Abstract

In this study, we first propose the use of edge-preserving regularization in optimizing an ill-conditioned problem in the reconstruction procedure for diffuse optical tomography to prevent unwanted edge smoothing, which usually degrades the attributes of images for distinguishing tumors from background tissues when using Tikhonov regularization. In the edge-preserving regularization method presented here, a potential function with edge-preserving properties is introduced as a regularized term in an objective function. With the minimization of this proposed objective function, an iterative method to solve this optimization problem is presented in which half-quadratic regularization is introduced to simplify the minimization task. Both numerical and experimental data are employed to justify the proposed technique. The reconstruction results indicate that edge-preserving regularization provides a superior performance over Tikhonov regularization.

© 2012 Optical Society of America

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    [CrossRef]

2009

B. Brendel and T. Nielsen, “Selection of optimal wavelengths for spectral reconstruction in diffuse optical tomography,” J. Biomed. Opt. 14, 034041 (2009).
[CrossRef] [PubMed]

P. Hiltunen, S. J. D. Prince, and S. Arridge, “A combined reconstruction–classification method for diffuse optical tomography,” Phys. Med. Biol. 54, 6457–6476 (2009).
[CrossRef] [PubMed]

M. C. Pan, C. H. Chen, M. C. Pan, and Y. M. Shyr, “Near infrared tomographic system based on high angular resolution mechanism—design, calibration, and performance,” Measurement 42, 377–389 (2009).
[CrossRef]

2008

H. Niu, P. Guo, L. Ji, Q. Zhao, and T. Jiang, “Improving image quality of diffuse optical tomography with a projection-error-based adaptive regularization method,” Opt. Express 16, 12423–12434 (2008).
[CrossRef] [PubMed]

M. E. Eames, J. Wang, B. W. Pogue, and H. Dehghani, “Wavelength band optimization in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden,” J. Biomed. Opt. 13, 054037(2008).
[CrossRef] [PubMed]

M. E. Eames and H. Dehghani, “Wavelength dependence of sensitivity in spectral diffuse optical imaging: effect of normalization on image reconstruction,” Opt. Express 16, 17780–17791 (2008).
[CrossRef] [PubMed]

M. C. Pan, C. H. Chen, L. Y. Chen, M. C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
[CrossRef] [PubMed]

Z. Yuan, Q. Zhang, E. S. Sobel, and H. Jiang, “Tomographic x-ray—guided three-dimensional diffuse optical tomography of osteoarthritis in the finger joints,” J. Biomed. Opt. 13, 044006 (2008).
[CrossRef] [PubMed]

Q. Zhu, S. Tannenbaum, P. Hegde, M. Kane, C. Xu, and S. H. Kurtzman, “Noninvasive monitoring of breast cancer during neoadjuvant chemotherapy using optical tomography with ultrasound localization,” Neoplasia 10, 1028–1040(2008).
[PubMed]

Z. Jiang, D. Piao, G. Xu, J. W. Ritchey, G. R. Holyoak, K. E. Bartels, C. F. Bunting, G. Slobodov, and J. S. Krasinki, “Trans-rectal ultrasound-coupled near-infrared optical tomography of the prostate, part II: experimental demonstration,” Opt. Express 16, 17505–17520 (2008).
[CrossRef] [PubMed]

J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
[CrossRef] [PubMed]

2007

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, “Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information,” Meas. Sci. Technol. 18, 87–95 (2007).
[CrossRef]

N. Cao, A. Nehorai, and M. Jacob, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express 15, 13695–13708 (2007).
[CrossRef] [PubMed]

2006

Q. Zhao, L. Ji, and T. Jiang, “Improving performance of reflectance diffuse optical imaging using a multicentered mode,” J. Biomed. Opt. 11, 064019 (2006).
[CrossRef]

2005

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef] [PubMed]

A. Li, G. Boverman, Y. Zhang, D. Brooks, E. L. Miller, M. E. Kilmer, Q. Zhang, E. M. C. Hillman, and D. A. Boas, “Optimal linear inverse solution with multiple priors in diffuse optical tomography,” Appl. Opt. 44, 1948–1956 (2005).
[CrossRef] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513–526 (2005).
[PubMed]

2004

K. Uludag, J. Steinbrink, A. Villringer, and H. Obriga, “Separability and cross talk: optimizing dual wavelength combinations for near-infrared spectroscopy of the adult head,” NeuroImage 22, 583–589 (2004).
[CrossRef] [PubMed]

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” NeuroImage 23, S275–S288 (2004).
[CrossRef] [PubMed]

A. H. Hielscher and S. Bartel, “Parallel programming of gradient-based iterative image reconstruction schemes for optical tomography,” Comput. Methods Programs Biomed. 73, 101–113 (2004).
[CrossRef] [PubMed]

2003

2002

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

V. Ntziachristos, A. G. Yodh, M. D. Schnall, and B. Chance, “MRI-guided diffuse optical spectroscopy of malignant and benign breast lesions,” Neoplasia 4, 347–354 (2002).
[CrossRef] [PubMed]

Y. Xu, X. Gu, T. Khan, and H. Jiang, “Absorption and scattering images of heterogeneous scattering media can be simultaneously reconstructed by use of dc data,” Appl. Opt. 41, 5427–5437 (2002).
[CrossRef] [PubMed]

2001

2000

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical mammography with ultrasound localization in a human subject,” J. Biomed. Opt. 5, 237–247(2000).
[CrossRef] [PubMed]

1999

J. P. Kaipio, V. Kolehmainen, M. Vauhkonen, and E. Somersalo, “Inverse problems with structural prior information,” Inverse Probl. 15, 713–729 (1999).
[CrossRef]

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

1998

A. Neumaier, “Solving ill-conditioned and singular linear systems: a tutorial on regularization,” SIAM Rev. 40, 636–666(1998).
[CrossRef]

1997

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311(1997).
[CrossRef] [PubMed]

1995

Abdoulaev, G. S.

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

Arridge, S.

P. Hiltunen, S. J. D. Prince, and S. Arridge, “A combined reconstruction–classification method for diffuse optical tomography,” Phys. Med. Biol. 54, 6457–6476 (2009).
[CrossRef] [PubMed]

Arridge, S. R.

Aubert, G.

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311(1997).
[CrossRef] [PubMed]

Barbour, R. L.

Barlaud, M.

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311(1997).
[CrossRef] [PubMed]

Bartel, S.

A. H. Hielscher and S. Bartel, “Parallel programming of gradient-based iterative image reconstruction schemes for optical tomography,” Comput. Methods Programs Biomed. 73, 101–113 (2004).
[CrossRef] [PubMed]

Bartels, K. E.

Beuthan, J.

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

Blanc-Feraud, L.

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311(1997).
[CrossRef] [PubMed]

Bluestone, A. Y.

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

Boas, D. A.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef] [PubMed]

A. Li, G. Boverman, Y. Zhang, D. Brooks, E. L. Miller, M. E. Kilmer, Q. Zhang, E. M. C. Hillman, and D. A. Boas, “Optimal linear inverse solution with multiple priors in diffuse optical tomography,” Appl. Opt. 44, 1948–1956 (2005).
[CrossRef] [PubMed]

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” NeuroImage 23, S275–S288 (2004).
[CrossRef] [PubMed]

Boverman, G.

Brendel, B.

B. Brendel and T. Nielsen, “Selection of optimal wavelengths for spectral reconstruction in diffuse optical tomography,” J. Biomed. Opt. 14, 034041 (2009).
[CrossRef] [PubMed]

Brooks, D.

Brooksby, B.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513–526 (2005).
[PubMed]

H. Dehghani, B. W. Pogue, B. Brooksby, S. Srinivasan, and K. D. Paulsen, “Image reconstruction strategies using dual modality MRI-NIR data,” in Proceedings of IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE, 2006), pp. 682–685.
[CrossRef]

Brukilacchio, T. J.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef] [PubMed]

Bunting, C. F.

Butler, J.

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical mammography with ultrasound localization in a human subject,” J. Biomed. Opt. 5, 237–247(2000).
[CrossRef] [PubMed]

Cao, N.

Chance, B.

V. Ntziachristos, A. G. Yodh, M. D. Schnall, and B. Chance, “MRI-guided diffuse optical spectroscopy of malignant and benign breast lesions,” Neoplasia 4, 347–354 (2002).
[CrossRef] [PubMed]

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical mammography with ultrasound localization in a human subject,” J. Biomed. Opt. 5, 237–247(2000).
[CrossRef] [PubMed]

Charbonnier, P.

P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud, “Deterministic edge-preserving regularization in computed imaging,” IEEE Trans. Image Process. 6, 298–311(1997).
[CrossRef] [PubMed]

Chaves, T.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef] [PubMed]

Chen, C. H.

M. C. Pan, C. H. Chen, M. C. Pan, and Y. M. Shyr, “Near infrared tomographic system based on high angular resolution mechanism—design, calibration, and performance,” Measurement 42, 377–389 (2009).
[CrossRef]

M. C. Pan, C. H. Chen, L. Y. Chen, M. C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
[CrossRef] [PubMed]

M. C. Pan, L. Y. Chen, M. C. Pan, and C. H. Chen, “Inverse solution regularized with the edge-preserving constraint for NIR DOT,” in Biomedical Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDPBMD1.
[PubMed]

Chen, L. Y.

M. C. Pan, C. H. Chen, L. Y. Chen, M. C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
[CrossRef] [PubMed]

L. Y. Chen, M. C. Pan, and M. C. Pan, “Frequency-domain diffuse optical tomography implemented with edge-preserving regularization,” in Biomedical Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper BME7.
[PubMed]

M. C. Pan, L. Y. Chen, M. C. Pan, and C. H. Chen, “Inverse solution regularized with the edge-preserving constraint for NIR DOT,” in Biomedical Optics, OSA Technical Digest (CD) (Optical Society of America, 2008), paper PDPBMD1.
[PubMed]

Choe, R.

Chorlton, M.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef] [PubMed]

Corlu, A.

Cubeddu, R.

Dale, A. M.

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” NeuroImage 23, S275–S288 (2004).
[CrossRef] [PubMed]

Danesini, G.

Davis, S. C.

J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
[CrossRef] [PubMed]

Dehghani, H.

M. E. Eames, J. Wang, B. W. Pogue, and H. Dehghani, “Wavelength band optimization in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden,” J. Biomed. Opt. 13, 054037(2008).
[CrossRef] [PubMed]

M. E. Eames and H. Dehghani, “Wavelength dependence of sensitivity in spectral diffuse optical imaging: effect of normalization on image reconstruction,” Opt. Express 16, 17780–17791 (2008).
[CrossRef] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513–526 (2005).
[PubMed]

H. Dehghani, B. W. Pogue, B. Brooksby, S. Srinivasan, and K. D. Paulsen, “Image reconstruction strategies using dual modality MRI-NIR data,” in Proceedings of IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE, 2006), pp. 682–685.
[CrossRef]

Douiri, A.

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, “Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information,” Meas. Sci. Technol. 18, 87–95 (2007).
[CrossRef]

Durduran, T.

Eames, M. E.

M. E. Eames, J. Wang, B. W. Pogue, and H. Dehghani, “Wavelength band optimization in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden,” J. Biomed. Opt. 13, 054037(2008).
[CrossRef] [PubMed]

M. E. Eames and H. Dehghani, “Wavelength dependence of sensitivity in spectral diffuse optical imaging: effect of normalization on image reconstruction,” Opt. Express 16, 17780–17791 (2008).
[CrossRef] [PubMed]

Fishkin, J.

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical mammography with ultrasound localization in a human subject,” J. Biomed. Opt. 5, 237–247(2000).
[CrossRef] [PubMed]

Franceschini, M. A.

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” NeuroImage 23, S275–S288 (2004).
[CrossRef] [PubMed]

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Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
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S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513–526 (2005).
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Prince, S. J. D.

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Shyr, Y. M.

M. C. Pan, C. H. Chen, M. C. Pan, and Y. M. Shyr, “Near infrared tomographic system based on high angular resolution mechanism—design, calibration, and performance,” Measurement 42, 377–389 (2009).
[CrossRef]

M. C. Pan, C. H. Chen, L. Y. Chen, M. C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
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Sobel, E. S.

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J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
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K. Uludag, J. Steinbrink, A. Villringer, and H. Obriga, “Separability and cross talk: optimizing dual wavelength combinations for near-infrared spectroscopy of the adult head,” NeuroImage 22, 583–589 (2004).
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Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
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Q. Zhu, S. Tannenbaum, P. Hegde, M. Kane, C. Xu, and S. H. Kurtzman, “Noninvasive monitoring of breast cancer during neoadjuvant chemotherapy using optical tomography with ultrasound localization,” Neoplasia 10, 1028–1040(2008).
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K. Uludag, J. Steinbrink, A. Villringer, and H. Obriga, “Separability and cross talk: optimizing dual wavelength combinations for near-infrared spectroscopy of the adult head,” NeuroImage 22, 583–589 (2004).
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J. P. Kaipio, V. Kolehmainen, M. Vauhkonen, and E. Somersalo, “Inverse problems with structural prior information,” Inverse Probl. 15, 713–729 (1999).
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K. Uludag, J. Steinbrink, A. Villringer, and H. Obriga, “Separability and cross talk: optimizing dual wavelength combinations for near-infrared spectroscopy of the adult head,” NeuroImage 22, 583–589 (2004).
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J. Wang, S. C. Davis, S. Srinivasan, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Spectral tomography with diffuse near-infrared light: inclusion of broadband frequency domain spectral data,” J. Biomed. Opt. 13, 041305 (2008).
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S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, W. A. Wells, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 4, 513–526 (2005).
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Q. Zhu, S. Tannenbaum, P. Hegde, M. Kane, C. Xu, and S. H. Kurtzman, “Noninvasive monitoring of breast cancer during neoadjuvant chemotherapy using optical tomography with ultrasound localization,” Neoplasia 10, 1028–1040(2008).
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Z. Yuan, Q. Zhang, E. S. Sobel, and H. Jiang, “Tomographic x-ray—guided three-dimensional diffuse optical tomography of osteoarthritis in the finger joints,” J. Biomed. Opt. 13, 044006 (2008).
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Z. Yuan, Q. Zhang, E. S. Sobel, and H. Jiang, “Tomographic x-ray—guided three-dimensional diffuse optical tomography of osteoarthritis in the finger joints,” J. Biomed. Opt. 13, 044006 (2008).
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Zhao, Q.

H. Niu, P. Guo, L. Ji, Q. Zhao, and T. Jiang, “Improving image quality of diffuse optical tomography with a projection-error-based adaptive regularization method,” Opt. Express 16, 12423–12434 (2008).
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Q. Zhu, S. Tannenbaum, P. Hegde, M. Kane, C. Xu, and S. H. Kurtzman, “Noninvasive monitoring of breast cancer during neoadjuvant chemotherapy using optical tomography with ultrasound localization,” Neoplasia 10, 1028–1040(2008).
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M. C. Pan, C. H. Chen, L. Y. Chen, M. C. Pan, and Y. M. Shyr, “Highly resolved diffuse optical tomography: a systematic approach using high-pass filtering for value-preserved images,” J. Biomed. Opt. 13, 024022 (2008).
[CrossRef] [PubMed]

Q. Zhao, L. Ji, and T. Jiang, “Improving performance of reflectance diffuse optical imaging using a multicentered mode,” J. Biomed. Opt. 11, 064019 (2006).
[CrossRef]

M. E. Eames, J. Wang, B. W. Pogue, and H. Dehghani, “Wavelength band optimization in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden,” J. Biomed. Opt. 13, 054037(2008).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef] [PubMed]

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Figures (13)

Fig. 1
Fig. 1

Flowchart of NIR DOT image reconstruction using TR or EPR.

Fig. 2
Fig. 2

(a) High-resolution mesh used by the finite-element forward solver for generating simulated data, (b) illustration of the node and element arrangements used in the image reconstruction; (c) three different directions used to calculate the first-order difference for EPR.

Fig. 3
Fig. 3

Simulated reconstructions of both the absorption and the reduced scattering images with a 3 1 contrast level for inclusions having the same size but at different off-center distances. (a) Exact absorption image, (b) reconstruction using TR, and (c) reconstruction using EPR; (d) exact reduced scattering image, (e) reconstruction using TR, and (f) reconstruction using EPR.

Fig. 4
Fig. 4

Simulated reconstructions of both the absorption and the reduced scattering images with a 3 1 contrast level for inclusions having different geometric sizes at a same off-center distance ( 20 mm ). (a) Exact absorption image, (b) reconstruction using TR, and (c) reconstruction using EPR; (d) exact reduced scattering image, (e) reconstruction using TR, and (f) reconstruction using EPR.

Fig. 5
Fig. 5

Comparison between exact (dotted line) and simulated (solid line) reconstructions by 1D circular profiles with a radius of 20 mm for the images in Fig. 4. (a), (b) 1D profiles of μ a using TR and EPR, respectively; (c), (d) 1D profiles of μ s using TR and EPR, respectively.

Fig. 6
Fig. 6

Simulated reconstructions of both the absorption and the reduced scattering images for three absorbing and/or scattering inclusions at same off-center distance ( 20 mm ) and having same size. (a) Exact absorption image, (b) reconstruction using TR, and (c) reconstruction using EPR; (d) exact reduced scattering image, (e) reconstruction using TR, and (f) reconstruction using EPR.

Fig. 7
Fig. 7

Comparison between exact (dotted line) and simulated (solid line) reconstructions by 1D circular profiles with a radius of 20 mm for the images in Fig. 6. (a), (b) 1D profiles of μ a using TR and EPR, respectively; (c), (d) 1D profiles of μ s using TR and EPR, respectively.

Fig. 8
Fig. 8

Simulated reconstructions of both the absorption and the reduced scattering images for a phantom of layered domain with an inclusion. (a) Exact absorption image, (b) reconstruction using TR, and (c) reconstruction using EPR; (d) exact reduced scattering image, (e) reconstruction using TR, and (f) reconstruction using EPR.

Fig. 9
Fig. 9

Comparison between exact (dotted line) and simulated (solid line) reconstructions by 1D horizontal line profiles through the centers of both the inclusion and the background for the images in Fig. 8. (a), (b) 1D profiles of μ a using TR and EPR, respectively; (c), (d) 1D profiles of μ s using TR and EPR, respectively.

Fig. 10
Fig. 10

Reconstructed images from experimental data obtained from an eccentrically located inclusion having a 4 1 contrast level with respect to the background medium. (a) Exact absorption image, (b) reconstruction using TR, and (c) reconstruction using EPR; (d) exact reduced scattering image, (e) reconstruction using TR, and (f) reconstruction using EPR.

Fig. 11
Fig. 11

Comparison between exact (dotted line) and simulated (solid line) reconstructions by 1D circular profiles with a radius of 12.5 mm for the images in Fig. 10. (a), (b) are 1D profiles of μ a using TR and EPR, respectively; (c), (d) are 1D profiles of μ s using TR and EPR, respectively.

Fig. 12
Fig. 12

Reconstructed images from experimental data obtained from two eccentrically located inclusions having a 4 1 contrast level with respect to the background medium. (a) Exact absorption image, (b) reconstruction using TR, and (c) reconstruction using EPR; (d) exact reduced scattering image, (e) reconstruction using TR, and (f) reconstruction using EPR.

Fig. 13
Fig. 13

Comparison between exact (dotted line) and simulated (solid line) reconstructions by 1D circular profiles through the centers of two inclusions at a radius of 12.5 mm for the images in Fig. 12. (a), (b) 1D profiles of μ a using TR and EPR, respectively; (c), (d) 1D profiles of μ s using TR and EPR, respectively.

Tables (2)

Tables Icon

Table 1 Evaluation on Contrast and Size Resolutions of 1D Profiles for TR and EPR

Tables Icon

Table 2 Evaluation on Contrast and Size Resolutions of 2D Images for TR and EPR

Equations (16)

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· κ ( r ) Φ ( r , ω ) [ μ a ( r ) i ω c ] Φ ( r , ω ) = S ( r , ω ) ,
χ 2 = i = 1 N M [ Φ i C Φ i M ] 2 ,
( Φ M ) ( Φ C ) + [ Φ C μ a ] ( Δ μ a ) + [ Φ C κ ] ( Δ κ ) ,
[ Φ C μ a Φ C κ ] ( Δ μ a Δ κ ) = ( Φ M Φ C ) ,
min Δ χ { Q Tk ( Δ χ ) } = min Δ χ { J Δ χ Δ Φ 2 2 + λ 2 L Δ χ 2 2 } ,
Q Tk ( Δ χ ) = J Δ χ Δ Φ λ L Δ χ 2 2 .
Q Tk ( Δ χ ) Δ χ = [ J T λ L T ] [ J Δ χ Δ Φ λ L Δ χ ] = ( J T J + λ 2 L T L ) Δ χ J T Δ Φ = 0 ,
( J T J + λ 2 L T L ) Δ χ = J T Δ Φ ,
Q Ep ( Δ χ ) = J Δ χ Δ Φ 2 2 + λ 2 l k φ [ ( D l Δ χ ) k ] ,
J T J Δ χ J T Δ Φ λ 2 Δ weighted Δ χ = 0 ,
Q Ep ( Δ χ ) = inf b Q Ep * ( Δ χ , b ) ,
Q Ep * ( Δ χ , b ) = J Δ χ Δ Φ 2 2 + λ 2 l k { ( b l ) k ( D l Δ χ ) k 2 + φ [ ( b l ) k ] } .
( b l n + 1 ) k = arg min ( b l ) k { Q Ep * ( Δ χ n , ( b l ) k ) } = φ [ ( D l Δ χ n ) k ] 2 ( D l Δ χ n ) k .
Δ χ n + 1 = arg min Δ χ { Q Ep * ( Δ χ , b n + 1 ) } = [ J T J + λ 2 Δ Ep n + 1 ] 1 J T Δ Φ ,
φ ( t ) 2 t = ( γ 2 ) m ( γ 2 + t 2 ) m ,
[ D l ] i , j = { 1 / δ i j , i = j 1 / δ i j , i j and i , j   are neighbors in   l   direction 0 , i j and i , j   are not neighbors ,

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