielscher, M. E. Rode, I. Forouzan, and B. Chance, “Photon migration through fetal head in utero using continuous wave, near infrared spectroscopy: clinical and experimental model studies,” J. Biomed. Opt. |

6. | S. R. Arridge, “Optical tomography in medical imaging,” Inv. Problems |

7. | N. Polydorides1 and H. McCann, “Electrode configurations for improved spatial resolution in electrical impedance tomography,” Meas. Sci. Technol. |

8. | E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A sub-millimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. |

9. | E. E. Graves, J. P. Culver, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Singular-value analysis and optimization of experimental parameters in fluorescence molecular tomography,” J. Opt. Soc. Am. A |

10. | H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt. |

11. | J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: A singular-value analysis,” App. Opt. |

12. | H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three dimensional near infrared tomography of the breast: Initial simulation, phantom and clinical results,” App. Opt. |

13. | H. Dehghani, B. W. Pogue, J. Shudong, B. Brooksby, and K. D. Paulsen, “Three dimensional optical tomography: Resolution in small object imaging,” App. Opt. |

14. | H. Dehghani, B. W. Pogue, S. Jiang, S. Poplack, K. D. Paulsen, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, eds., Proc. SPIE 4955, 191–198 (2003). |

15. | B. W. Pogue, S. Geimer, T. Mcbride, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary conditions and geometry analysis for a finite element reconstruction algorithm,” Appl. Opt. |

16. | J. C. Hebden, H. Veenstra, H. H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Three dimensional time-resolved optical tomography of a conical breast phantom,” App. Opt. |

17. | A. Gibson, R. M. Yusof, E. M. C. Hillman, H. Dehghani, J. Riley, N. Everdale, R. Richards, J. C. Hebden, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Optical tomography of a realistic neonatal head phantom,” Appl. Opt. |

18. | J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. |

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

20. | M. Schweiger, S R Arridge, M Hiroaka, and D T Delpy, “The finite element model for the propagation of light in scattering media: Boundary and source Conditions,” Med. Phys. |

21. | S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part2: Finite-element-method calculations,” App. Opt. |

22. | B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, “Magnetic resonance guided near infrared tomography of the breast”, Rev. Sci. Inst. |

23. | M. Schweiger and S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori region boundary information,” Phys. Med. Biol. |

24. | H. Jiang, K. D. Paulsen, U. L. Osterberg, and M. Patterson, “Improved continuous light diffusion imaging in single and multiple target tissue-like phantoms,” Phys. Med. Biol. |

25. | Q. Zhu, N. G. Chen, and S. C. Kurtzman, “Imaging tumor angiogenesis by use of combined near-infrared diffusive light and ultrasound,” Opt. Lett. |

26. | M. Molinari, B. H. Blott, S. J. Cox, and G. J. Daniell, “Optimal imaging with adaptive mesh refinement in electrical impedance tomography,” Physiol. Meas. |

**OCIS Codes**

(100.3190) Image processing : Inverse problems

(170.0170) Medical optics and biotechnology : Medical optics and biotechnology

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

(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine

(170.7050) Medical optics and biotechnology : Turbid media

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: May 3, 2006

Revised Manuscript: June 19, 2006

Manuscript Accepted: June 20, 2006

Published: June 26, 2006

**Virtual Issues**

Vol. 1, Iss. 7 *Virtual Journal for Biomedical Optics*

**Citation**

Phaneendra K. Yalavarthy, Hamid Dehghani, Brian W. Pogue, and Keith D. Paulsen, "Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis," Opt. Express **14**, 6113-6127 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-13-6113

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### References

- D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Signal Process. Mag. 18, 57-75 (2001). [CrossRef]
- B. W. Pogue, M. Testorf, T. Mcbride, U. L. Osterberg, and K. D. Paulsen, "Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,".Opt. Express 1, 391-403 (1997). [CrossRef] [PubMed]
- S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, "Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in vivo by near-infrared breast tomography," Proc. Natl. Acad. Sci. U.S.A. 100,12349-12354 (2003). [CrossRef] [PubMed]
- J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, "Three-dimensional optical tomography of the premature infant brain," Phys. Med. Biol. 42, 4155-4166 (2002). [CrossRef]
- N. Ramanujam, G. Vishnoi, A. H. Hielscher, M. E. Rode, I. Forouzan and B. Chance, "Photon migration through fetal head in utero using continuous wave, near infrared spectroscopy: clinical and experimental model studies," J. Biomed. Opt. 5, 173-184 (2000). [CrossRef] [PubMed]
- S. R. Arridge, "Optical tomography in medical imaging," Inv.Problems 5, R41-R93 (1999). [CrossRef]
- N. Polydorides1 and H. McCann, "Electrode configurations for improved spatial resolution in electrical impedance tomography," Meas. Sci. Technol. 13, 1862-1870 (2002). [CrossRef]
- E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A sub-millimeter resolution fluorescence molecular imaging system for small animal imaging," Med. Phys. 30, 901-911 (2003). [CrossRef] [PubMed]
- E. E. Graves, J. P. Culver, J. Ripoll, R. Weissleder, and V. Ntziachristos, "Singular-value analysis and optimization of experimental parameters in fluorescence molecular tomography," J. Opt. Soc. Am. A 21, 231-241 (2004). [CrossRef]
- H. Xu, H. Dehghani, B. W. Pogue, R. Springett, K. D. Paulsen and J. F. Dunn, "Near-infrared imaging in the small animal brain: optimization of fiber positions," J. Biomed. Opt. 8, 102-110 (2003). [CrossRef] [PubMed]
- J. P. Culver, V. Ntziachristos, M. J. Holboke and A. G. Yodh, "Optimization of optode arrangements for diffuse optical tomography: A singular-value analysis," App. Opt. 26, 701-703 (2001).
- H. Dehghani, B. W. Pogue S. P. Poplack and K. D. Paulsen, "Multiwavelength three dimensional near infrared tomography of the breast: Initial simulation, phantom and clinical results," App. Opt. 42, 135-145 (2003). [CrossRef]
- H. Dehghani, B. W. Pogue, J. Shudong, B. Brooksby, and K. D. Paulsen, "Three dimensional optical tomography: Resolution in small object imaging," App. Opt. 42, 3117-3128 (2003). [CrossRef]
- H. Dehghani, B. W. Pogue, S. Jiang, S. Poplack and K. D. Paulsen, "Optical images from Pathophysiological signals within breast tissue using three-dimensional near-infrared light," in Optical Tomography and Spectroscopy of Tissue V, B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, eds., Proc. SPIE 4955, 191-198 (2003).
- B. W. Pogue, S. Geimer, T. Mcbride, S. Jiang, U. L. Osterberg, and K. D. Paulsen, "Three-dimensional simulation of near-infrared diffusion in tissue: boundary conditions and geometry analysis for a finite element reconstruction algorithm," Appl. Opt. 40, 588-600 (2001). [CrossRef]
- J. C. Hebden, H. Veenstra, H. H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, "Three dimensional time-resolved optical tomography of a conical breast phantom," App. Opt. 40, 3278-3287 (2001). [CrossRef]
- A. Gibson, R. M. Yusof, E. M. C. Hillman, H. Dehghani, J. Riley, N. Everdale, R. Richards, J. C. Hebden, M. Schweiger, S. R. Arridge, and D. T. Delpy, "Optical tomography of a realistic neonatal head phantom," Appl. Opt. 42, 3109-3116 (2003). [CrossRef] [PubMed]
- J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance and A. G. Yodh, "Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging," Med. Phys. 30, 235-247 (2003). [CrossRef] [PubMed]
- H. Jiang, K. D. Paulsen, and U. Osterberg, B. W. Pogue and MichaelS. Patterson, "Optical image reconstruction using frequency domain data: simulations and experiments," J. Opt. Soc. Am. A 13, 253-266 (1996). [CrossRef]
- M. Schweiger, S R Arridge, M Hiroaka and D T Delpy, "The finite element model for the propagation of light in scattering media: Boundary and source Conditions," Med. Phys. 22, 1779-1792 (1995). [CrossRef] [PubMed]
- S. R. Arridge and M. Schweiger, "Photon-measurement density functions. Part2: Finite-element-method calculations," App. Opt. 34, 8026-8037 (1995). [CrossRef]
- B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W Pogue, and K. D Paulsen, "Magnetic resonance guided near infrared tomography of the breast", Rev. Sci. Inst. 75, 5262-5270 (2004). [CrossRef]
- M. Schweiger and S. R. Arridge, "Optical tomographic reconstruction in a complex head model using a priori region boundary information," Phys. Med. Biol. 44, 2703-2722 (1999). [CrossRef] [PubMed]
- H. Jiang, K. D. Paulsen, U. L. Osterberg, and M. Patterson, "Improved continuous light diffusion imaging in single and multiple target tissue-like phantoms," Phys. Med. Biol. 43, 675-693 (1998). [CrossRef] [PubMed]
- Q. Zhu, N. G. Chen, and S. C. Kurtzman, "Imaging tumor angiogenesis by use of combined near-infrared diffusive light and ultrasound," Opt. Lett. 28, 337 - 339 (2003). [CrossRef] [PubMed]
- M. Molinari, B. H. Blott, S. J. Cox, and G. J. Daniell, "Optimal imaging with adaptive mesh refinement in electrical impedance tomography," Physiol. Meas. 23, 121-128 (2002). [CrossRef] [PubMed]

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