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[CrossRef]

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[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]

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]

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]

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]

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]

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]

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).

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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]

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).

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[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]

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]

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

[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]

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).

[CrossRef]

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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]

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, 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]

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]

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]

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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]

J. J. Duderstadt and W. R. Martin, Transport Theory (Wiley, 1979).

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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