Abstract

Diffuse optical tomographic imaging is known to be an ill-posed problem, and a penalty/regularization term is used in image reconstruction (inverse problem) to overcome this limitation. Two schemes that are prevalent are spatially varying (exponential) and constant (standard) regularizations/penalties. A scheme that is also spatially varying but uses the model information is introduced based on the model-resolution matrix. This scheme, along with exponential and standard regularization schemes, is evaluated objectively based on model-resolution and data-resolution matrices. This objective analysis showed that resolution characteristics are better for spatially varying penalties compared to standard regularization; and among spatially varying regularization schemes, the model-resolution based regularization fares well in providing improved data-resolution and model-resolution characteristics. The verification of the same is achieved by performing numerical experiments in reconstructing 1% noisy data involving simple two- and three-dimensional imaging domains.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  27. L. Borcea, “Electrical impedance tomography,” Inverse Probl. 18, R99–R136 (2002).
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  28. M. Soleimani, P. K. Yalavarthy, and H. Dehghani, “Helmholtz-type regularization method for permittivity reconstruction using experimental phantom data of electrical capacitance tomography,” IEEE Trans. Instrum. Meas. 59, 78–83 (2010).
    [CrossRef]

2011 (1)

2010 (1)

M. Soleimani, P. K. Yalavarthy, and H. Dehghani, “Helmholtz-type regularization method for permittivity reconstruction using experimental phantom data of electrical capacitance tomography,” IEEE Trans. Instrum. Meas. 59, 78–83 (2010).
[CrossRef]

2009 (3)

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).

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]

2008 (4)

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

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53, 3921–3942 (2008).
[CrossRef]

H. Niu, P. Guo, L. Ji, Q. Zhao, and T. Jiang, “Improving image quality of diffuse optical tomography with a projection-error-based adaptive regularization method,” Opt. Express 16, 12423–12434 (2008).
[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]

2007 (4)

2006 (1)

2005 (3)

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]

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (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]

2002 (1)

L. Borcea, “Electrical impedance tomography,” Inverse Probl. 18, R99–R136 (2002).
[CrossRef]

2001 (2)

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]

1999 (2)

1998 (1)

1997 (1)

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

1995 (2)

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]

Ahn, S.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53, 3921–3942 (2008).
[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]

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

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

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]

Borcea, L.

L. Borcea, “Electrical impedance tomography,” Inverse Probl. 18, R99–R136 (2002).
[CrossRef]

Bouman, C. A.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53, 3921–3942 (2008).
[CrossRef]

Brooks, D. H.

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

Cao, 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).

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.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[CrossRef]

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]

Chaudhari, A. J.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53, 3921–3942 (2008).
[CrossRef]

Darvas, F.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53, 3921–3942 (2008).
[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).

S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066–4082, (2007).
[CrossRef]

Dehghani, H.

M. Soleimani, P. K. Yalavarthy, and H. Dehghani, “Helmholtz-type regularization method for permittivity reconstruction using experimental phantom data of electrical capacitance tomography,” IEEE Trans. Instrum. Meas. 59, 78–83 (2010).
[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).

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

S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066–4082, (2007).
[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]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[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]

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).

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]

Fantini, S.

Gaudette, R. J.

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

Gibson, A.

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

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

Guo, P.

Guven, M.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[CrossRef]

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]

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. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[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]

Intes, X.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[CrossRef]

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]

Ji, L.

Jiang, S.

Jiang, T.

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]

Larusson, F.

Leahy, R. M.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53, 3921–3942 (2008).
[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]

Miller, E. L.

F. Larusson, S. Fantini, and E. L. Miller, “Hyperspectral image reconstruction for diffuse optical tomography,” Biomed. Opt. Express 2, 946–965 (2011).
[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]

Nehorai, A.

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.

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]

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).

S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066–4082, (2007).
[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]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[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, 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]

Pogue, B. W.

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).

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]

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, 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]

S. C. Davis, H. Dehghani, J. Wang, S. Jiang, B. W. Pogue, and K. D. Paulsen, “Image-guided diffuse optical fluorescence tomography implemented with Laplacian-type regularization,” Opt. Express 15, 4066–4082, (2007).
[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, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[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, 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]

Prewitt, J.

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

Soleimani, M.

M. Soleimani, P. K. Yalavarthy, and H. Dehghani, “Helmholtz-type regularization method for permittivity reconstruction using experimental phantom data of electrical capacitance tomography,” IEEE Trans. Instrum. Meas. 59, 78–83 (2010).
[CrossRef]

Srinivasan, S.

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).

Wang, J.

Yalavarthy, P. K.

M. Soleimani, P. K. Yalavarthy, and H. Dehghani, “Helmholtz-type regularization method for permittivity reconstruction using experimental phantom data of electrical capacitance tomography,” IEEE Trans. Instrum. Meas. 59, 78–83 (2010).
[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).

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]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[CrossRef]

Yazici, B.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[CrossRef]

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]

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.

Zhdanov, M. S.

M. S. Zhdanov, Geophysical Inverse Theory and Regularization Problems1st ed. (Elsevier Science, 2002).

Appl. Opt. (3)

Biomed. Opt. Express (1)

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).

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. Instrum. Meas. (1)

M. Soleimani, P. K. Yalavarthy, and H. Dehghani, “Helmholtz-type regularization method for permittivity reconstruction using experimental phantom data of electrical capacitance tomography,” IEEE Trans. Instrum. Meas. 59, 78–83 (2010).
[CrossRef]

Inverse Probl. (2)

L. Borcea, “Electrical impedance tomography,” Inverse Probl. 18, R99–R136 (2002).
[CrossRef]

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

J. Biomed. Opt. (1)

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

Med. Phys. (2)

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

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

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]

Phys. Med. Biol. (6)

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]

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[CrossRef]

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, “Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography,” Phys. Med. Biol. 53, 3921–3942 (2008).
[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]

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. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[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]

Other (1)

M. S. Zhdanov, Geophysical Inverse Theory and Regularization Problems1st ed. (Elsevier Science, 2002).

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Figures (7)

Fig. 1.
Fig. 1.

Plot of diagonal of model-resolution matrix (M, Eq. 13) versus spatial location in the imaging domain as a function of λ (values are given in the legend).

Fig. 2.
Fig. 2.

Plot of diagonal of model-resolution matrices for the regularization schemes versus the spatial location in the imaging domain. The model-resolution equation for standard regularization is given by Eq. 13, exponential by Eq. 14, and model-resolution one by Eq. 18.

Fig. 3.
Fig. 3.

Plot of the diagonal of the data-resolution matrix (D, Eq. 20) for the regularization schemes used in this work versus the measurement number.

Fig. 4.
Fig. 4.

(a). Comparison of reconstruction performance in 2D using three regularization schemes discussed in this work for the circular targets located close to the center with numerically generated 1% noisy data. The reconstructed images obtained along with corresponding regularization scheme (given on top of image) are given along with the target image. (b). 1D cross-sectional plot of μa along the vertical line (x=0mm) for the target and reconstructed results presented in (a).

Fig. 5.
Fig. 5.

Similar effort to Fig. 4 except the targets are located close to the boundary (edge) of the imaging domain.

Fig. 6.
Fig. 6.

(a). Comparison of reconstruction performance in 3D using three regularization schemes discussed in this work for the cylindrical targets located close to the center with numerically generated 1% noisy data. 2D cross sections of the 3D cylindrical volume in 9 mm increments spanning from z=50mm to z=50mm from left to right are shown. The reconstructed distributions obtained along with corresponding regularization scheme (given on top of images) are given along with the target distribution. (b). 1D cross-sectional plot of μa at Z=0mm along the vertical line (X=0mm) for the target and reconstructed results presented in (a).

Fig. 7.
Fig. 7.

Similar effort to Fig. 6 with targets located close to the boundary (edge) of the imaging domain.

Equations (20)

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.κ(r)Φ(r)+μa(r)Φ(r)=Qo(r),
κ(r)=13[μa(r)+μs(r)],
Ω=yG(μa)2+P(μa),
P(μa)=λμa2,
[JTJ+λI]Δμa=JT(yG(μa)),
P(μa)=λ(r)μa2,
λ(r)=λeexp(rR)+λc,
[JTJ+λ(r)I]Δμa=JT(yG(μa)).
y=G(μa)=G(μa0)+G(μa)(μaμa0)+(μaμa0)TG(μa)(μaμa0)+,
y=G(μa0)+J(μaμa0)
δ=Jμa~.
Δμa=[JTJ+λI]1JTJΔμa˜.
M=[JTJ+λI]1JTJ,
Mr=[JTJ+λ(r)I]1JTJ,
λi=Miimax(Mii)fori=1,2,,NN,
P(μa)=cλiμa2,
[JTJ+cλiI]Δμa=JT(yG(μa)).
Mi=[JTJ+cλiI]1JTJ.
δp=JΔμa,
D=J[JTJ+λ˜I]1JT,

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