Abstract

The common approach to diffuse optical tomography is to solve a nonlinear and ill-posed inverse problem using a linearized iteration process that involves repeated use of the forward and inverse solvers on an appropriately discretized domain of interest. This scheme normally brings severe computation and storage burdens to its applications on large-sized tissues, such as breast tumor diagnosis and brain functional imaging, and prevents from using the matrix-fashioned linear inversions for improved image quality. To cope with the difficulties, we propose in this paper a parallelized full domain-decomposition scheme, which divides the whole domain into several overlapped subdomains and solves the corresponding subinversions independently within the framework of the Schwarz-type iterations, with the support of a combined multicore CPU and multithread graphics processing unit (GPU) parallelization strategy. The numerical and phantom experiments both demonstrate that the proposed method can effectively reduce the computation time and memory occupation for the large-sized problem and improve the quantitative performance of the reconstruction.

© 2014 Optical Society of America

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  1. T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
    [CrossRef]
  2. A. Gibson and H. Dehghani, “Diffuse optical imaging,” Phil. Trans. R. Soc. A 367, 3055–3072 (2009).
    [CrossRef]
  3. A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
    [CrossRef]
  4. 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]
  5. S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
    [CrossRef]
  6. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
    [CrossRef]
  7. W. Bangerth and A. Joshi, “Adaptive finite element methods for the solution of inverse problems in optical tomography,” Inverse Probl. 24, 034011 (2008).
    [CrossRef]
  8. Y. Zhai and S. A. Cummer, “Fast tomographic reconstruction strategy for diffuse optical tomography,” Opt. Express 17, 5285–5297 (2009).
    [CrossRef]
  9. M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, and E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
    [CrossRef]
  10. A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations (Oxford Science, 1999).
  11. A. Boag, Y. Bresler, and E. Michielssen, “A multilevel domain decomposition algorithm for fast O (N2 log N) reprojection of tomographic images,” IEEE Trans. Image Process. 9, 1573–1582 (2000).
    [CrossRef]
  12. M. J. Eppstein and D. E. Dougherty, “Optimal 3-D travel time tomography,” Geophysics 63, 1053–1061 (1998).
    [CrossRef]
  13. C. J. Palansuriya, C.-H. Lai, C. S. Lerotheou, and K. A. Pericleous, “A domain decomposition based algorithm for nonlinear 2D inverse heat conduction problems,” Contemp Math. 218, 515–522 (1998).
    [CrossRef]
  14. K. Kwon, B. Yazici, and M. Guven, “Two-level domain decomposition methods for diffuse tomography,” Inverse Probl. 22, 1533–1559 (2006).
    [CrossRef]
  15. F. Yang, F. Gao, P.-Q. Ruan, and H.-J. Zhao, “Combined domain-decomposition and matrix-decomposition scheme for large-scale diffuse optical tomography,” Appl. Opt. 49, 3111–3126 (2010).
    [CrossRef]
  16. 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, 5898–5910 (2000).
    [CrossRef]
  17. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–399 (1993).
    [CrossRef]
  18. M. Schweiger, “GPU-accelerated finite element method for modeling light transport in diffuse optical tomography,” Int. J. Biomed. Imag. 2011, 403892 (2011).
    [CrossRef]
  19. X. Wang, B. Zhang, X. Cao, F. Liu, J.-W. Luo, and J. Bai, “Acceleration of early-photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).
  20. D.-F. Wang, H.-T. Qiao, X.-L. Song, Y.-B. Fan, and D.-Y. Li, “Fluorescence molecular tomography using a two-step three-dimensional shape-based reconstruction with graphic processing unit acceleration,” Appl. Opt. 51, 8731–8744 (2012).
    [CrossRef]
  21. W. Zhang, L.-H. Wu, W.-J. Ma, J. Li, W.-T. Chen, X. Wang, X. Yi, Y.-M. Lu, Z.-X. Zhou, L.-M. Zhang, H.-J. Zhao, and F. Gao, “Combined time-domain hemoglobin and fluorescence diffuse optical tomography for breast tumor diagnosis: a methodological study,” Biomed. Opt. Express 4, 331–348 (2013).
    [CrossRef]
  22. A. Toselli and O. Widlund, Domain Decomposition Methods Algorithm and Theory (Springer, 2005).
  23. L. Badea, “On the Schwarz alternation method with more than two subdomains for nonlinear monotone problems,” SIAM J. Numer. Anal. 28, 179–204 (1991).
    [CrossRef]
  24. A. Wathen and T. Rees, “Chebyshev semi-iteration in preconditioning for problems including the mass matrix,” Electron. Trans. Numer. Anal. 34, 125–135 (2009).
  25. P. C. Hansen, “Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank,” SIAM J. Sci. Comput. 11, 503–518 (1990).
    [CrossRef]
  26. P. C. Hansen, “The truncated SVD as a method for regularization,” BIT 27, 534–553 (1987).
    [CrossRef]
  27. X. Yi, W.-T. Chen, L.-H. Wu, W.-J. Ma, W. Zhang, J. Li, X. Wang, and F. Gao, “GPU-accelerated Monte Carlo modeling for fluorescence propagation in turbid medium,” Proc. SPIE 8216, 82160U (2012).
    [CrossRef]
  28. J. Li, X. Yi, X. Wang, Y.-M. Lu, L.-M. Zhang, H.-J. Zhao, and F. Gao, “Overlap time-gating approach for improving time-domain diffuse fluorescence tomography based on the IRF-calibrated Born normalization,” Opt. Lett. 38, 1841–1843 (2013).
    [CrossRef]

2013 (3)

2012 (2)

D.-F. Wang, H.-T. Qiao, X.-L. Song, Y.-B. Fan, and D.-Y. Li, “Fluorescence molecular tomography using a two-step three-dimensional shape-based reconstruction with graphic processing unit acceleration,” Appl. Opt. 51, 8731–8744 (2012).
[CrossRef]

X. Yi, W.-T. Chen, L.-H. Wu, W.-J. Ma, W. Zhang, J. Li, X. Wang, and F. Gao, “GPU-accelerated Monte Carlo modeling for fluorescence propagation in turbid medium,” Proc. SPIE 8216, 82160U (2012).
[CrossRef]

2011 (1)

M. Schweiger, “GPU-accelerated finite element method for modeling light transport in diffuse optical tomography,” Int. J. Biomed. Imag. 2011, 403892 (2011).
[CrossRef]

2010 (2)

F. Yang, F. Gao, P.-Q. Ruan, and H.-J. Zhao, “Combined domain-decomposition and matrix-decomposition scheme for large-scale diffuse optical tomography,” Appl. Opt. 49, 3111–3126 (2010).
[CrossRef]

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

2009 (4)

A. Gibson and H. Dehghani, “Diffuse optical imaging,” Phil. Trans. R. Soc. A 367, 3055–3072 (2009).
[CrossRef]

A. Wathen and T. Rees, “Chebyshev semi-iteration in preconditioning for problems including the mass matrix,” Electron. Trans. Numer. Anal. 34, 125–135 (2009).

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

Y. Zhai and S. A. Cummer, “Fast tomographic reconstruction strategy for diffuse optical tomography,” Opt. Express 17, 5285–5297 (2009).
[CrossRef]

2008 (1)

W. Bangerth and A. Joshi, “Adaptive finite element methods for the solution of inverse problems in optical tomography,” Inverse Probl. 24, 034011 (2008).
[CrossRef]

2006 (1)

K. Kwon, B. Yazici, and M. Guven, “Two-level domain decomposition methods for diffuse tomography,” Inverse Probl. 22, 1533–1559 (2006).
[CrossRef]

2005 (1)

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[CrossRef]

2001 (2)

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]

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, and E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef]

2000 (2)

A. Boag, Y. Bresler, and E. Michielssen, “A multilevel domain decomposition algorithm for fast O (N2 log N) reprojection of tomographic images,” IEEE Trans. Image Process. 9, 1573–1582 (2000).
[CrossRef]

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, 5898–5910 (2000).
[CrossRef]

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

1998 (2)

M. J. Eppstein and D. E. Dougherty, “Optimal 3-D travel time tomography,” Geophysics 63, 1053–1061 (1998).
[CrossRef]

C. J. Palansuriya, C.-H. Lai, C. S. Lerotheou, and K. A. Pericleous, “A domain decomposition based algorithm for nonlinear 2D inverse heat conduction problems,” Contemp Math. 218, 515–522 (1998).
[CrossRef]

1993 (1)

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–399 (1993).
[CrossRef]

1991 (1)

L. Badea, “On the Schwarz alternation method with more than two subdomains for nonlinear monotone problems,” SIAM J. Numer. Anal. 28, 179–204 (1991).
[CrossRef]

1990 (1)

P. C. Hansen, “Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank,” SIAM J. Sci. Comput. 11, 503–518 (1990).
[CrossRef]

1987 (1)

P. C. Hansen, “The truncated SVD as a method for regularization,” BIT 27, 534–553 (1987).
[CrossRef]

Arridge, S. R.

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–399 (1993).
[CrossRef]

Badea, L.

L. Badea, “On the Schwarz alternation method with more than two subdomains for nonlinear monotone problems,” SIAM J. Numer. Anal. 28, 179–204 (1991).
[CrossRef]

Bai, J.

X. Wang, B. Zhang, X. Cao, F. Liu, J.-W. Luo, and J. Bai, “Acceleration of early-photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).

Baker, W. B.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

Bangerth, W.

W. Bangerth and A. Joshi, “Adaptive finite element methods for the solution of inverse problems in optical tomography,” Inverse Probl. 24, 034011 (2008).
[CrossRef]

Boag, A.

A. Boag, Y. Bresler, and E. Michielssen, “A multilevel domain decomposition algorithm for fast O (N2 log N) reprojection of tomographic images,” IEEE Trans. Image Process. 9, 1573–1582 (2000).
[CrossRef]

Boas, D. A.

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]

Bresler, Y.

A. Boag, Y. Bresler, and E. Michielssen, “A multilevel domain decomposition algorithm for fast O (N2 log N) reprojection of tomographic images,” IEEE Trans. Image Process. 9, 1573–1582 (2000).
[CrossRef]

Brooks, D. H.

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]

Cao, X.

X. Wang, B. Zhang, X. Cao, F. Liu, J.-W. Luo, and J. Bai, “Acceleration of early-photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).

Chen, W.-T.

Choe, R.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

Cummer, S. A.

Dehghani, H.

A. Gibson and H. Dehghani, “Diffuse optical imaging,” Phil. Trans. R. Soc. A 367, 3055–3072 (2009).
[CrossRef]

Delpy, D. T.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–399 (1993).
[CrossRef]

DiMarzio, C. A.

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]

Dougherty, D. E.

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, and E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef]

M. J. Eppstein and D. E. Dougherty, “Optimal 3-D travel time tomography,” Geophysics 63, 1053–1061 (1998).
[CrossRef]

Durduran, T.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

Eppstein, M. J.

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, and E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef]

M. J. Eppstein and D. E. Dougherty, “Optimal 3-D travel time tomography,” Geophysics 63, 1053–1061 (1998).
[CrossRef]

Fan, Y.-B.

Gao, F.

Gaudette, R. J.

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]

Gibson, A.

A. Gibson and H. Dehghani, “Diffuse optical imaging,” Phil. Trans. R. Soc. A 367, 3055–3072 (2009).
[CrossRef]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[CrossRef]

Guven, M.

K. Kwon, B. Yazici, and M. Guven, “Two-level domain decomposition methods for diffuse tomography,” Inverse Probl. 22, 1533–1559 (2006).
[CrossRef]

Hansen, P. C.

P. C. Hansen, “Truncated singular value decomposition solutions to discrete ill-posed problems with ill-determined numerical rank,” SIAM J. Sci. Comput. 11, 503–518 (1990).
[CrossRef]

P. C. Hansen, “The truncated SVD as a method for regularization,” BIT 27, 534–553 (1987).
[CrossRef]

Hawrysz, D. J.

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, and E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1–R43 (2005).
[CrossRef]

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–399 (1993).
[CrossRef]

Joshi, A.

W. Bangerth and A. Joshi, “Adaptive finite element methods for the solution of inverse problems in optical tomography,” Inverse Probl. 24, 034011 (2008).
[CrossRef]

Kilmer, M.

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]

Kwon, K.

K. Kwon, B. Yazici, and M. Guven, “Two-level domain decomposition methods for diffuse tomography,” Inverse Probl. 22, 1533–1559 (2006).
[CrossRef]

Lai, C.-H.

C. J. Palansuriya, C.-H. Lai, C. S. Lerotheou, and K. A. Pericleous, “A domain decomposition based algorithm for nonlinear 2D inverse heat conduction problems,” Contemp Math. 218, 515–522 (1998).
[CrossRef]

Lerotheou, C. S.

C. J. Palansuriya, C.-H. Lai, C. S. Lerotheou, and K. A. Pericleous, “A domain decomposition based algorithm for nonlinear 2D inverse heat conduction problems,” Contemp Math. 218, 515–522 (1998).
[CrossRef]

Li, D.-Y.

Li, J.

Liu, F.

X. Wang, B. Zhang, X. Cao, F. Liu, J.-W. Luo, and J. Bai, “Acceleration of early-photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).

Lu, Y.-M.

Luo, J.-W.

X. Wang, B. Zhang, X. Cao, F. Liu, J.-W. Luo, and J. Bai, “Acceleration of early-photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).

Ma, W.-J.

Michielssen, E.

A. Boag, Y. Bresler, and E. Michielssen, “A multilevel domain decomposition algorithm for fast O (N2 log N) reprojection of tomographic images,” IEEE Trans. Image Process. 9, 1573–1582 (2000).
[CrossRef]

Miller, E. L.

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]

Palansuriya, C. J.

C. J. Palansuriya, C.-H. Lai, C. S. Lerotheou, and K. A. Pericleous, “A domain decomposition based algorithm for nonlinear 2D inverse heat conduction problems,” Contemp Math. 218, 515–522 (1998).
[CrossRef]

Pericleous, K. A.

C. J. Palansuriya, C.-H. Lai, C. S. Lerotheou, and K. A. Pericleous, “A domain decomposition based algorithm for nonlinear 2D inverse heat conduction problems,” Contemp Math. 218, 515–522 (1998).
[CrossRef]

Poulet, P.

Qiao, H.-T.

Quarteroni, A.

A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations (Oxford Science, 1999).

Rees, T.

A. Wathen and T. Rees, “Chebyshev semi-iteration in preconditioning for problems including the mass matrix,” Electron. Trans. Numer. Anal. 34, 125–135 (2009).

Ruan, P.-Q.

Schotland, J. C.

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

Schweiger, M.

M. Schweiger, “GPU-accelerated finite element method for modeling light transport in diffuse optical tomography,” Int. J. Biomed. Imag. 2011, 403892 (2011).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–399 (1993).
[CrossRef]

Sevick-Muraca, E. M.

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, and E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef]

Song, X.-L.

Toselli, A.

A. Toselli and O. Widlund, Domain Decomposition Methods Algorithm and Theory (Springer, 2005).

Valli, A.

A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations (Oxford Science, 1999).

Wang, D.-F.

Wang, X.

W. Zhang, L.-H. Wu, W.-J. Ma, J. Li, W.-T. Chen, X. Wang, X. Yi, Y.-M. Lu, Z.-X. Zhou, L.-M. Zhang, H.-J. Zhao, and F. Gao, “Combined time-domain hemoglobin and fluorescence diffuse optical tomography for breast tumor diagnosis: a methodological study,” Biomed. Opt. Express 4, 331–348 (2013).
[CrossRef]

X. Wang, B. Zhang, X. Cao, F. Liu, J.-W. Luo, and J. Bai, “Acceleration of early-photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).

J. Li, X. Yi, X. Wang, Y.-M. Lu, L.-M. Zhang, H.-J. Zhao, and F. Gao, “Overlap time-gating approach for improving time-domain diffuse fluorescence tomography based on the IRF-calibrated Born normalization,” Opt. Lett. 38, 1841–1843 (2013).
[CrossRef]

X. Yi, W.-T. Chen, L.-H. Wu, W.-J. Ma, W. Zhang, J. Li, X. Wang, and F. Gao, “GPU-accelerated Monte Carlo modeling for fluorescence propagation in turbid medium,” Proc. SPIE 8216, 82160U (2012).
[CrossRef]

Wathen, A.

A. Wathen and T. Rees, “Chebyshev semi-iteration in preconditioning for problems including the mass matrix,” Electron. Trans. Numer. Anal. 34, 125–135 (2009).

Widlund, O.

A. Toselli and O. Widlund, Domain Decomposition Methods Algorithm and Theory (Springer, 2005).

Wu, L.-H.

Yamada, Y.

Yang, F.

Yazici, B.

K. Kwon, B. Yazici, and M. Guven, “Two-level domain decomposition methods for diffuse tomography,” Inverse Probl. 22, 1533–1559 (2006).
[CrossRef]

Yi, X.

Yodh, A. G.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

Zhai, Y.

Zhang, B.

X. Wang, B. Zhang, X. Cao, F. Liu, J.-W. Luo, and J. Bai, “Acceleration of early-photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).

Zhang, L.-M.

Zhang, Q.

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]

Zhang, W.

Zhao, H.-J.

Zhou, Z.-X.

Appl. Opt. (3)

Biomed. Opt. Express (1)

BIT (1)

P. C. Hansen, “The truncated SVD as a method for regularization,” BIT 27, 534–553 (1987).
[CrossRef]

Comput. Math. Methods Med. (1)

X. Wang, B. Zhang, X. Cao, F. Liu, J.-W. Luo, and J. Bai, “Acceleration of early-photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).

Contemp Math. (1)

C. J. Palansuriya, C.-H. Lai, C. S. Lerotheou, and K. A. Pericleous, “A domain decomposition based algorithm for nonlinear 2D inverse heat conduction problems,” Contemp Math. 218, 515–522 (1998).
[CrossRef]

Electron. Trans. Numer. Anal. (1)

A. Wathen and T. Rees, “Chebyshev semi-iteration in preconditioning for problems including the mass matrix,” Electron. Trans. Numer. Anal. 34, 125–135 (2009).

Geophysics (1)

M. J. Eppstein and D. E. Dougherty, “Optimal 3-D travel time tomography,” Geophysics 63, 1053–1061 (1998).
[CrossRef]

IEEE Signal Process. Mag. (1)

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]

IEEE Trans. Image Process. (1)

A. Boag, Y. Bresler, and E. Michielssen, “A multilevel domain decomposition algorithm for fast O (N2 log N) reprojection of tomographic images,” IEEE Trans. Image Process. 9, 1573–1582 (2000).
[CrossRef]

IEEE Trans. Med. Imaging (1)

M. J. Eppstein, D. E. Dougherty, D. J. Hawrysz, and E. M. Sevick-Muraca, “Three-dimensional Bayesian optical image reconstruction with domain decomposition,” IEEE Trans. Med. Imaging 20, 147–163 (2001).
[CrossRef]

Int. J. Biomed. Imag. (1)

M. Schweiger, “GPU-accelerated finite element method for modeling light transport in diffuse optical tomography,” Int. J. Biomed. Imag. 2011, 403892 (2011).
[CrossRef]

Inverse Probl. (4)

K. Kwon, B. Yazici, and M. Guven, “Two-level domain decomposition methods for diffuse tomography,” Inverse Probl. 22, 1533–1559 (2006).
[CrossRef]

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

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