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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).

[Crossref]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “Approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inverse Probl. 26, 015005 (2010).

[Crossref]

S. Arridge and J. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).

[Crossref]

T. Tarvainen, M. Vauhkonen, and S. Arridge, “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 2767–2778 (2008).

[Crossref]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. Arridge, and J. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50, 4913–4930 (2005).

[Crossref]

S. Wright, M. Schweiger, and S. Arridge, “Solutions to the transport equation using variable order angular basis,” Proc. SPIE 5859, 585914 (2005).

[Crossref]

P. S. Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys. 230, 7364–7383 (2011).

[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]

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

[Crossref]

S. R. Arridge and W. R. B. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998).

[Crossref]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).

[Crossref]

F. Asllanaj and S. Fumeron, “Applying a new computational method for biological tissue optics based on the time-dependent two-dimensional radiative transfer equation,” J. Biomed. Opt. 17, 075007 (2012).

[Crossref]

E. Aydin, C. de Oliveira, and A. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).

[Crossref]

K. Ren, G. Bal, and A. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28, 1463–1489 (2006).

[Crossref]

K. Ren, G. Abdoulaev, G. Bal, and A. Hielscher, “Algorithm for solving the equation of radiative transfer in the frequency domain,” Opt. Lett. 29, 578–580 (2004).

[Crossref]

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous Galerkin forumulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Radiat. Transfer 113, 805–814 (2012).

[Crossref]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).

[Crossref]

A. Jha, M. Kupinski, H. Barrett, E. Clarkson, and J. Hartman, “Three-dimensional Neumann-series approach to model light transport in nonuniform media,” J. Opt. Soc. Am. A 29, 1885–1898 (2012).

[Crossref]

A. Jha, M. Kupinski, T. Masumura, E. Clarkson, A. Maslov, and H. Barrett, “Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach,” J. Opt. Soc. Am. A 29, 1741–1756 (2012).

[Crossref]

N. Ducros, C. D’Andrea, A. Bassi, and F. Peyrin, “Fluorescence diffuse optical tomography: time-resolved versus continuous-wave in the reflectance configuration,” IRBM 32, 243–250 (2011).

[Crossref]

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[Crossref]

A. Klose, U. Netz, J. Beuthan, and A. Hielscher, “Optical tomography using the time-independent equation of radiative transfer—Part 1: forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).

[Crossref]

J. Selb, A. Dale, and D. Boas, “Linear 3D reconstruction of time-domain diffuse optical imaging differential data: improved depth localization and lateral resolution,” Opt. Express 15, 16400–16412 (2007).

[Crossref]

J. Selb, D. Joseph, and D. Boas, “Time-gated optical system for depth-resolved functional brain imaging,” J. Biomed. Opt. 11, 044008 (2006).

[Crossref]

E. Boman, J. Tervo, and M. Vauhkonen, “Modelling the transport of ionizing radiation using the finite element method,” Phys. Med. Biol. 50, 265–280 (2005).

[Crossref]

M. Addam, A. Bouhamidi, and K. Jbilou, “Signal reconstruction for the diffusion transport equation using tensorial spline galerking approximation,” Appl. Numer. Math. 62, 1089–1108 (2012).

[Crossref]

M. Addam, A. Bouhamidi, and K. Jbilou, “A numerical method for one-dimensional diffusion problem using Fourier transform and the B-spline Galerkin method,” Appl. Math. Comput. 215, 4067–4079 (2010).

[Crossref]

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous Galerkin forumulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Radiat. Transfer 113, 805–814 (2012).

[Crossref]

J. Boulanger and A. Charette, “Reconstruction optical spectroscopy using transient radiative transfer equation and pulsed laser: a numerical study,” J. Quant. Spectrosc. Radiat. Transfer 93, 325–336 (2005).

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[Crossref]

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous Galerkin forumulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Radiat. Transfer 113, 805–814 (2012).

[Crossref]

H. K. Kim and A. Charette, “A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 104, 24–39 (2007).

[Crossref]

J. Boulanger and A. Charette, “Reconstruction optical spectroscopy using transient radiative transfer equation and pulsed laser: a numerical study,” J. Quant. Spectrosc. Radiat. Transfer 93, 325–336 (2005).

[Crossref]

K. Peng, X. Gao, X. Qu, N. Ren, X. Chen, X. He, X. Wang, J. Liang, and J. Tian, “Graphics processing unit parallel accelerated solution of the discrete ordinates for photon transport in biological tissues,” Appl. Opt. 50, 3808–3823 (2011).

[Crossref]

A. Jha, M. Kupinski, H. Barrett, E. Clarkson, and J. Hartman, “Three-dimensional Neumann-series approach to model light transport in nonuniform media,” J. Opt. Soc. Am. A 29, 1885–1898 (2012).

[Crossref]

A. Jha, M. Kupinski, T. Masumura, E. Clarkson, A. Maslov, and H. Barrett, “Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach,” J. Opt. Soc. Am. A 29, 1741–1756 (2012).

[Crossref]

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[Crossref]

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[Crossref]

N. Ducros, C. D’Andrea, A. Bassi, and F. Peyrin, “Fluorescence diffuse optical tomography: time-resolved versus continuous-wave in the reflectance configuration,” IRBM 32, 243–250 (2011).

[Crossref]

E. Aydin, C. de Oliveira, and A. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).

[Crossref]

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

[Crossref]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).

[Crossref]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).

[Crossref]

O. Dorn, “A transport–backtransport method for optical tomography,” Inverse Probl. 14, 1107–1130 (1998).

[Crossref]

N. Ducros, C. D’Andrea, A. Bassi, and F. Peyrin, “Fluorescence diffuse optical tomography: time-resolved versus continuous-wave in the reflectance configuration,” IRBM 32, 243–250 (2011).

[Crossref]

W. Martin, C. Yehnert, L. Lorence, and J. Duderstadt, “Phase-space finite element methods applied to the first order form of the transport equation,” Ann. Nucl. Energy 8, 633–646 (1981).

[Crossref]

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

[Crossref]

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous Galerkin forumulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Radiat. Transfer 113, 805–814 (2012).

[Crossref]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, P. Taroni, V. Quaresima, M. Ferrari, and R. Cubeddu, “Multichannel time-resolved tissue oximeter for functional imaging of the brain,” IEEE Trans. Instrum. Meas. 55, 85–90 (2006).

[Crossref]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).

[Crossref]

F. Asllanaj and S. Fumeron, “Applying a new computational method for biological tissue optics based on the time-dependent two-dimensional radiative transfer equation,” J. Biomed. Opt. 17, 075007 (2012).

[Crossref]

H. Gao and H. Zhao, “A fast-forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192 (2009).

[Crossref]

H. Gao and H. Zhao, “A fast-forward solver of radiative transfer equation,” Transp. Theory Stat.. Phys. 38, 149–192 (2009).

[Crossref]

K. Peng, X. Gao, X. Qu, N. Ren, X. Chen, X. He, X. Wang, J. Liang, and J. Tian, “Graphics processing unit parallel accelerated solution of the discrete ordinates for photon transport in biological tissues,” Appl. Opt. 50, 3808–3823 (2011).

[Crossref]

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

[Crossref]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (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]

E. Aydin, C. de Oliveira, and A. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).

[Crossref]

D. Gorpas, D. Yova, and K. Politopoulos, “A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging,” J. Quant. Spectrosc. Radiat. Transfer 111, 553–568 (2010).

[Crossref]

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).

[Crossref]

M. Charest, C. Groth, and Ö. Gülder, “Solution of the equation of radiative transfer using a Newton–Krylov approach and adaptive mesh refinement,” J. Comput. Phys. 231, 3023–3040 (2012).

[Crossref]

M. Charest, C. Groth, and Ö. Gülder, “Solution of the equation of radiative transfer using a Newton–Krylov approach and adaptive mesh refinement,” J. Comput. Phys. 231, 3023–3040 (2012).

[Crossref]

K. Peng, X. Gao, X. Qu, N. Ren, X. Chen, X. He, X. Wang, J. Liang, and J. Tian, “Graphics processing unit parallel accelerated solution of the discrete ordinates for photon transport in biological tissues,” Appl. Opt. 50, 3808–3823 (2011).

[Crossref]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (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]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).

[Crossref]

J. Tervo, P. Kolmonen, M. Vauhkonen, L. Heikkinen, and J. Kaipio, “A finite-element model of electron transport in radiation therapy and a related inverse problem,” Inverse Probl. 15, 1345–1361 (1999).

[Crossref]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[Crossref]

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