Abstract

An lp (0 < p ≤ 1) sparsity regularization is applied to time-domain diffuse optical tomography with a gradient-based nonlinear optimization scheme to improve the spatial resolution and the robustness to noise. The expression of the lp sparsity regularization is reformulated as a differentiable function of a parameter to avoid the difficulty in calculating its gradient in the optimization process. The regularization parameter is selected by the L-curve method. Numerical experiments show that the lp sparsity regularization improves the spatial resolution and recovers the difference in the absorption coefficients between two targets, although a target with a small absorption coefficient may disappear due to the strong effect of the lp sparsity regularization when the value of p is too small. The lp sparsity regularization with small p values strongly localizes the target, and the reconstructed region of the target becomes smaller as the value of p decreases. A phantom experiment validates the numerical simulations.

© 2011 OSA

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2010

2009

2008

P. Hiltunen, D. Calvetti, and E. Somersalo, “An adaptive smoothness regularization algorithm for optical tomography,” Opt, Express16(24), 19957–19977, (2008).
[CrossRef]

P. M. Shankar and M. A. Neifeld, “Sparsity constrained regularization for multiframe image restoration,” J. Opt. Soc. Am. A25(5), 1199–1214 (2008).
[CrossRef]

2007

2006

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S.R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography for passive motor evoked responses in the neonate,” NueroImage30, 521–528 (2006).
[CrossRef]

2005

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol.50, 3941–3956 (2005).
[CrossRef] [PubMed]

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

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol.50, 2451–2468 (2005).
[CrossRef] [PubMed]

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol.50, 2503–2517 (2005).
[CrossRef] [PubMed]

2002

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

2001

1999

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

B. W. Pogue, T. O. McBride, J. Prewitt, U. Lösterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt.38(13), 2950–2961, (1999).
[CrossRef]

D. Grosenick, H. Wabnitz, H. H. Rinneberg, T. Moesta, and P. M. Schlag, “Development of a time-domain optical mammography and first in vivo applications,” Appl. Opt.38(13), 2927–2943 (1999).
[CrossRef]

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

1998

S. R. Arridge, “A gradient-based optimization scheme for optical tomography,” Opt. Express12(6), 213–226 (1998).
[CrossRef]

1993

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. Compt.14(6), 1487–1503 (1993).
[CrossRef]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite-element method for the forward and inverse model in optical tomography,” J. Math. Imaging Vis.3, 263–283 (1993).
[CrossRef]

Adibi, A.

Arridge, S. R.

C. Panagiotou, S. Somayajula, A. P. Gibson, M. Schweiger, R. M. Leahy, and S. R. Arridge, “Information theoretic regularization in diffuse optical tomography,” J. Opt. Soc. Am. A26(5), 1277–1290 (2009).
[CrossRef]

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, “Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information,” Meas. Sci. Technol.18, 87–95 (2007).
[CrossRef]

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol.50, 2503–2517 (2005).
[CrossRef] [PubMed]

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

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt.40 (19), 3278–32887 (2001).
[CrossRef]

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

S. R. Arridge, “A gradient-based optimization scheme for optical tomography,” Opt. Express12(6), 213–226 (1998).
[CrossRef]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite-element method for the forward and inverse model in optical tomography,” J. Math. Imaging Vis.3, 263–283 (1993).
[CrossRef]

Arridge, S.R.

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S.R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography for passive motor evoked responses in the neonate,” NueroImage30, 521–528 (2006).
[CrossRef]

Austin, T.

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S.R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography for passive motor evoked responses in the neonate,” NueroImage30, 521–528 (2006).
[CrossRef]

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

Baillet, S.

S. Baillet, J. C. Mosher, and R. M. Leahy, “Electromagnetic brain mapping,” IEEE Signal Process. Mag.18, 14–30 (2001).
[CrossRef]

Boas, D. A.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol.50, 3941–3956 (2005).
[CrossRef] [PubMed]

Boverman, G.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol.50, 3941–3956 (2005).
[CrossRef] [PubMed]

Brooks, D. H.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol.50, 3941–3956 (2005).
[CrossRef] [PubMed]

Calvetti, D.

P. Hiltunen, D. Calvetti, and E. Somersalo, “An adaptive smoothness regularization algorithm for optical tomography,” Opt, Express16(24), 19957–19977, (2008).
[CrossRef]

Cao, N.

Carpenter, C. M.

Chan, T. F.

Chatziioannou, A. F.

Chaves, T.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol.50, 3941–3956 (2005).
[CrossRef] [PubMed]

Chen, H.

P. Xu, Y. Tian, H. Chen, and D. Yao, “Lp Norm iterative sparse solution for EEG source localization,” IEEE Trans. Biomed. Eng.54 (3), 400–409 (2007).
[CrossRef] [PubMed]

Cichocki, A.

Z. He, A. Cichocki, R. Zdunek, and S. Xie, “Improved FOCCUS Method With conjugate gradient iterations,” IEEE Tras. Signal Process.57 (1), 399–404 (2009).
[CrossRef]

Dehghani, H.

Delpy, D. T.

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S.R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography for passive motor evoked responses in the neonate,” NueroImage30, 521–528 (2006).
[CrossRef]

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt.40 (19), 3278–32887 (2001).
[CrossRef]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite-element method for the forward and inverse model in optical tomography,” J. Math. Imaging Vis.3, 263–283 (1993).
[CrossRef]

Douek, M.

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol.50, 2503–2517 (2005).
[CrossRef] [PubMed]

Douiri, A.

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, “Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information,” Meas. Sci. Technol.18, 87–95 (2007).
[CrossRef]

Douraghy, A.

Eda, H.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Eftekhar, A. A.

Everdell, N.

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol.50, 2503–2517 (2005).
[CrossRef] [PubMed]

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

Everdell, N. L.

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S.R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography for passive motor evoked responses in the neonate,” NueroImage30, 521–528 (2006).
[CrossRef]

Gebauer, B.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

Gibson, A.

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol.50, 2503–2517 (2005).
[CrossRef] [PubMed]

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

Gibson, A. P.

C. Panagiotou, S. Somayajula, A. P. Gibson, M. Schweiger, R. M. Leahy, and S. R. Arridge, “Information theoretic regularization in diffuse optical tomography,” J. Opt. Soc. Am. A26(5), 1277–1290 (2009).
[CrossRef]

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S.R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography for passive motor evoked responses in the neonate,” NueroImage30, 521–528 (2006).
[CrossRef]

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

Grosenick, D.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol.50, 2451–2468 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, H. H. Rinneberg, T. Moesta, and P. M. Schlag, “Development of a time-domain optical mammography and first in vivo applications,” Appl. Opt.38(13), 2927–2943 (1999).
[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. Compt.14(6), 1487–1503 (1993).
[CrossRef]

He, Z.

Z. He, A. Cichocki, R. Zdunek, and S. Xie, “Improved FOCCUS Method With conjugate gradient iterations,” IEEE Tras. Signal Process.57 (1), 399–404 (2009).
[CrossRef]

Hebdan, C.

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol.50, 2503–2517 (2005).
[CrossRef] [PubMed]

Hebden, J. C.

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S.R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography for passive motor evoked responses in the neonate,” NueroImage30, 521–528 (2006).
[CrossRef]

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

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt.40 (19), 3278–32887 (2001).
[CrossRef]

Hillman, E. M. C.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt.40 (19), 3278–32887 (2001).
[CrossRef]

Hiltunen, P.

P. Hiltunen, D. Calvetti, and E. Somersalo, “An adaptive smoothness regularization algorithm for optical tomography,” Opt, Express16(24), 19957–19977, (2008).
[CrossRef]

Holder, S.

S. Holder, Electrical Impedance Tomography: Methods, History and Applications (Institute of Physics Publishing, Bristol, 2005).

Huang, J.

Ito, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Jacob, M.

Jiang, S.

Leahy, R. M.

Li, A.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol.50, 3941–3956 (2005).
[CrossRef] [PubMed]

Lösterberg, U.

Lu, Y.

McBride, T. O.

Meek, J. H.

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S.R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography for passive motor evoked responses in the neonate,” NueroImage30, 521–528 (2006).
[CrossRef]

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

Miller, E. L.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol.50, 3941–3956 (2005).
[CrossRef] [PubMed]

Moesta, K. T.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol.50, 2451–2468 (2005).
[CrossRef] [PubMed]

Moesta, T.

Mohajerani, P.

Möller, M.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

Mosher, J. C.

S. Baillet, J. C. Mosher, and R. M. Leahy, “Electromagnetic brain mapping,” IEEE Signal Process. Mag.18, 14–30 (2001).
[CrossRef]

Mucke, J.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol.50, 2451–2468 (2005).
[CrossRef] [PubMed]

Nehorai, A.

Neifeld, M. A.

O’Leary, D. P.

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. Compt.14(6), 1487–1503 (1993).
[CrossRef]

Oda, I.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Oda, M.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Oikawa, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Okawa, S.

Panagiotou, C.

Paulsen, K. D.

Pogue, B. W.

Prewitt, J.

Riley, J.

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, “Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information,” Meas. Sci. Technol.18, 87–95 (2007).
[CrossRef]

Rinneberg, H.

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol.50, 2451–2468 (2005).
[CrossRef] [PubMed]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

Rinneberg, H. H.

Sassaroli, A.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Schlag, P. M.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol.50, 2451–2468 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, H. H. Rinneberg, T. Moesta, and P. M. Schlag, “Development of a time-domain optical mammography and first in vivo applications,” Appl. Opt.38(13), 2927–2943 (1999).
[CrossRef]

Schweiger, M.

C. Panagiotou, S. Somayajula, A. P. Gibson, M. Schweiger, R. M. Leahy, and S. R. Arridge, “Information theoretic regularization in diffuse optical tomography,” J. Opt. Soc. Am. A26(5), 1277–1290 (2009).
[CrossRef]

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, “Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information,” Meas. Sci. Technol.18, 87–95 (2007).
[CrossRef]

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S.R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography for passive motor evoked responses in the neonate,” NueroImage30, 521–528 (2006).
[CrossRef]

J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M. Schweiger, S. R. Arridge, and D. T. Delpy, “Three-dimensional time-resolved optical tomography of a conical breast phantom,” Appl. Opt.40 (19), 3278–32887 (2001).
[CrossRef]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite-element method for the forward and inverse model in optical tomography,” J. Math. Imaging Vis.3, 263–283 (1993).
[CrossRef]

Shankar, P. M.

Somayajula, S.

Somersalo, E.

P. Hiltunen, D. Calvetti, and E. Somersalo, “An adaptive smoothness regularization algorithm for optical tomography,” Opt, Express16(24), 19957–19977, (2008).
[CrossRef]

Stout, D.

Stroszczynski, C.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

Tamura, N.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Tian, J.

Tian, Y.

P. Xu, Y. Tian, H. Chen, and D. Yao, “Lp Norm iterative sparse solution for EEG source localization,” IEEE Trans. Biomed. Eng.54 (3), 400–409 (2007).
[CrossRef] [PubMed]

Tsunazawa, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Tuchiya, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Veenstra, H.

Vogel, C. R.

C. R. Vogel, Computational Methods for Inverse Problems, Frontiers in Applied Mathematics (SIAM, Philadelphia, 2002).
[CrossRef]

Wabnitz, H.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol.50, 2451–2468 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, H. H. Rinneberg, T. Moesta, and P. M. Schlag, “Development of a time-domain optical mammography and first in vivo applications,” Appl. Opt.38(13), 2927–2943 (1999).
[CrossRef]

Wada, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Wassermann, B.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

Wyatt, J. S.

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S.R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography for passive motor evoked responses in the neonate,” NueroImage30, 521–528 (2006).
[CrossRef]

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

Xie, S.

Z. He, A. Cichocki, R. Zdunek, and S. Xie, “Improved FOCCUS Method With conjugate gradient iterations,” IEEE Tras. Signal Process.57 (1), 399–404 (2009).
[CrossRef]

Xu, P.

P. Xu, Y. Tian, H. Chen, and D. Yao, “Lp Norm iterative sparse solution for EEG source localization,” IEEE Trans. Biomed. Eng.54 (3), 400–409 (2007).
[CrossRef] [PubMed]

Yalavarthy, P. K.

Yamada, Y.

S. Okawa and Y. Yamada, “Reconstruction of fluorescence/bioluminescence sources in biological medium with spatial filter,” Opt. Express18(12), 13151–13172 (2010).
[CrossRef] [PubMed]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Yamashita, Y.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

Yao, D.

P. Xu, Y. Tian, H. Chen, and D. Yao, “Lp Norm iterative sparse solution for EEG source localization,” IEEE Trans. Biomed. Eng.54 (3), 400–409 (2007).
[CrossRef] [PubMed]

Yates, T.

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol.50, 2503–2517 (2005).
[CrossRef] [PubMed]

Yusof, R. M.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

Zdunek, R.

Z. He, A. Cichocki, R. Zdunek, and S. Xie, “Improved FOCCUS Method With conjugate gradient iterations,” IEEE Tras. Signal Process.57 (1), 399–404 (2009).
[CrossRef]

Zhang, Q.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol.50, 3941–3956 (2005).
[CrossRef] [PubMed]

Zhang, X.

Appl. Opt.

IEEE Signal Process. Mag.

S. Baillet, J. C. Mosher, and R. M. Leahy, “Electromagnetic brain mapping,” IEEE Signal Process. Mag.18, 14–30 (2001).
[CrossRef]

IEEE Trans. Biomed. Eng.

P. Xu, Y. Tian, H. Chen, and D. Yao, “Lp Norm iterative sparse solution for EEG source localization,” IEEE Trans. Biomed. Eng.54 (3), 400–409 (2007).
[CrossRef] [PubMed]

IEEE Tras. Signal Process.

Z. He, A. Cichocki, R. Zdunek, and S. Xie, “Improved FOCCUS Method With conjugate gradient iterations,” IEEE Tras. Signal Process.57 (1), 399–404 (2009).
[CrossRef]

Inverse Prob.

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

J. Math. Imaging Vis.

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite-element method for the forward and inverse model in optical tomography,” J. Math. Imaging Vis.3, 263–283 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Meas. Sci. Technol.

A. Douiri, M. Schweiger, J. Riley, and S. R. Arridge, “Anisotropic diffusion regularization methods for diffuse optical tomography using edge prior information,” Meas. Sci. Technol.18, 87–95 (2007).
[CrossRef]

NueroImage

A. P. Gibson, T. Austin, N. L. Everdell, M. Schweiger, S.R. Arridge, J. H. Meek, J. S. Wyatt, D. T. Delpy, and J. C. Hebden, “Three-dimensional whole-head optical tomography for passive motor evoked responses in the neonate,” NueroImage30, 521–528 (2006).
[CrossRef]

Opt, Express

P. Hiltunen, D. Calvetti, and E. Somersalo, “An adaptive smoothness regularization algorithm for optical tomography,” Opt, Express16(24), 19957–19977, (2008).
[CrossRef]

Opt. Express

Phys. Med. Biol.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol.47, 4155–4166 (2002)
[CrossRef] [PubMed]

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol.50, 3941–3956 (2005).
[CrossRef] [PubMed]

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

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol.50, 2429–2449 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol.50, 2451–2468 (2005).
[CrossRef] [PubMed]

T. Yates, C. Hebdan, A. Gibson, N. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol.50, 2503–2517 (2005).
[CrossRef] [PubMed]

Rev. Sci. Instrum.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, Y. Tuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and N. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum.70(9), 3595–3602 (1999).
[CrossRef]

SIAM J. Sci. Compt.

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. Compt.14(6), 1487–1503 (1993).
[CrossRef]

Other

S. Holder, Electrical Impedance Tomography: Methods, History and Applications (Institute of Physics Publishing, Bristol, 2005).

C. R. Vogel, Computational Methods for Inverse Problems, Frontiers in Applied Mathematics (SIAM, Philadelphia, 2002).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

L-curves for the reconstructions with (a) p = 2, (b) p = 1, (c) p = 1/2, (d) p = 1/4 in the simulations in section 3.2.1. R = log10 ||M–M̂||2 for the abscissa and F = log10f(z) for the ordinate.

Fig. 2
Fig. 2

The μa distributions reconstructed using (a) Tikhonov regularization with p = 2 and using the lp sparsity regularization with (b) p = 1, (c) p = 1/2 and (d) p = 1/4 in the simulations in section 3.2.1. The black open circles indicate the true positions of the targets.

Fig. 3
Fig. 3

The quantitative evaluations of the reconstructed images obtained by the simulations in section 3.2.1: (a) The profiles of Δμa along the lines in the y-direction passing through the two peaks of μa, reconstructed with p = 2 (green line), p = 1 (red line), p = 1/2 (blue line) and (d) p = 1/4 (black line), (b) ζ = Δμaminμamax as a function of p with the minimum of Δμa reconstructed between the peaks, Δμamin, and the average of the peaks of Δμa, Δμamax, (c) the average of Δμamax of the two peaks as a function of p with the true Δμamax = 0.0070 mm−1 and (d) the area at half maximum of Δμa peak as a function of p with the true S = 157 mm2.

Fig. 4
Fig. 4

Reconstructed μa distributions using (a) Tikhonov regularization with p = 2 and the lp sparsity regularization with (b) p = 1, (c) p = 1/2 and (d) p = 1/4 in the simulations in section 3.2.2. The black open circles indicate the true positions of the targets.

Fig. 5
Fig. 5

The quantitative evaluations of the reconstructed images obtained by the simulations in section 3.2.2: (a) The reconstructed peaks of Δμa of the two targets at (x,y) = (20 mm, 10 mm) (times symbols, true Δμa1max = 0.0035 mm−1) and (x,y) = (20mm,−10mm) (open circles, true Δμa2max = 0.0070 mm−1), and (b) the contrast γ between the two peaks reconstructed with p = 1/4,1/2,1 and 2 (true γ = Δμa1maxμa2max = 0.5).

Fig. 6
Fig. 6

Reconstructed μa distributions using (a) Tikhonov regularization with p = 2 and the lp sparsity regularization with (b) p = 1, (c) p = 1/2 and (d) p = 1/4 in the simulations in section 3.2.3. The black open circle indicates the true position of the target.

Fig. 7
Fig. 7

The quantitative evaluations of the reconstructed images obtained by the simulations in section 3.2.3: (a) Reconstructed peaks of Δμa with the true Δμa = 0.0070 mm−1, and (b) the area at half maximum of Δμa, S, reconstructed with p = 1/4,1/2,1 and 2 (true S = 314 mm2).

Fig. 8
Fig. 8

L-curves for the reconstructions with (a) p = 2, (b) p = 1, (c) p = 1/2, (d) p = 1/4 in the phantom experiment. R = log10 ||M||2 for the abscissa and F = log10f(z) for the ordinate

Fig. 9
Fig. 9

The μa distributions reconstructed with (a) Tikhonov regularization with p = 2 and the lp sparsity regularization with (b) p = 1, (c) p = 1/2 and (d) p = 1/4 in the phantom experiment. The black open circle indicates the true position of the target.

Fig. 10
Fig. 10

The quantitative evaluations of the reconstructed images obtained by the phantom experiment: (a) Reconstructed peaks of Δμa with the true Δμa = 0.0020 mm−1, and (b) the area at half maximum of Δμa, S, reconstructed with p = 1/4,1/2,1 and 2 (true S = 314 mm2).

Equations (5)

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

{ D ( r ) + μ a ( r ) + 1 c t } Φ ( r , t ) = q 0 ( r , t ) ,
min μ a M M ^ ( μ a ) 2 + λ f ( μ a ) ,
Δ μ a i = | z i | 2 / p sgn ( z i ) .
μ a i = μ ¯ a + Δ μ a i ,
min z M M ^ ( z ) 2 + λ i = 1 I | z i | 2 ,

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