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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    [CrossRef]
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    [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]
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    [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).
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    [CrossRef] [PubMed]
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    [CrossRef]
  15. 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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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  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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  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).
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2008

S.L. Jacques, 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, 1682-1696 (2008).
[CrossRef] [PubMed]

2007

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, 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 Transactions on Magnetics 43, 1888-1897 (2007).
[CrossRef]

2006

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

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]

2005

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, "Looking and listening to light: the evolution of whole-body photonic imaging," Nat. Biotechnol. 23, 313-320 (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

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

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]

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

M. Schweiger, A. Gibson and S. R. Arridge, "Computational aspects of diffuse optical tomography," Comput. Sci. Eng. 5, 33-41 (2003).
[CrossRef]

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

2001

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

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

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

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.

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.

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]

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, 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, 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]

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]

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]

Gibson, A.

M. Schweiger, A. Gibson and S. R. Arridge, "Computational aspects of diffuse optical tomography," Comput. Sci. Eng. 5, 33-41 (2003).
[CrossRef]

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.

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

Jacques, S.L.

S.L. Jacques, 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, 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," Nat. 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, 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, 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]

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]

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, 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, 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, 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," Nat. 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]

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.

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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 Transactions on Magnetics 43, 1888-1897 (2007).
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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).
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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," Nat. 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," Nat. Biotechnol. 23, 313-320 (2005).
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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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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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Xu, Y.

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

Yalavarthy, P. K.

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, 1682-1696 (2008).
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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, 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 Transactions on 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]

Appl. Opt.

Comput. Sci. Eng.

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.

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]

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]

IEEE Trans. Image Process.

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 Transactions on Magnetics

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]

Y. Zhai and L. Vu-Quoc, "Analysis of power magnetic components with nonlinear static hysteresis: Proper orthogonal decomposition and model reduction," IEEE Transactions on Magnetics 43, 1888-1897 (2007).
[CrossRef]

J. Biomed. Opt.

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).
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S.L. Jacques, B.W. Pogue, "Tutorial on diffuse light transport," J. Biomed. Opt. 13, 041302 (2008).
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Y. Zhai and S. A. Cummer, "An orthogonal projection and regularization technique for magnetospheric radio tomography," J. Geophys. Res. 111, A03207 (2006).
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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.

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).
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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]

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, 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, 1682-1696 (2008).
[CrossRef] [PubMed]

Nat. Biotechnol.

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

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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.

Fig. 2.
Fig. 2.

The MOR-based tomographic reconstruction.

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).

Fig. 4.
Fig. 4.

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

Fig. 5.
Fig. 5.

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

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.

Tables (3)

Tables Icon

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

Tables Icon

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

Tables Icon

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

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 ) + 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 ) ; 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 ) + 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 + = 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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