Abstract

We have developed an efficient fully three-dimensional (3D) reconstruction algorithm for diffuse optical tomography (DOT). The 3D DOT, a severely ill-posed problem, is tackled through a pseudodynamic (PD) approach wherein an ordinary differential equation representing the evolution of the solution on pseudotime is integrated that bypasses an explicit inversion of the associated, ill-conditioned system matrix. One of the most computationally expensive parts of the iterative DOT algorithm, the reevaluation of the Jacobian in each of the iterations, is avoided by using the adjoint-Broyden update formula to provide low rank updates to the Jacobian. In addition, wherever feasible, we have also made the algorithm efficient by integrating along the quadratic path provided by the perturbation equation containing the Hessian. These algorithms are then proven by reconstruction, using simulated and experimental data and verifying the PD results with those from the popular Gauss–Newton scheme. The major findings of this work are as follows: (i) the PD reconstructions are comparatively artifact free, providing superior absorption coefficient maps in terms of quantitative accuracy and contrast recovery; (ii) the scaling of computation time with the dimension of the measurement set is much less steep with the Jacobian update formula in place than without it; and (iii) an increase in the data dimension, even though it renders the reconstruction problem less ill conditioned and thus provides relatively artifact-free reconstructions, does not necessarily provide better contrast property recovery. For the latter, one should also take care to uniformly distribute the measurement points, avoiding regions close to the source so that the relative strength of the derivatives for measurements away from the source does not become insignificant.

© 2012 Optical Society of America

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2011 (3)

2009 (2)

S. Schlenkrich and A. Walther, “Global convergence of quasi-Newton methods based on adjoint Broyden updates,” Appl. Num. Math. 59, 1120–1136 (2009).
[CrossRef]

B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamical systems approach to a class of inverse problems in engineering,” Proc. R. Soc. A 465, 1561 (2009).
[CrossRef]

2007 (1)

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]

2006 (1)

B. Kanmani and R. M. Vasu, “Diffuse optical tomography through solving a system of quadratic equations: theory and simulations,” Phys. Med. Biol. 51, 981–998 (2006).
[CrossRef]

2005 (2)

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

M. Schweiger, S. R. Arridge, and I. Nissila, “Gauss–Newton method for image reconstruction in diffuse optical tomography,” Phys. Med. Biol. 50, 2365–2386 (2005).
[CrossRef]

2003 (1)

2002 (1)

Y. Xu, N. Iftima, H. Jiang, L. L. Key, and M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef]

2001 (5)

H. Jiang, Y. Xu, N. Iftimia, L. Baron, and J. Eggert, “Three dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
[CrossRef]

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

E. M. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. Schmidt, D. T. Delpy, and S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef]

B. W. Pogue, S. Geimer, T. O. McBride, S. D. Jiang, U. L. Osterberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001).
[CrossRef]

D. Roy, “A new numeric-analytical principle for nonlinear deterministic and stochastic dynamical systems,” Proc. R. Soc. Lond. A 457, 539–566 (2001).
[CrossRef]

2000 (3)

D. Roy, “Explorations of the phase space linearization method for deterministic and stochastic non-linear dynamical systems,” Nonlin. Dynam. 23, 225–258 (2000).
[CrossRef]

H. B. Jiang, Y. Xu, and N. Iftimia, “Experimental three-dimensional optical image reconstruction of heterogeneous turbid media from continuous-wave data,” Opt. Express 7, 204–209 (2000).
[CrossRef]

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

1999 (1)

A. H. Heilscher, A. D. Close, and K. M. Hansen, “Gradient based iterative image reconstruction scheme for time resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

1998 (1)

1997 (1)

S. Arridge and J. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–854 (1997).
[CrossRef]

1994 (1)

1965 (1)

C. G. Broyden, “A class of methods for solving nonlinear simultaneous equations,” Math. Comp. 19, 577–593 (1965).
[CrossRef]

Arridge,

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

Arridge, S.

M. Schweiger and S. Arridge, “Comparison of two- and three-dimensional reconstruction methods in optical tomography,” Appl. Opt. 37, 7419–7428 (1998).
[CrossRef]

S. Arridge and J. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–854 (1997).
[CrossRef]

Arridge, S. R.

M. Schweiger, S. R. Arridge, and I. Nissila, “Gauss–Newton method for image reconstruction in diffuse optical tomography,” Phys. Med. Biol. 50, 2365–2386 (2005).
[CrossRef]

E. M. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. Schmidt, D. T. Delpy, and S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef]

Banerjee, B.

B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamical systems approach to a class of inverse problems in engineering,” Proc. R. Soc. A 465, 1561 (2009).
[CrossRef]

Barbaro, A.

Barbieri, B.

Baron, L.

H. Jiang, Y. Xu, N. Iftimia, L. Baron, and J. Eggert, “Three dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
[CrossRef]

Biswas, S. K.

Boas, D. A.

Bolster, M.

Y. Xu, N. Iftimia, L. L. Key, and M. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef]

Bolster, M. B.

Y. Xu, N. Iftima, H. Jiang, L. L. Key, and M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef]

Broyden, C. G.

C. G. Broyden, “A class of methods for solving nonlinear simultaneous equations,” Math. Comp. 19, 577–593 (1965).
[CrossRef]

Butler, J.

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

Chance, B.

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

Close, A. D.

A. H. Heilscher, A. D. Close, and K. M. Hansen, “Gradient based iterative image reconstruction scheme for time resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

Dehghani, H.

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]

E. M. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. Schmidt, D. T. Delpy, and S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef]

Delpy, D. T.

E. M. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. Schmidt, D. T. Delpy, and S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef]

Eggert, J.

H. Jiang, Y. Xu, N. Iftimia, L. Baron, and J. Eggert, “Three dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
[CrossRef]

Fantini, S.

Fishkin, J.

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

Franceschini, M. A.

Geimer, S.

Gibson, A. P.

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

Gratton, E.

Gupta, S.

Hansen, K. M.

A. H. Heilscher, A. D. Close, and K. M. Hansen, “Gradient based iterative image reconstruction scheme for time resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

Hebden, J.

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

S. Arridge and J. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–854 (1997).
[CrossRef]

Hebden, J. C.

E. M. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. Schmidt, D. T. Delpy, and S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef]

Heilscher, A. H.

A. H. Heilscher, A. D. Close, and K. M. Hansen, “Gradient based iterative image reconstruction scheme for time resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

Hillman, E. M.

E. M. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. Schmidt, D. T. Delpy, and S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef]

Holboke, M. J.

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

Iftima, N.

Y. Xu, N. Iftima, H. Jiang, L. L. Key, and M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef]

Iftimia, N.

H. Jiang, Y. Xu, N. Iftimia, L. Baron, and J. Eggert, “Three dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
[CrossRef]

H. B. Jiang, Y. Xu, and N. Iftimia, “Experimental three-dimensional optical image reconstruction of heterogeneous turbid media from continuous-wave data,” Opt. Express 7, 204–209 (2000).
[CrossRef]

Y. Xu, N. Iftimia, L. L. Key, and M. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef]

Jiang, H.

Y. Xu, N. Iftima, H. Jiang, L. L. Key, and M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef]

H. Jiang, Y. Xu, N. Iftimia, L. Baron, and J. Eggert, “Three dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
[CrossRef]

Jiang, H. B.

Jiang, S. D.

Joshua, B. F.

Kanhirodan, R.

Kanmani, B.

B. Kanmani and R. M. Vasu, “Diffuse optical tomography through solving a system of quadratic equations: theory and simulations,” Phys. Med. Biol. 51, 981–998 (2006).
[CrossRef]

Key, L. L.

Y. Xu, N. Iftima, H. Jiang, L. L. Key, and M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef]

Y. Xu, N. Iftimia, L. L. Key, and M. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef]

Kidney, D.

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

Kilmer, M. E.

Li, X.

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

McBride, T. O.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

B. W. Pogue, S. Geimer, T. O. McBride, S. D. Jiang, U. L. Osterberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001).
[CrossRef]

Miller, E. L.

Nissila, I.

M. Schweiger, S. R. Arridge, and I. Nissila, “Gauss–Newton method for image reconstruction in diffuse optical tomography,” Phys. Med. Biol. 50, 2365–2386 (2005).
[CrossRef]

Osterberg, U. L.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

B. W. Pogue, S. Geimer, T. O. McBride, S. D. Jiang, U. L. Osterberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001).
[CrossRef]

Osterman, K. S.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Paulsen, K. D.

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]

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

B. W. Pogue, S. Geimer, T. O. McBride, S. D. Jiang, U. L. Osterberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001).
[CrossRef]

Pogue, B. W.

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]

B. W. Pogue, S. Geimer, T. O. McBride, S. D. Jiang, U. L. Osterberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001).
[CrossRef]

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Poplack, S. P.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Rajan, K.

S. K. Biswas, K. Rajan, and R. M. Vasu, “Accelerated gradient based diffuse optical tomographic image reconstruction,” Med. Phys. 38, 539–547 (2011).
[CrossRef]

Raveendran, T.

Roy, D.

S. K. Biswas, R. Kanhirodan, R. M. Vasu, and D. Roy, “A pseudo-dynamical systems approach based on a quadratic approximation of update equations for diffuse optical tomography,” J. Opt. Soc. Am. A 28, 1784–1795 (2011).
[CrossRef]

T. Raveendran, S. Gupta, R. M. Vasu, and D. Roy, “Pseudo-time particle filtering for diffuse optical tomography,” J. Opt. Soc. Am. A 28, 2070–2081 (2011).
[CrossRef]

B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamical systems approach to a class of inverse problems in engineering,” Proc. R. Soc. A 465, 1561 (2009).
[CrossRef]

D. Roy, “A new numeric-analytical principle for nonlinear deterministic and stochastic dynamical systems,” Proc. R. Soc. Lond. A 457, 539–566 (2001).
[CrossRef]

D. Roy, “Explorations of the phase space linearization method for deterministic and stochastic non-linear dynamical systems,” Nonlin. Dynam. 23, 225–258 (2000).
[CrossRef]

Schlenkrich, S.

S. Schlenkrich and A. Walther, “Global convergence of quasi-Newton methods based on adjoint Broyden updates,” Appl. Num. Math. 59, 1120–1136 (2009).
[CrossRef]

Schmidt, F. E.

E. M. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. Schmidt, D. T. Delpy, and S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef]

Schweiger, M.

M. Schweiger, S. R. Arridge, and I. Nissila, “Gauss–Newton method for image reconstruction in diffuse optical tomography,” Phys. Med. Biol. 50, 2365–2386 (2005).
[CrossRef]

E. M. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. Schmidt, D. T. Delpy, and S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef]

M. Schweiger and S. Arridge, “Comparison of two- and three-dimensional reconstruction methods in optical tomography,” Appl. Opt. 37, 7419–7428 (1998).
[CrossRef]

Shah, N.

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

Tromberg, B.

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

Vasu, R. M.

S. K. Biswas, R. Kanhirodan, R. M. Vasu, and D. Roy, “A pseudo-dynamical systems approach based on a quadratic approximation of update equations for diffuse optical tomography,” J. Opt. Soc. Am. A 28, 1784–1795 (2011).
[CrossRef]

T. Raveendran, S. Gupta, R. M. Vasu, and D. Roy, “Pseudo-time particle filtering for diffuse optical tomography,” J. Opt. Soc. Am. A 28, 2070–2081 (2011).
[CrossRef]

S. K. Biswas, K. Rajan, and R. M. Vasu, “Accelerated gradient based diffuse optical tomographic image reconstruction,” Med. Phys. 38, 539–547 (2011).
[CrossRef]

B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamical systems approach to a class of inverse problems in engineering,” Proc. R. Soc. A 465, 1561 (2009).
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S. Schlenkrich and A. Walther, “Global convergence of quasi-Newton methods based on adjoint Broyden updates,” Appl. Num. Math. 59, 1120–1136 (2009).
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B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Xu, Y.

Y. Xu, N. Iftima, H. Jiang, L. L. Key, and M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
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H. Jiang, Y. Xu, N. Iftimia, L. Baron, and J. Eggert, “Three dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
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Y. Xu, N. Iftimia, L. L. Key, and M. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
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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).
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M. J. Holboke, B. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance, and A. Yodh, “Three-dimensional diffuse optical mammography with ultrasound localization in a human subject,” J. Biomed. Opt. 5, 237–247 (2000).
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Appl. Num. Math. (1)

S. Schlenkrich and A. Walther, “Global convergence of quasi-Newton methods based on adjoint Broyden updates,” Appl. Num. Math. 59, 1120–1136 (2009).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Med. Imaging (2)

H. Jiang, Y. Xu, N. Iftimia, L. Baron, and J. Eggert, “Three dimensional optical tomographic imaging of breast in a human subject,” IEEE Trans. Med. Imaging 20, 1334–1340 (2001).
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J. Biomed. Opt. (3)

Y. Xu, N. Iftima, H. Jiang, L. L. Key, and M. B. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
[CrossRef]

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

Y. Xu, N. Iftimia, L. L. Key, and M. Bolster, “Three-dimensional diffuse optical tomography of bones and joints,” J. Biomed. Opt. 7, 88–92 (2002).
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J. Opt. Soc. Am. A (2)

Math. Comp. (1)

C. G. Broyden, “A class of methods for solving nonlinear simultaneous equations,” Math. Comp. 19, 577–593 (1965).
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Med. Phys. (2)

S. K. Biswas, K. Rajan, and R. M. Vasu, “Accelerated gradient based diffuse optical tomographic image reconstruction,” Med. Phys. 38, 539–547 (2011).
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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).
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D. Roy, “Explorations of the phase space linearization method for deterministic and stochastic non-linear dynamical systems,” Nonlin. Dynam. 23, 225–258 (2000).
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Opt. Express (1)

Phys. Med. Biol. (5)

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B. Kanmani and R. M. Vasu, “Diffuse optical tomography through solving a system of quadratic equations: theory and simulations,” Phys. Med. Biol. 51, 981–998 (2006).
[CrossRef]

Proc. R. Soc. A (1)

B. Banerjee, D. Roy, and R. M. Vasu, “A pseudo-dynamical systems approach to a class of inverse problems in engineering,” Proc. R. Soc. A 465, 1561 (2009).
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Proc. R. Soc. Lond. A (1)

D. Roy, “A new numeric-analytical principle for nonlinear deterministic and stochastic dynamical systems,” Proc. R. Soc. Lond. A 457, 539–566 (2001).
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Radiology (1)

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

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Figures (9)

Fig. 1.
Fig. 1.

(a) Geometry of data collection. Data are gathered from seven planes altogether into which the cylindrical object is divided. The source is always in the midplane. (b) Source–detector configuration in a plane, here the midplane. (c) Meshed cylindrical object.

Fig. 2.
Fig. 2.

The dimension of the dataset is reduced from 588 (using all the seven planes, denoted P7) to 168 (using two planes, denoted P2).

Fig. 3.
Fig. 3.

Results of reconstruction of μa using the GN, ABGN, PD, and ABPD schemes (grouped column-wise) with data from seven, five, four, three, and two planes (grouped row-wise).The plane highlighted is the one passing through the centers of the spherical inhomogeneities.

Fig. 4.
Fig. 4.

Comparison of cross-sectional line plots through the center of the reconstructed μa inhomogeneities (with the original) as the data dimension decreased, using the (a) GN, (b) ABGN, (c) PD, and (d) ABPD algorithms.

Fig. 5.
Fig. 5.

Comparison of the rise of computation time of GN and PD algorithms as the data dimension increased with those using the AB strategy (denoted as ABGN and ABPD).

Fig. 6.
Fig. 6.

(a) Schematic diagram of the experimental setup and (b) the photograph.

Fig. 7.
Fig. 7.

Results of reconstruction of μa using the GN, ABGN, PD, and ABPD schemes (shown column-wise) using data from five, four, three, and two planes (shown row-wise). The emphasized planes are the ones passing through the axes of the two cylindrical inclusions.

Fig. 8.
Fig. 8.

Comparison of cross-sectional line plots through the centers of the reconstructed inclusions taken at different heights (Z) (with that of the original) obtained using GN, ABGN, PD, and ABPD algorithms.

Fig. 9.
Fig. 9.

Comparison of rise of computation time of GN and PD algorithms, as the (experimental) data dimension increased, with (denoted as ABGN and ABPD) and without using the AB strategy.

Tables (1)

Tables Icon

Table 1. Comparison of Performance of the Reconstruction Algorithms Using the Elapsed CPU Time as the Yardstick (Processor: Intel Core-2 Duo, 1.92 MHz, 2 GB RAM)

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

·(κ(r)Φ(r))+μa(r)Φ(r)=Q0δ(rr0),
with2Aκ(m)Φ(m)n+Φ(m)=0.
F(μ)=M.
[F(μb)TF(μb)+λI]Δμ=F(μb)TΔM,
ΔM=F(μb).Δμ.
[FTF+i=1dFiΔMi]ΔμFTΔM=0.
[FTFΔμ+FΔMΔμ]=FTΔM.
FTFΔμ+FTΔμTFΔμ=FTΔM.
μ˙+S(μi,λ)[μ(t)μi]+G=0,
S=SQ(μi,λ)FTFΔμ+FTΔμTFΔμ+λI.
μi+1=exp(S(μi,λ)(hi))μi+titi+1exp(S(μi,λ)(ti+1t))f(t)dt,
f(μ)F(μ)Me=0.
Ai,0=Ai1+f(μi)f(μi)T(f(μi)Ai1)f(μi)Tf(μi).
Δμi,0=(Ai,0)1f(μi).
Ai,j+1=Ai,j+ηi,jηi,jTηi,jTηi,j(f(μi)Ai,j)whereηi,j=(f(μi)Ai,j)Δμi,j.
Ai,j+1Δμi,j+1=f(μi).
Ai=Ai,qandΔμi=Δμi,q.
f(μi+1)rf(μi).

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