Abstract

A new approach that can easily incorporate any generic penalty function into the diffuse optical tomographic image reconstruction is introduced to show the utility of nonquadratic penalty functions. The penalty functions that were used include quadratic (2), absolute (1), Cauchy, and Geman–McClure. The regularization parameter in each of these cases was obtained automatically by using the generalized cross-validation method. The reconstruction results were systematically compared with each other via utilization of quantitative metrics, such as relative error and Pearson correlation. The reconstruction results indicate that, while the quadratic penalty may be able to provide better separation between two closely spaced targets, its contrast recovery capability is limited, and the sparseness promoting penalties, such as 1, Cauchy, and Geman–McClure have better utility in reconstructing high-contrast and complex-shaped targets, with the Geman–McClure penalty being the most optimal one.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]

2013 (1)

K. B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

2012 (2)

R. P. K. Jagannath and P. K. Yalavarthy, “Minimal residual method provides optimal regularization parameter for diffuse optical tomography,” J. Biomed. Opt. 17, 106015 (2012).
[CrossRef]

S. H. Katamreddy and P. K. Yalavarthy, “Model-resolution based regularization improves near infrared diffuse optical tomography,” J. Opt. Soc. Am. A 29, 649–656 (2012).
[CrossRef]

2009 (3)

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

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, “Numerical modelling and image reconstruction in diffuse optical tomography,” Phil. Trans. R. Soc. A 367, 3073–3093 (2009).
[CrossRef]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near Infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

2008 (3)

2007 (4)

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

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

P. Zwartjes and A. Gisolf, “Fourier reconstruction with sparse inversion,” Geophys. Prospect. 55, 199–221 (2007).
[CrossRef]

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]

2005 (2)

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]

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

2004 (1)

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef]

2003 (1)

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef]

2001 (4)

N. Nguyen, P. Milanfar, and G. Golub, “A computationally efficient superresolution image reconstruction algorithm,” IEEE Trans. Image Process. 10, 573–583 (2001).
[CrossRef]

A. H. Hielscher and S. Bartel, “Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography,” J. Biomed. Opt. 6, 183–192 (2001).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

2000 (1)

B. W. Pogue, C. Abele, H. Kaufman, and K. D. Paulsen, “Calibration of near infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
[CrossRef]

1999 (2)

1998 (2)

M D. Sacchi, T. J. Ulrych, and C. Walker, “Interpolation and extrapolation using a high resolution discrete Fourier transform,” IEEE Trans. Signal Process. 46, 31–38 (1998).
[CrossRef]

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead Simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

1997 (3)

G. Golub and U. von Matt, “Generalized cross-validation for large-scale problems,” J. Comput. Graph. Stat. 6, 1–34 (1997).
[CrossRef]

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

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

1996 (1)

1995 (2)

S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part 2: finite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995).
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef]

1994 (1)

R. Acar and C. R. Vogel, “Analysis of bounded variation penalty methods for ill-posed problems,” Inverse Probl. 10, 1217–1229 (1994).
[CrossRef]

1993 (1)

P. C. Hansen and D. P. O. Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

1965 (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Abele, C.

B. W. Pogue, C. Abele, H. Kaufman, and K. D. Paulsen, “Calibration of near infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
[CrossRef]

Acar, R.

R. Acar and C. R. Vogel, “Analysis of bounded variation penalty methods for ill-posed problems,” Inverse Probl. 10, 1217–1229 (1994).
[CrossRef]

Arridge, S. R.

A. Gibson, J. C. Hebden, and S. R. 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]

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

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

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef]

S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part 2: finite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995).
[CrossRef]

Aster, R.

R. Aster, B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems (Academic, 2005).

Aubert, G.

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

Barlaud, M.

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

Bartel, S.

A. H. Hielscher and S. Bartel, “Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography,” J. Biomed. Opt. 6, 183–192 (2001).
[CrossRef]

Bartling, S.

K. B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

Blanc-Feraud, L.

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

Boas, D. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Borchers, B.

R. Aster, B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems (Academic, 2005).

Brooks, D. H.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Cao, N.

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near Infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

Chance, B.

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef]

Charbonnier, P.

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

Choe, R.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef]

Culver, J. P.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef]

Davis, S. C.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near Infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Dehghani, H.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near Infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

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

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, “Numerical modelling and image reconstruction in diffuse optical tomography,” Phil. Trans. R. Soc. A 367, 3073–3093 (2009).
[CrossRef]

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

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

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]

Delpy, D. T.

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef]

DiMarzio, C. A.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Durduran, T.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef]

Eames, M. E.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near Infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

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

Fessler, J. A.

J. W. Stayman and J. A. Fessler, “Spatially-variant roughness penalty design for uniform resolution in penalized-likelihood image reconstruction,” in Proc. of International Conference on Image Processing (ICIP), Chicago, IL, (4–7, October 1998, Vol. 2, IEEE), pp. 685–689.

Flach, K. B.

K. B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

Gaudette, R. J.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Gibson, A.

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, “Numerical modelling and image reconstruction in diffuse optical tomography,” Phil. Trans. R. Soc. A 367, 3073–3093 (2009).
[CrossRef]

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

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

Gisolf, A.

P. Zwartjes and A. Gisolf, “Fourier reconstruction with sparse inversion,” Geophys. Prospect. 55, 199–221 (2007).
[CrossRef]

Golub, G.

N. Nguyen, P. Milanfar, and G. Golub, “A computationally efficient superresolution image reconstruction algorithm,” IEEE Trans. Image Process. 10, 573–583 (2001).
[CrossRef]

G. Golub and U. von Matt, “Generalized cross-validation for large-scale problems,” J. Comput. Graph. Stat. 6, 1–34 (1997).
[CrossRef]

Guo, P.

Guven, M.

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef]

Hansen, P. C.

P. C. Hansen and D. P. O. Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

Hebden, J. C.

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

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

Hielscher, A. H.

A. H. Hielscher and S. Bartel, “Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography,” J. Biomed. Opt. 6, 183–192 (2001).
[CrossRef]

Hiroaka, M.

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef]

Holboke, M. J.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef]

Intes, X.

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef]

Jacob, M.

Jacques, S. L.

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

Jagannath, R. P. K.

R. P. K. Jagannath and P. K. Yalavarthy, “Minimal residual method provides optimal regularization parameter for diffuse optical tomography,” J. Biomed. Opt. 17, 106015 (2012).
[CrossRef]

Ji, L.

Jiang, H.

Jiang, S.

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

Jiang, T.

Kachelrie, M.

K. B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

Katamreddy, S. H.

Kaufman, H.

B. W. Pogue, C. Abele, H. Kaufman, and K. D. Paulsen, “Calibration of near infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
[CrossRef]

Kilmer, M.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Kueres, R.

K. B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead Simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Leary, D. P. O.

P. C. Hansen and D. P. O. Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

Maloux, C.

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef]

McBride, T.

McBride, T. O.

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

Mead, R.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Milanfar, P.

N. Nguyen, P. Milanfar, and G. Golub, “A computationally efficient superresolution image reconstruction algorithm,” IEEE Trans. Image Process. 10, 573–583 (2001).
[CrossRef]

Miller, E. L.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Nehorai, A.

Nelder, J. A.

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Nguyen, N.

N. Nguyen, P. Milanfar, and G. Golub, “A computationally efficient superresolution image reconstruction algorithm,” IEEE Trans. Image Process. 10, 573–583 (2001).
[CrossRef]

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]

Niu, H.

Ntziachristos, V.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef]

Osterberg, U.

Osterberg, U. L.

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

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

Patterson, M. S.

Paulsen, K. D.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near Infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

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]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

B. W. Pogue, C. Abele, H. Kaufman, and K. D. Paulsen, “Calibration of near infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
[CrossRef]

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

H. Jiang, K. D. Paulsen, U. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

Pogue, B. W.

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, “Numerical modelling and image reconstruction in diffuse optical tomography,” Phil. Trans. R. Soc. A 367, 3073–3093 (2009).
[CrossRef]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near Infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

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

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

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]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

B. W. Pogue, C. Abele, H. Kaufman, and K. D. Paulsen, “Calibration of near infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
[CrossRef]

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

H. Jiang, K. D. Paulsen, U. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

Prewitt, J.

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead Simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Sacchi, M D.

M D. Sacchi, T. J. Ulrych, and C. Walker, “Interpolation and extrapolation using a high resolution discrete Fourier transform,” IEEE Trans. Signal Process. 46, 31–38 (1998).
[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]

S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part 2: finite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995).
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef]

Semmler, W.

K. B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

Slemp, A.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef]

Srinivasan, S.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near Infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, “Numerical modelling and image reconstruction in diffuse optical tomography,” Phil. Trans. R. Soc. A 367, 3073–3093 (2009).
[CrossRef]

Stayman, J. W.

J. W. Stayman and J. A. Fessler, “Spatially-variant roughness penalty design for uniform resolution in penalized-likelihood image reconstruction,” in Proc. of International Conference on Image Processing (ICIP), Chicago, IL, (4–7, October 1998, Vol. 2, IEEE), pp. 685–689.

Thurber, C. H.

R. Aster, B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems (Academic, 2005).

Ulrych, T. J.

M D. Sacchi, T. J. Ulrych, and C. Walker, “Interpolation and extrapolation using a high resolution discrete Fourier transform,” IEEE Trans. Signal Process. 46, 31–38 (1998).
[CrossRef]

Vogel, C. R.

R. Acar and C. R. Vogel, “Analysis of bounded variation penalty methods for ill-posed problems,” Inverse Probl. 10, 1217–1229 (1994).
[CrossRef]

von Matt, U.

G. Golub and U. von Matt, “Generalized cross-validation for large-scale problems,” J. Comput. Graph. Stat. 6, 1–34 (1997).
[CrossRef]

Walker, C.

M D. Sacchi, T. J. Ulrych, and C. Walker, “Interpolation and extrapolation using a high resolution discrete Fourier transform,” IEEE Trans. Signal Process. 46, 31–38 (1998).
[CrossRef]

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead Simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead Simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Yalavarthy, P. K.

R. P. K. Jagannath and P. K. Yalavarthy, “Minimal residual method provides optimal regularization parameter for diffuse optical tomography,” J. Biomed. Opt. 17, 106015 (2012).
[CrossRef]

S. H. Katamreddy and P. K. Yalavarthy, “Model-resolution based regularization improves near infrared diffuse optical tomography,” J. Opt. Soc. Am. A 29, 649–656 (2012).
[CrossRef]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near Infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15, 8043–8058 (2007).
[CrossRef]

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]

Yazici, B.

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef]

Yodh, A. G.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef]

Zhang, Q.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

Zhao, Q.

Zubkov, L.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef]

Zwartjes, P.

P. Zwartjes and A. Gisolf, “Fourier reconstruction with sparse inversion,” Geophys. Prospect. 55, 199–221 (2007).
[CrossRef]

Appl. Opt. (2)

Commun. Numer. Methods Eng. (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near Infrared optical tomography using NIRFAST: algorithms for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Comput. J. (1)

J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Geophys. Prospect. (1)

P. Zwartjes and A. Gisolf, “Fourier reconstruction with sparse inversion,” Geophys. Prospect. 55, 199–221 (2007).
[CrossRef]

IEEE Signal Process. Mag. (1)

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, “Imaging the body with diffuse optical tomography,” IEEE Signal Process. Mag. 18, 57–75 (2001).
[CrossRef]

IEEE Trans. Image Process. (2)

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

N. Nguyen, P. Milanfar, and G. Golub, “A computationally efficient superresolution image reconstruction algorithm,” IEEE Trans. Image Process. 10, 573–583 (2001).
[CrossRef]

IEEE Trans. Signal Process. (1)

M D. Sacchi, T. J. Ulrych, and C. Walker, “Interpolation and extrapolation using a high resolution discrete Fourier transform,” IEEE Trans. Signal Process. 46, 31–38 (1998).
[CrossRef]

Inverse Probl. (2)

R. Acar and C. R. Vogel, “Analysis of bounded variation penalty methods for ill-posed problems,” Inverse Probl. 10, 1217–1229 (1994).
[CrossRef]

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

J. Biomed. Opt. (4)

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

A. H. Hielscher and S. Bartel, “Use of penalty terms in gradient-based iterative reconstruction schemes for optical tomography,” J. Biomed. Opt. 6, 183–192 (2001).
[CrossRef]

R. P. K. Jagannath and P. K. Yalavarthy, “Minimal residual method provides optimal regularization parameter for diffuse optical tomography,” J. Biomed. Opt. 17, 106015 (2012).
[CrossRef]

B. W. Pogue, C. Abele, H. Kaufman, and K. D. Paulsen, “Calibration of near infrared frequency-domain tissue spectroscopy for absolute absorption coefficient quantitation in neonatal head-simulating phantoms,” J. Biomed. Opt. 5, 185–193 (2000).
[CrossRef]

J. Comput. Graph. Stat. (1)

G. Golub and U. von Matt, “Generalized cross-validation for large-scale problems,” J. Comput. Graph. Stat. 6, 1–34 (1997).
[CrossRef]

J. Opt. Soc. Am. A (2)

Med. Phys. (3)

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, “Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,” Med. Phys. 30, 235–247 (2003).
[CrossRef]

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]

M. Schweiger, S. R. Arridge, M. Hiroaka, and D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef]

Opt. Express (4)

Phil. Trans. R. Soc. A (2)

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

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, “Numerical modelling and image reconstruction in diffuse optical tomography,” Phil. Trans. R. Soc. A 367, 3073–3093 (2009).
[CrossRef]

Phys. Med. Biol. (5)

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49, N155–N163 (2004).
[CrossRef]

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

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

K. B. Flach, R. Kueres, W. Semmler, M. Kachelrie, and S. Bartling, “Constrained reconstructions for 4D intervention guidance,” Phys. Med. Biol. 58, 3283–3300 (2013).
[CrossRef]

Rev. Sci. Instrum. (1)

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “A parallel-detection frequency-domain near-infrared tomography system for hemoglobin imaging of the breast in vivo,” Rev. Sci. Instrum. 72, 1817–1824 (2001).
[CrossRef]

SIAM J. Optim. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead Simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

SIAM J. Sci. Comput. (1)

P. C. Hansen and D. P. O. Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. 14, 1487–1503 (1993).
[CrossRef]

Other (2)

R. Aster, B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems (Academic, 2005).

J. W. Stayman and J. A. Fessler, “Spatially-variant roughness penalty design for uniform resolution in penalized-likelihood image reconstruction,” in Proc. of International Conference on Image Processing (ICIP), Chicago, IL, (4–7, October 1998, Vol. 2, IEEE), pp. 685–689.

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Figures (6)

Fig. 1.
Fig. 1.

Reconstructed images using the penalization functions discussed here (Table 1) in the numerical experiment with 1% noisy data where target distribution is given as in the top left-hand corner. The penalization functions used are given at the top of each corresponding reconstructed image. The one-dimensional cross-sectional profile along the solid line of the target distribution is given at the top right-hand corner.

Fig. 2.
Fig. 2.

Similar to Fig. 1 except that the data noise level is 3%; the target distribution is the same as in Fig. 1.

Fig. 3.
Fig. 3.

Similar to Fig. 1 except that the absorption targets are placed asymmetrically close to the boundary (top left-hand corner).

Fig. 4.
Fig. 4.

Similar to Fig. 1 except the target is located at the center and has a contrast of 41.

Fig. 5.
Fig. 5.

Similar to Fig. 1 except for an L-shaped target.

Fig. 6.
Fig. 6.

Reconstructed optical images with various penalty functions listed in Table 1, using a realistic MRI derived patient mesh. The one-dimensional cross-sectional profile along the sold line of target distribution is given at the top right-hand corner.

Tables (3)

Tables Icon

Table 1. Different Penalty Functions and Their Derivatives Used for Estimation of Optical Properties from Eq. (10)

Tables Icon

Table 2. Quantitative Comparison of RE [Eq. (13)] of Reconstruction Results Using the Discussed Penalty Functions

Tables Icon

Table 3. Quantitative Comparison of Pearson Correlation (PC) [Eq. (14)] of the Reconstruction Results Using the Discussed Penalty Functions

Equations (22)

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

·[D(r)Φ(r)]+μa(r)Φ(r)=So(r),
D(r)=13[μa(r)+μs(r)],
Ω=yG(μa)2+λμaμa02,
G(μa)=G(μa0)+G|μa0(μaμa0)+,
Ω=δJΔμa2+λΔμa2,
[JTJ+λI]Δμa=JTδ.
[Ji1TJi1+λiI]Δμai=Ji1Tδi1,
Ω=12δJΔμa2+λρ(Δμa),
JT(δJΔμa)+λρ(Δμa)=0.
[Ji1TJi1+λiDΔμai1]Δμai=Ji1Tδi1,
G(λ)=1NN(IA(λ))δ2[1NNtrace(IA(λ))]2,
A(λ)=[Ji1(Ji1TJi1+NN·λ·DΔμai1)1Ji1T].
RE=[([μa]TRUE[μa]RECON)2([μa]TRUE)2]×100,
PC([μa]TRUE,[μa]RECON)=COV([μa]TRUE,[μa]RECON)σ([μa]TRUE),
Ω=yG(μa)2.
Ω=12yG(μa)2+λρ(μaμa0),
Ω=12(δJΔμa)2+λρ(Δμa),
JT(δJΔμa)+λρ(Δμa)=0.
JTδ+JTJΔμa+λρ(Δμa)=0.
[JTJ+λDΔμa]Δμa=JTδ,
(DΔμa)ii=(ρ(Δμa)Δμa)ifori=1,2,NN,
(DΔμa)ii=1σΔμa2fori=1,2,NN,

Metrics