Abstract

Diffuse Optical Tomography (DOT) has been growing significantly in the past two decades as a promising tool for in-vivo and non-invasive imaging of tissues using near-infrared light. It can improve our ability to probe complex biologic interactions dynamically and to study disease and treatment responses over time in near real time. Recent advances on the transfer of techniques from laboratory to clinics have led to the development of various diagnostic applications such as imaging of the female breast and infant brain. The potential value of the promising tool, however, can be limited by the reconstruction time for tomographically imaging tissue optical properties. The current solution procedure in DOT consumes a considerable amount of time due to discretization of the problem domain and nonlinear nature of tissue optical properties. It is becoming ever more important to develop faster imaging tools as measurement data sets increase in size as a result of the application of newer generation instruments. Here we provide a fast solution strategy that significantly reduces imaging effort for DOT. The fast imaging strategy adopts advanced model-order reduction (MOR) techniques for reducing system complexity, while preserving (to the greatest possible extent) system input-output behavior for the forward problem. Our results demonstrate that the MOR-based imaging method can be an order of magnitude faster than the conventional approach while maintaining a relatively small error tolerance. The goal is to develop inexpensive, noninvasive imaging system that can run at patient’s bedside in real time and produce data continuously over a long period of time.

©2009 Optical Society of America

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References

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  1. V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nature Biotechnol. 23, 313–320 (2005).
    [Crossref]
  2. A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R01–R43 (2005).
    [Crossref]
  3. B.W. Pogue, S.C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11, 033001 (2006).
    [Crossref]
  4. S.L. Jacques and B.W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13, 041302 (2008).
    [Crossref] [PubMed]
  5. 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, 2443–2451 (2008).
    [Crossref] [PubMed]
  6. M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
    [Crossref]
  7. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
    [Crossref] [PubMed]
  8. K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
    [Crossref] [PubMed]
  9. The Biomedical Optics Research Laboratory at University College London, http://www.medphys.ucl.ac.uk/research/borl/.
  10. The Near Infrared Imaging Group at Dartmouth College, http://www-nml.dartmouth.edu/nir/.
  11. P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critically computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113, (2006).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. N. S. Shah, A. E. Cerussi, D. Gordon, A. Durkin, L. Wenzel, B. Hill, M. Compton, and B. J. Tromberg, “Integration of diffuse optical technology into clinical settings for breast health applications,” Frontiers in Optics, The 90th OSA Annual Meeting, 2006.
  14. J. Ripoll, M. Nieto-Vesperinas, R. Weissleder, and V. Ntziachristos, “Fast analytical approximation for arbitrary geometries in diffuse optical tomography,” Opt. Lett. 27, 527, (2002).
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  15. X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
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  16. J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, “Nonlinear multigrid algorithms for Bayesian optical diffusion tomography,” IEEE Trans. Image Process. 10, 909–922 (2001).
    [Crossref]
  17. 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,” Appl. Opt. 42, 135–145 (2003).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  19. S. R. Arridge and J. C. Hebden. “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. in Med. Biol. 42, 841–853 (1997).
    [Crossref]
  20. L. Vu-Quoc, Y. Zhai, and K. D. T. Ngo, “Efficient simulation of coupled circuit-field problems: Generalized Falk method,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 23, 1209–1219 (2004).
    [Crossref]
  21. P. Feldmann and R. Freund, “Reduced order modeling of large linear subcircuits via a block Lanczos algorithm,” In Proceedings Design Automation Conference (Piscataway, NJ, USA, 1995), pp.474–479.
  22. Y. Zhai, “Model-order reduction for efficient simulation of nonlinear electro-magneto-thermal coupled problems,” Ph.D. Thesis, University of Florida, 2003.
  23. J. Phillips, “Projection-based approaches for model reduction of weakly nonlinear, time-varying systems,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 22, 171–187 (2003).
    [Crossref]
  24. M. Rewienski and J. White, “A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 22, 155–169 (2003).
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  25. Y. Zhai and L. Vu-Quoc, “Analysis of power magnetic components with nonlinear static hysteresis: Finite-element formulation,” IEEE Transactions on Magnetics 41, 2243–2256 (2005).
    [Crossref]
  26. Y. Zhai and L. Vu-Quoc, “Analysis of power magnetic components with nonlinear static hysteresis: Proper orthogonal decomposition and model reduction,” IEEE Trans. Magnetics 43, 1888–1897 (2007).
    [Crossref]
  27. Y. Zhai and S. A. Cummer, “An orthogonal projection and regularization technique for magnetospheric radio tomography,” J. Geophys. Res. 111, A03207 (2006).
    [Crossref]
  28. B. Brooksby, S. Jiang, H. Dehghani, B. W. Powgue, and K. D. Paulsen, “Combining near-infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. of Biomed. Opt. 10, 0515041–10 (2005).
  29. The Breast Cancer Multi-Dimentional Diffuse Optical Imaging Network, http://www.bli.uci.edu/ntroi/.

2008 (3)

S.L. Jacques and B.W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13, 041302 (2008).
[Crossref] [PubMed]

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, 2443–2451 (2008).
[Crossref] [PubMed]

P. K. Yalavarthy, D.R. Lynch, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems,” Med. Phys. 35(5), 1682–1696, (2008).
[Crossref] [PubMed]

2007 (2)

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

Y. Zhai and L. Vu-Quoc, “Analysis of power magnetic components with nonlinear static hysteresis: Proper orthogonal decomposition and model reduction,” IEEE Trans. Magnetics 43, 1888–1897 (2007).
[Crossref]

2006 (4)

Y. Zhai and S. A. Cummer, “An orthogonal projection and regularization technique for magnetospheric radio tomography,” J. Geophys. Res. 111, A03207 (2006).
[Crossref]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critically computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113, (2006).
[Crossref] [PubMed]

N. S. Shah, A. E. Cerussi, D. Gordon, A. Durkin, L. Wenzel, B. Hill, M. Compton, and B. J. Tromberg, “Integration of diffuse optical technology into clinical settings for breast health applications,” Frontiers in Optics, The 90th OSA Annual Meeting, 2006.

B.W. Pogue, S.C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11, 033001 (2006).
[Crossref]

2005 (4)

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

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R01–R43 (2005).
[Crossref]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Powgue, and K. D. Paulsen, “Combining near-infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. of Biomed. Opt. 10, 0515041–10 (2005).

Y. Zhai and L. Vu-Quoc, “Analysis of power magnetic components with nonlinear static hysteresis: Finite-element formulation,” IEEE Transactions on Magnetics 41, 2243–2256 (2005).
[Crossref]

2004 (1)

L. Vu-Quoc, Y. Zhai, and K. D. T. Ngo, “Efficient simulation of coupled circuit-field problems: Generalized Falk method,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 23, 1209–1219 (2004).
[Crossref]

2003 (5)

J. Phillips, “Projection-based approaches for model reduction of weakly nonlinear, time-varying systems,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 22, 171–187 (2003).
[Crossref]

M. Rewienski and J. White, “A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 22, 155–169 (2003).
[Crossref]

M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
[Crossref]

X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
[Crossref] [PubMed]

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,” Appl. Opt. 42, 135–145 (2003).
[Crossref] [PubMed]

2002 (1)

2001 (1)

J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, “Nonlinear multigrid algorithms for Bayesian optical diffusion tomography,” IEEE Trans. Image Process. 10, 909–922 (2001).
[Crossref]

1997 (1)

S. R. Arridge and J. C. Hebden. “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. in Med. Biol. 42, 841–853 (1997).
[Crossref]

1995 (1)

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[Crossref] [PubMed]

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, 299–309 (1993).
[Crossref] [PubMed]

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R01–R43 (2005).
[Crossref]

M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
[Crossref]

S. R. Arridge and J. C. Hebden. “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. in Med. Biol. 42, 841–853 (1997).
[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, 299–309 (1993).
[Crossref] [PubMed]

Boas, D.A.

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, 2443–2451 (2008).
[Crossref] [PubMed]

Bouman, C. A.

J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, “Nonlinear multigrid algorithms for Bayesian optical diffusion tomography,” IEEE Trans. Image Process. 10, 909–922 (2001).
[Crossref]

Brooksby, B.

B. Brooksby, S. Jiang, H. Dehghani, B. W. Powgue, and K. D. Paulsen, “Combining near-infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. of Biomed. Opt. 10, 0515041–10 (2005).

Brooksby, B. A.

B.W. Pogue, S.C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11, 033001 (2006).
[Crossref]

Cerussi, A. E.

N. S. Shah, A. E. Cerussi, D. Gordon, A. Durkin, L. Wenzel, B. Hill, M. Compton, and B. J. Tromberg, “Integration of diffuse optical technology into clinical settings for breast health applications,” Frontiers in Optics, The 90th OSA Annual Meeting, 2006.

Cerussi, A.E.

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, 2443–2451 (2008).
[Crossref] [PubMed]

Compton, M.

N. S. Shah, A. E. Cerussi, D. Gordon, A. Durkin, L. Wenzel, B. Hill, M. Compton, and B. J. Tromberg, “Integration of diffuse optical technology into clinical settings for breast health applications,” Frontiers in Optics, The 90th OSA Annual Meeting, 2006.

Cummer, S. A.

Y. Zhai and S. A. Cummer, “An orthogonal projection and regularization technique for magnetospheric radio tomography,” J. Geophys. Res. 111, A03207 (2006).
[Crossref]

Davis, S.C.

B.W. Pogue, S.C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11, 033001 (2006).
[Crossref]

Dehghani, H.

P. K. Yalavarthy, D.R. Lynch, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems,” Med. Phys. 35(5), 1682–1696, (2008).
[Crossref] [PubMed]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

B.W. Pogue, S.C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11, 033001 (2006).
[Crossref]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critically computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113, (2006).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Powgue, and K. D. Paulsen, “Combining near-infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. of Biomed. Opt. 10, 0515041–10 (2005).

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,” Appl. Opt. 42, 135–145 (2003).
[Crossref] [PubMed]

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, 299–309 (1993).
[Crossref] [PubMed]

Durkin, A.

N. S. Shah, A. E. Cerussi, D. Gordon, A. Durkin, L. Wenzel, B. Hill, M. Compton, and B. J. Tromberg, “Integration of diffuse optical technology into clinical settings for breast health applications,” Frontiers in Optics, The 90th OSA Annual Meeting, 2006.

Feldmann, P.

P. Feldmann and R. Freund, “Reduced order modeling of large linear subcircuits via a block Lanczos algorithm,” In Proceedings Design Automation Conference (Piscataway, NJ, USA, 1995), pp.474–479.

Freund, R.

P. Feldmann and R. Freund, “Reduced order modeling of large linear subcircuits via a block Lanczos algorithm,” In Proceedings Design Automation Conference (Piscataway, NJ, USA, 1995), pp.474–479.

Gibson, A.

M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
[Crossref]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R01–R43 (2005).
[Crossref]

Gordon, D.

N. S. Shah, A. E. Cerussi, D. Gordon, A. Durkin, L. Wenzel, B. Hill, M. Compton, and B. J. Tromberg, “Integration of diffuse optical technology into clinical settings for breast health applications,” Frontiers in Optics, The 90th OSA Annual Meeting, 2006.

Gu, X.

X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
[Crossref] [PubMed]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R01–R43 (2005).
[Crossref]

S. R. Arridge and J. C. Hebden. “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. in Med. Biol. 42, 841–853 (1997).
[Crossref]

Hill, B.

N. S. Shah, A. E. Cerussi, D. Gordon, A. Durkin, L. Wenzel, B. Hill, M. Compton, and B. J. Tromberg, “Integration of diffuse optical technology into clinical settings for breast health applications,” Frontiers in Optics, The 90th OSA Annual Meeting, 2006.

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, 299–309 (1993).
[Crossref] [PubMed]

Jacques, S.L.

S.L. Jacques and B.W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13, 041302 (2008).
[Crossref] [PubMed]

Jiang, H.

X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
[Crossref] [PubMed]

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[Crossref] [PubMed]

Jiang, S.

B. Brooksby, S. Jiang, H. Dehghani, B. W. Powgue, and K. D. Paulsen, “Combining near-infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. of Biomed. Opt. 10, 0515041–10 (2005).

Lynch, D.R.

P. K. Yalavarthy, D.R. Lynch, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems,” Med. Phys. 35(5), 1682–1696, (2008).
[Crossref] [PubMed]

Millane, R. P.

J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, “Nonlinear multigrid algorithms for Bayesian optical diffusion tomography,” IEEE Trans. Image Process. 10, 909–922 (2001).
[Crossref]

Ngo, K. D. T.

L. Vu-Quoc, Y. Zhai, and K. D. T. Ngo, “Efficient simulation of coupled circuit-field problems: Generalized Falk method,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 23, 1209–1219 (2004).
[Crossref]

Nieto-Vesperinas, M.

Ntziachristos, V.

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

J. Ripoll, M. Nieto-Vesperinas, R. Weissleder, and V. Ntziachristos, “Fast analytical approximation for arbitrary geometries in diffuse optical tomography,” Opt. Lett. 27, 527, (2002).
[Crossref]

Paulsen, K. D.

P. K. Yalavarthy, D.R. Lynch, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems,” Med. Phys. 35(5), 1682–1696, (2008).
[Crossref] [PubMed]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

B.W. Pogue, S.C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11, 033001 (2006).
[Crossref]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critically computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113, (2006).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, H. Dehghani, B. W. Powgue, and K. D. Paulsen, “Combining near-infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. of Biomed. Opt. 10, 0515041–10 (2005).

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,” Appl. Opt. 42, 135–145 (2003).
[Crossref] [PubMed]

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[Crossref] [PubMed]

Paulsen, K.D.

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, 2443–2451 (2008).
[Crossref] [PubMed]

Phillips, J.

J. Phillips, “Projection-based approaches for model reduction of weakly nonlinear, time-varying systems,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 22, 171–187 (2003).
[Crossref]

Pogue, B. W.

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, 2443–2451 (2008).
[Crossref] [PubMed]

P. K. Yalavarthy, D.R. Lynch, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems,” Med. Phys. 35(5), 1682–1696, (2008).
[Crossref] [PubMed]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critically computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113, (2006).
[Crossref] [PubMed]

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,” Appl. Opt. 42, 135–145 (2003).
[Crossref] [PubMed]

Pogue, B.W.

S.L. Jacques and B.W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13, 041302 (2008).
[Crossref] [PubMed]

B.W. Pogue, S.C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11, 033001 (2006).
[Crossref]

Poplack, S. P.

Powgue, B. W.

B. Brooksby, S. Jiang, H. Dehghani, B. W. Powgue, and K. D. Paulsen, “Combining near-infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. of Biomed. Opt. 10, 0515041–10 (2005).

Rewienski, M.

M. Rewienski and J. White, “A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 22, 155–169 (2003).
[Crossref]

Ripoll, J.

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

J. Ripoll, M. Nieto-Vesperinas, R. Weissleder, and V. Ntziachristos, “Fast analytical approximation for arbitrary geometries in diffuse optical tomography,” Opt. Lett. 27, 527, (2002).
[Crossref]

Schweiger, M.

M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
[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, 299–309 (1993).
[Crossref] [PubMed]

Shah, N. S.

N. S. Shah, A. E. Cerussi, D. Gordon, A. Durkin, L. Wenzel, B. Hill, M. Compton, and B. J. Tromberg, “Integration of diffuse optical technology into clinical settings for breast health applications,” Frontiers in Optics, The 90th OSA Annual Meeting, 2006.

Song, X.

B.W. Pogue, S.C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11, 033001 (2006).
[Crossref]

Tromberg, B. J.

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, 2443–2451 (2008).
[Crossref] [PubMed]

N. S. Shah, A. E. Cerussi, D. Gordon, A. Durkin, L. Wenzel, B. Hill, M. Compton, and B. J. Tromberg, “Integration of diffuse optical technology into clinical settings for breast health applications,” Frontiers in Optics, The 90th OSA Annual Meeting, 2006.

Vu-Quoc, L.

Y. Zhai and L. Vu-Quoc, “Analysis of power magnetic components with nonlinear static hysteresis: Proper orthogonal decomposition and model reduction,” IEEE Trans. Magnetics 43, 1888–1897 (2007).
[Crossref]

Y. Zhai and L. Vu-Quoc, “Analysis of power magnetic components with nonlinear static hysteresis: Finite-element formulation,” IEEE Transactions on Magnetics 41, 2243–2256 (2005).
[Crossref]

L. Vu-Quoc, Y. Zhai, and K. D. T. Ngo, “Efficient simulation of coupled circuit-field problems: Generalized Falk method,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 23, 1209–1219 (2004).
[Crossref]

Wang, L. V.

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

Webb, K. J.

J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, “Nonlinear multigrid algorithms for Bayesian optical diffusion tomography,” IEEE Trans. Image Process. 10, 909–922 (2001).
[Crossref]

Weissleder, R.

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

J. Ripoll, M. Nieto-Vesperinas, R. Weissleder, and V. Ntziachristos, “Fast analytical approximation for arbitrary geometries in diffuse optical tomography,” Opt. Lett. 27, 527, (2002).
[Crossref]

Wenzel, L.

N. S. Shah, A. E. Cerussi, D. Gordon, A. Durkin, L. Wenzel, B. Hill, M. Compton, and B. J. Tromberg, “Integration of diffuse optical technology into clinical settings for breast health applications,” Frontiers in Optics, The 90th OSA Annual Meeting, 2006.

White, J.

M. Rewienski and J. White, “A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 22, 155–169 (2003).
[Crossref]

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X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
[Crossref] [PubMed]

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P. K. Yalavarthy, D.R. Lynch, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems,” Med. Phys. 35(5), 1682–1696, (2008).
[Crossref] [PubMed]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critically computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113, (2006).
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Ye, J. C.

J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, “Nonlinear multigrid algorithms for Bayesian optical diffusion tomography,” IEEE Trans. Image Process. 10, 909–922 (2001).
[Crossref]

Yodh, A.G.

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, 2443–2451 (2008).
[Crossref] [PubMed]

Zhai, Y.

Y. Zhai and L. Vu-Quoc, “Analysis of power magnetic components with nonlinear static hysteresis: Proper orthogonal decomposition and model reduction,” IEEE Trans. Magnetics 43, 1888–1897 (2007).
[Crossref]

Y. Zhai and S. A. Cummer, “An orthogonal projection and regularization technique for magnetospheric radio tomography,” J. Geophys. Res. 111, A03207 (2006).
[Crossref]

Y. Zhai and L. Vu-Quoc, “Analysis of power magnetic components with nonlinear static hysteresis: Finite-element formulation,” IEEE Transactions on Magnetics 41, 2243–2256 (2005).
[Crossref]

L. Vu-Quoc, Y. Zhai, and K. D. T. Ngo, “Efficient simulation of coupled circuit-field problems: Generalized Falk method,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 23, 1209–1219 (2004).
[Crossref]

Y. Zhai, “Model-order reduction for efficient simulation of nonlinear electro-magneto-thermal coupled problems,” Ph.D. Thesis, University of Florida, 2003.

Appl. Opt. (1)

Comput. Sci. Eng. (1)

M. Schweiger, A. Gibson, and S. R. Arridge, “Computational aspects of diffuse optical tomography,” Comput. Sci. Eng. 5, 33–41 (2003).
[Crossref]

IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. (3)

L. Vu-Quoc, Y. Zhai, and K. D. T. Ngo, “Efficient simulation of coupled circuit-field problems: Generalized Falk method,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 23, 1209–1219 (2004).
[Crossref]

J. Phillips, “Projection-based approaches for model reduction of weakly nonlinear, time-varying systems,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 22, 171–187 (2003).
[Crossref]

M. Rewienski and J. White, “A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst. 22, 155–169 (2003).
[Crossref]

IEEE Trans. Image Process. (1)

J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, “Nonlinear multigrid algorithms for Bayesian optical diffusion tomography,” IEEE Trans. Image Process. 10, 909–922 (2001).
[Crossref]

IEEE Trans. Magnetics (1)

Y. Zhai and L. Vu-Quoc, “Analysis of power magnetic components with nonlinear static hysteresis: Proper orthogonal decomposition and model reduction,” IEEE Trans. Magnetics 43, 1888–1897 (2007).
[Crossref]

IEEE Transactions on Magnetics (1)

Y. Zhai and L. Vu-Quoc, “Analysis of power magnetic components with nonlinear static hysteresis: Finite-element formulation,” IEEE Transactions on Magnetics 41, 2243–2256 (2005).
[Crossref]

J. Biomed. Opt. (2)

B.W. Pogue, S.C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11, 033001 (2006).
[Crossref]

S.L. Jacques and B.W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13, 041302 (2008).
[Crossref] [PubMed]

J. Geophys. Res. (1)

Y. Zhai and S. A. Cummer, “An orthogonal projection and regularization technique for magnetospheric radio tomography,” J. Geophys. Res. 111, A03207 (2006).
[Crossref]

J. of Biomed. Opt. (1)

B. Brooksby, S. Jiang, H. Dehghani, B. W. Powgue, and K. D. Paulsen, “Combining near-infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure,” J. of Biomed. Opt. 10, 0515041–10 (2005).

Med. Phys. (6)

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, 2443–2451 (2008).
[Crossref] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[Crossref] [PubMed]

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[Crossref] [PubMed]

X. Gu, Y. Xu, and H. Jiang, “Mesh-based enhancement schemes in diffuse optical tomography,” Med. Phys. 30, 861–869 (2003).
[Crossref] [PubMed]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[Crossref] [PubMed]

P. K. Yalavarthy, D.R. Lynch, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems,” Med. Phys. 35(5), 1682–1696, (2008).
[Crossref] [PubMed]

Nature Biotechnol. (1)

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

Opt. Express (1)

Opt. Lett. (1)

Phys. in Med. Biol. (1)

S. R. Arridge and J. C. Hebden. “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. in Med. Biol. 42, 841–853 (1997).
[Crossref]

Phys. Med. Biol. (1)

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R01–R43 (2005).
[Crossref]

Other (6)

The Biomedical Optics Research Laboratory at University College London, http://www.medphys.ucl.ac.uk/research/borl/.

The Near Infrared Imaging Group at Dartmouth College, http://www-nml.dartmouth.edu/nir/.

N. S. Shah, A. E. Cerussi, D. Gordon, A. Durkin, L. Wenzel, B. Hill, M. Compton, and B. J. Tromberg, “Integration of diffuse optical technology into clinical settings for breast health applications,” Frontiers in Optics, The 90th OSA Annual Meeting, 2006.

The Breast Cancer Multi-Dimentional Diffuse Optical Imaging Network, http://www.bli.uci.edu/ntroi/.

P. Feldmann and R. Freund, “Reduced order modeling of large linear subcircuits via a block Lanczos algorithm,” In Proceedings Design Automation Conference (Piscataway, NJ, USA, 1995), pp.474–479.

Y. Zhai, “Model-order reduction for efficient simulation of nonlinear electro-magneto-thermal coupled problems,” Ph.D. Thesis, University of Florida, 2003.

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Figures (6)

Fig. 1.
Fig. 1.

Concept of projection-based MOR. This figure depicts three essential steps to extract a reduced-order model from a large full-order model system through orthogonal projection.

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Fig. 2.
Fig. 2.

The MOR-based tomographic reconstruction.

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Fig. 3.
Fig. 3.

The simulated photon density distribution of a test phantom from the full-order model (left) and that from the reduced-order model (right).

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Fig. 4.
Fig. 4.

The original absorption μa (left) and reduced scattering μ′s (right) coefficients of a test phantom.

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Fig. 5.
Fig. 5.

The reconstructed absorption μa (left) and reduced scattering μ′s (right) coefficients of a test phantom.

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Fig. 6.
Fig. 6.

The reduced-order model converges to the full-order model with increased number of trial vectors for MOR and comparison of various Krylov-type MOR methods.

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Tables (3)

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Table 1. Speed-up ratio for linear forward problem of DOT using the WYD method

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Table 2. Speed-up ratio for nonlinear DOT imaging using the WYD method

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Table 3. Speed-up ratio for nonlinear DOT imaging using the POD-based MOR technique

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Equations (30)

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1 c ∂ ρ ( r , t ) ∂ t + ( μ a ( r ) ) − ∇ · ( κ ( r ) ∇ ) ) ρ ( r , t ) = s ( r , t ) ,
( ∇ · ( κ ( r ) ∇ ) ) ρ ( r , ω ) − ( μ a ( r ) + iω c ) ρ ( r , ω ) = − s ( r , ω ) ,
M d u d t + Ku = s ,
B ij = ∫ Ω κ ( r ) ∇ N j ( r ) · ∇ N i ( r ) d Ω ; C ij = ∫ Ω μ a ( r ) N j ( r ) N i ( r ) d Ω ;
M ij = ∫ Ω N j ( r ) N i ( r ) dΩ ; s j ( t ) = ∫ Ω N j ( r ) S ( r , t ) d Ω + ∫ ∂ Ω N j ( r ) Γ ( r , t ) d ∂ Ω ;
Ku = s , C ij = ∫ Ω ( μ a ( r ) + iω c ) N j ( r ) N i ( r ) d Ω
χ 2 = ∥ ∂ u ∂ θ ∥ Δ θ − Δ θ 2 + λ ∥ Δ θ ∥ 2
Δ θ = ( J T J + λI ) − 1 J T Δ u ,
u n × 1 = Q n × r η r × 1 ,
K z i * = M z i − 1 ⇒ z i * = K − 1 M z i − 1
c i − 1 = z i * T M z i − 1
z i * * = z i * − c i − 1 z i − 1 − b i − 1 z i − 2 ( M − orthogonalization and M − normalization )
b i = z i * * T M z i * *
z i = z i * * b i
T r = [ c 1 b 2 0 … … 0 b 2 c 2 b 3 … … 0 0 b 3 c 3 … … 0 0 … … … … 0 0 … … b r − 1 c r − 1 b r 0 … … 0 b r c r ] r × r .
K w i * = M w i − 1 ⇒ w i * = K − 1 M w i − 1
c i , j = w j T M w i *
w i * * = w i * − ∑ j = 1 i − 1 c i , j w j ( M − orthogonalization and M − normalization )
b i = w i * * T M w i * *
w i = w i * * b i
K − 1 M [ w 1 w 2 … w r ] = [ w 1 w 2 … w r ] H ,
H = [ c 2,1 c 3,1 c 4,1 … … c r + 1,1 b 2 c 3,2 c 4,2 … … c r + 1,2 0 b 3 c 4,3 … … … 0 0 b 4 … … … 0 … … b r − 1 c r , r − 1 c r + 1 , r − 1 0 … … 0 b r c r + 1 , r ] r × r
W T M K − 1 MW = H ,
( Z T M K − 1 MZ ) d η dt + ( Z T MZ ) η = Z T M K − 1 s .
T r d η dt + Iη = Z T M K − 1 s .
I d η dt + K * η = W T s .
K * η = s * ( η ) ,
U = Ψ ∑ V T .
u n × 1 = Ψ n × r η r × 1 ,
M * d η dt + K * η = s * ,

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