Abstract

Sequential quadratic programming (SQP) is used as an optimization algorithm to reconstruct the optical parameters based on the time-domain radiative transfer equation (TD-RTE). Numerous time-resolved measurement signals are obtained using the TD-RTE as forward model. For a high computational efficiency, the gradient of objective function is calculated using an adjoint equation technique. SQP algorithm is employed to solve the inverse problem and the regularization term based on the generalized Gaussian Markov random field (GGMRF) model is used to overcome the ill-posed problem. Simulated results show that the proposed reconstruction scheme performs efficiently and accurately.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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2016 (2)

B. Zhang, C. L. Xu, and S. M. Wang, “An inverse method for flue gas shielded metal surface temperature measurement based on infrared radiation,” Meas. Sci. Technol. 27(7), 074002 (2016).
[Crossref]

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “An efficient and robust reconstruction method for optical tomography with the time-domain radiative transfer equation,” Opt. Lasers Eng. 78, 155–164 (2016).
[Crossref]

2015 (2)

H. Qi, Y. B. Qiao, S. C. Sun, Y. C. Yao, and L. M. Ruan, “Image reconstruction of two-dimensional highly scattering inhomogeneous medium using MAP-based estimation,” Math. Probl. Eng. 2015, 1–9 (2015).

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation,” Opt. Commun. 351, 75–84 (2015).
[Crossref]

2014 (1)

M. Marin, F. Asllanaj, and D. Maillet, “Sensitivity analysis to optical properties of biological tissues subjected to a short-pulsed laser using the time-dependent radiative transfer equation,” J. Quant. Spectrosco Ra. 133, 117–127 (2014).
[Crossref]

2013 (1)

J. Guan, S. Fang, and C. Guo, “Optical tomography reconstruction algorithm based on the radiative transfer equation considering refractive index: Part 2. Inverse model,” Comput. Med. Imaging Graph. 37(3), 256–262 (2013).
[Crossref] [PubMed]

2012 (2)

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous galerkin formulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Ra. 113(10), 805–814 (2012).
[Crossref]

T. Tarvainen, B. T. Cox, J. P. Kaipio, and S. R. Arridge, “Reconstructing absorption and scattering distributions in quantitative photoacoustic tomography,” Inverse Probl. 28(8), 1067–1079 (2012).
[Crossref]

2011 (1)

P. Ben-Abdallah, S. A. Biehs, and K. Joulain, “Many-body radiative heat transfer theory,” Phys. Rev. Lett. 107(11), 114301 (2011).
[Crossref] [PubMed]

2010 (1)

A. D. Klose, “The forward and inverse problem in tissue optics based on the radiative transfer equation: a brief review,” J. Quant. Spectrosc. Radiat. Transf. 111(11), 1852–1853 (2010).
[Crossref] [PubMed]

2009 (2)

H. K. Kim and A. H. Hielscher, “A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer,” Inverse Probl. 25(1), 711–723 (2009).
[Crossref]

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009).
[Crossref] [PubMed]

2008 (3)

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[Crossref] [PubMed]

A. Charette, J. Boulanger, and H. K. Kim, “An overview on recent radiation transport algorithm development for optical tomography imaging,” J. Quant. Spectrosco Ra. 109(17–18), 2743–2766 (2008).
[Crossref]

R. Hernández and J. Ballester, “Flame imaging as a diagnostic tool for industrial combustion,” Combust. Flame 155(3), 509–528 (2008).
[Crossref]

2007 (2)

R. Zirak and M. Khademi, “An efficient method for model refinement in diffuse optical tomography,” Opt. Commun. 279(2), 273–284 (2007).
[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. Ra. 104(1), 24–39 (2007).
[Crossref]

2006 (3)

K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28(4), 1463–1489 (2006).
[Crossref]

E. Jonathan, “Non-contact and non-destructive testing of silicon V-grooves: a non-medical application of optical coherence tomography (OCT),” Opt. Lasers Eng. 44(11), 1117–1131 (2006).
[Crossref]

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, ““Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Tran. 49(11), 1820–1832 (2006).
[Crossref]

2005 (1)

J. Boulanger and A. Charette, “Numerical developments for Short-Pulsed near Infra-red laser spectroscopy. Part II: inverse treatment,” J. Quant. Spectrosc. Ra. 91(3), 297–318 (2005).
[Crossref]

2004 (2)

2003 (1)

S. A. Gassan and H. H. Andreas, “Three-dimensional optical tomography with the equation of radiative transfer,” J. Electron. Imaging 12(4), 594–601 (2003).
[Crossref]

2002 (3)

R. Elaloufi, R. Carminati, and J. J. Greffet, “Time-dependent transport through scattering media: from radiative transfer to diffusion,” J. Opt. A, Pure Appl. Opt. 4(5), S103–S108 (2002).
[Crossref]

A. D. Klose and A. H. Hielscher, “Optical tomography using the time-independent equation of radiative transfer—Part 2: inverse model,” J. Quant. Spectrosc. Ra. 72(5), 715–732 (2002).
[Crossref]

T. Dierkes, O. Dorn, F. Natterer, V. Palamodov, and H. Sielschott, “Fréchet derivatives for some bilinear inverse problems,” SIAM J. Appl. Math. 62(6), 2092–2113 (2002).
[Crossref]

2001 (2)

2000 (1)

1999 (4)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[Crossref] [PubMed]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
[Crossref]

A. D. Klose and A. H. Hielscher, “Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26(8), 1698–1707 (1999).
[Crossref] [PubMed]

J. C. Ye, K. J. Webb, C. A. Bouman, and R. P. Millane, “Optical diffusion tomography by iterative-coordinate-descent optimization in a Bayesian framework,” J. Opt. Soc. Am. A 16(10), 2400–2412 (1999).
[Crossref]

1998 (1)

O. Dorn, “A transport-backtransport method for optical tomography,” Inverse Probl. 14(5), 1107–1130 (1998).
[Crossref]

1997 (1)

S. S. Saquib, K. M. Hanson, and G. S. Cunningham, “Model-based image reconstruction from time-resolved diffusion data,” Proc. SPIE 3034, 369–380 (1997).
[Crossref]

1986 (1)

M. Fukushima, “A successive quadratic programming algorithm with global and superlinear convergence properties,” Math. Program. 35(3), 253–264 (1986).
[Crossref]

1982 (1)

K. Schittkowski, “The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function,” Numer. Math. 38(1), 83–114 (1982).
[Crossref]

1978 (1)

M. J. D. Powell, “The convergence of variable metric methods for non-linearly constrained optimization calculations,” Nonlinear Program 3(2), 27–63 (1978).

1941 (1)

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

Andreas, H. H.

S. A. Gassan and H. H. Andreas, “Three-dimensional optical tomography with the equation of radiative transfer,” J. Electron. Imaging 12(4), 594–601 (2003).
[Crossref]

Arridge, S. R.

T. Tarvainen, B. T. Cox, J. P. Kaipio, and S. R. Arridge, “Reconstructing absorption and scattering distributions in quantitative photoacoustic tomography,” Inverse Probl. 28(8), 1067–1079 (2012).
[Crossref]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
[Crossref]

Asllanaj, F.

M. Marin, F. Asllanaj, and D. Maillet, “Sensitivity analysis to optical properties of biological tissues subjected to a short-pulsed laser using the time-dependent radiative transfer equation,” J. Quant. Spectrosco Ra. 133, 117–127 (2014).
[Crossref]

Bal, G.

K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28(4), 1463–1489 (2006).
[Crossref]

Balima, O.

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous galerkin formulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Ra. 113(10), 805–814 (2012).
[Crossref]

Ballester, J.

R. Hernández and J. Ballester, “Flame imaging as a diagnostic tool for industrial combustion,” Combust. Flame 155(3), 509–528 (2008).
[Crossref]

Ben-Abdallah, P.

P. Ben-Abdallah, S. A. Biehs, and K. Joulain, “Many-body radiative heat transfer theory,” Phys. Rev. Lett. 107(11), 114301 (2011).
[Crossref] [PubMed]

Biehs, S. A.

P. Ben-Abdallah, S. A. Biehs, and K. Joulain, “Many-body radiative heat transfer theory,” Phys. Rev. Lett. 107(11), 114301 (2011).
[Crossref] [PubMed]

Boulanger, J.

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous galerkin formulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Ra. 113(10), 805–814 (2012).
[Crossref]

A. Charette, J. Boulanger, and H. K. Kim, “An overview on recent radiation transport algorithm development for optical tomography imaging,” J. Quant. Spectrosco Ra. 109(17–18), 2743–2766 (2008).
[Crossref]

J. Boulanger and A. Charette, “Numerical developments for Short-Pulsed near Infra-red laser spectroscopy. Part II: inverse treatment,” J. Quant. Spectrosc. Ra. 91(3), 297–318 (2005).
[Crossref]

Bouman, C. A.

Carminati, R.

R. Elaloufi, R. Carminati, and J. J. Greffet, “Time-dependent transport through scattering media: from radiative transfer to diffusion,” J. Opt. A, Pure Appl. Opt. 4(5), S103–S108 (2002).
[Crossref]

Charette, A.

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous galerkin formulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Ra. 113(10), 805–814 (2012).
[Crossref]

A. Charette, J. Boulanger, and H. K. Kim, “An overview on recent radiation transport algorithm development for optical tomography imaging,” J. Quant. Spectrosco Ra. 109(17–18), 2743–2766 (2008).
[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. Ra. 104(1), 24–39 (2007).
[Crossref]

J. Boulanger and A. Charette, “Numerical developments for Short-Pulsed near Infra-red laser spectroscopy. Part II: inverse treatment,” J. Quant. Spectrosc. Ra. 91(3), 297–318 (2005).
[Crossref]

Chen, Q.

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “An efficient and robust reconstruction method for optical tomography with the time-domain radiative transfer equation,” Opt. Lasers Eng. 78, 155–164 (2016).
[Crossref]

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation,” Opt. Commun. 351, 75–84 (2015).
[Crossref]

Chu, M.

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009).
[Crossref] [PubMed]

Chugh, P.

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, ““Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Tran. 49(11), 1820–1832 (2006).
[Crossref]

Cox, B. T.

T. Tarvainen, B. T. Cox, J. P. Kaipio, and S. R. Arridge, “Reconstructing absorption and scattering distributions in quantitative photoacoustic tomography,” Inverse Probl. 28(8), 1067–1079 (2012).
[Crossref]

Cunningham, G. S.

S. S. Saquib, K. M. Hanson, and G. S. Cunningham, “Model-based image reconstruction from time-resolved diffusion data,” Proc. SPIE 3034, 369–380 (1997).
[Crossref]

Dehghani, H.

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009).
[Crossref] [PubMed]

Dierkes, T.

T. Dierkes, O. Dorn, F. Natterer, V. Palamodov, and H. Sielschott, “Fréchet derivatives for some bilinear inverse problems,” SIAM J. Appl. Math. 62(6), 2092–2113 (2002).
[Crossref]

Dorn, O.

T. Dierkes, O. Dorn, F. Natterer, V. Palamodov, and H. Sielschott, “Fréchet derivatives for some bilinear inverse problems,” SIAM J. Appl. Math. 62(6), 2092–2113 (2002).
[Crossref]

O. Dorn, “A transport-backtransport method for optical tomography,” Inverse Probl. 14(5), 1107–1130 (1998).
[Crossref]

Elaloufi, R.

R. Elaloufi, R. Carminati, and J. J. Greffet, “Time-dependent transport through scattering media: from radiative transfer to diffusion,” J. Opt. A, Pure Appl. Opt. 4(5), S103–S108 (2002).
[Crossref]

Fang, S.

J. Guan, S. Fang, and C. Guo, “Optical tomography reconstruction algorithm based on the radiative transfer equation considering refractive index: Part 2. Inverse model,” Comput. Med. Imaging Graph. 37(3), 256–262 (2013).
[Crossref] [PubMed]

Favennec, Y.

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous galerkin formulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Ra. 113(10), 805–814 (2012).
[Crossref]

Fukushima, M.

M. Fukushima, “A successive quadratic programming algorithm with global and superlinear convergence properties,” Math. Program. 35(3), 253–264 (1986).
[Crossref]

Gassan, S. A.

S. A. Gassan and H. H. Andreas, “Three-dimensional optical tomography with the equation of radiative transfer,” J. Electron. Imaging 12(4), 594–601 (2003).
[Crossref]

Greenstein, J. L.

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

Greffet, J. J.

R. Elaloufi, R. Carminati, and J. J. Greffet, “Time-dependent transport through scattering media: from radiative transfer to diffusion,” J. Opt. A, Pure Appl. Opt. 4(5), S103–S108 (2002).
[Crossref]

Guan, J.

J. Guan, S. Fang, and C. Guo, “Optical tomography reconstruction algorithm based on the radiative transfer equation considering refractive index: Part 2. Inverse model,” Comput. Med. Imaging Graph. 37(3), 256–262 (2013).
[Crossref] [PubMed]

Guo, C.

J. Guan, S. Fang, and C. Guo, “Optical tomography reconstruction algorithm based on the radiative transfer equation considering refractive index: Part 2. Inverse model,” Comput. Med. Imaging Graph. 37(3), 256–262 (2013).
[Crossref] [PubMed]

Guo, Z.

Hanson, K. M.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[Crossref] [PubMed]

S. S. Saquib, K. M. Hanson, and G. S. Cunningham, “Model-based image reconstruction from time-resolved diffusion data,” Proc. SPIE 3034, 369–380 (1997).
[Crossref]

Henyey, L. G.

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

Hernández, R.

R. Hernández and J. Ballester, “Flame imaging as a diagnostic tool for industrial combustion,” Combust. Flame 155(3), 509–528 (2008).
[Crossref]

Hielscher, A. H.

H. K. Kim and A. H. Hielscher, “A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer,” Inverse Probl. 25(1), 711–723 (2009).
[Crossref]

K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28(4), 1463–1489 (2006).
[Crossref]

A. D. Klose and A. H. Hielscher, “Optical tomography using the time-independent equation of radiative transfer—Part 2: inverse model,” J. Quant. Spectrosc. Ra. 72(5), 715–732 (2002).
[Crossref]

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[Crossref] [PubMed]

A. D. Klose and A. H. Hielscher, “Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26(8), 1698–1707 (1999).
[Crossref] [PubMed]

Jonathan, E.

E. Jonathan, “Non-contact and non-destructive testing of silicon V-grooves: a non-medical application of optical coherence tomography (OCT),” Opt. Lasers Eng. 44(11), 1117–1131 (2006).
[Crossref]

Joshi, A.

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[Crossref] [PubMed]

Joulain, K.

P. Ben-Abdallah, S. A. Biehs, and K. Joulain, “Many-body radiative heat transfer theory,” Phys. Rev. Lett. 107(11), 114301 (2011).
[Crossref] [PubMed]

Kaipio, J. P.

T. Tarvainen, B. T. Cox, J. P. Kaipio, and S. R. Arridge, “Reconstructing absorption and scattering distributions in quantitative photoacoustic tomography,” Inverse Probl. 28(8), 1067–1079 (2012).
[Crossref]

Khademi, M.

R. Zirak and M. Khademi, “An efficient method for model refinement in diffuse optical tomography,” Opt. Commun. 279(2), 273–284 (2007).
[Crossref]

Kim, H. K.

H. K. Kim and A. H. Hielscher, “A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer,” Inverse Probl. 25(1), 711–723 (2009).
[Crossref]

A. Charette, J. Boulanger, and H. K. Kim, “An overview on recent radiation transport algorithm development for optical tomography imaging,” J. Quant. Spectrosco Ra. 109(17–18), 2743–2766 (2008).
[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. Ra. 104(1), 24–39 (2007).
[Crossref]

Klose, A. D.

A. D. Klose, “The forward and inverse problem in tissue optics based on the radiative transfer equation: a brief review,” J. Quant. Spectrosc. Radiat. Transf. 111(11), 1852–1853 (2010).
[Crossref] [PubMed]

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009).
[Crossref] [PubMed]

A. D. Klose and A. H. Hielscher, “Optical tomography using the time-independent equation of radiative transfer—Part 2: inverse model,” J. Quant. Spectrosc. Ra. 72(5), 715–732 (2002).
[Crossref]

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[Crossref] [PubMed]

A. D. Klose and A. H. Hielscher, “Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26(8), 1698–1707 (1999).
[Crossref] [PubMed]

Kumar, P.

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, ““Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Tran. 49(11), 1820–1832 (2006).
[Crossref]

Kumar, S.

Maillet, D.

M. Marin, F. Asllanaj, and D. Maillet, “Sensitivity analysis to optical properties of biological tissues subjected to a short-pulsed laser using the time-dependent radiative transfer equation,” J. Quant. Spectrosco Ra. 133, 117–127 (2014).
[Crossref]

Marin, M.

M. Marin, F. Asllanaj, and D. Maillet, “Sensitivity analysis to optical properties of biological tissues subjected to a short-pulsed laser using the time-dependent radiative transfer equation,” J. Quant. Spectrosco Ra. 133, 117–127 (2014).
[Crossref]

McGhee, J.

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[Crossref] [PubMed]

Millane, R. P.

Mishra, S. C.

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, ““Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Tran. 49(11), 1820–1832 (2006).
[Crossref]

Mitra, K.

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, ““Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Tran. 49(11), 1820–1832 (2006).
[Crossref]

Natterer, F.

T. Dierkes, O. Dorn, F. Natterer, V. Palamodov, and H. Sielschott, “Fréchet derivatives for some bilinear inverse problems,” SIAM J. Appl. Math. 62(6), 2092–2113 (2002).
[Crossref]

Palamodov, V.

T. Dierkes, O. Dorn, F. Natterer, V. Palamodov, and H. Sielschott, “Fréchet derivatives for some bilinear inverse problems,” SIAM J. Appl. Math. 62(6), 2092–2113 (2002).
[Crossref]

Powell, M. J. D.

M. J. D. Powell, “The convergence of variable metric methods for non-linearly constrained optimization calculations,” Nonlinear Program 3(2), 27–63 (1978).

Qi, H.

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “An efficient and robust reconstruction method for optical tomography with the time-domain radiative transfer equation,” Opt. Lasers Eng. 78, 155–164 (2016).
[Crossref]

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation,” Opt. Commun. 351, 75–84 (2015).
[Crossref]

H. Qi, Y. B. Qiao, S. C. Sun, Y. C. Yao, and L. M. Ruan, “Image reconstruction of two-dimensional highly scattering inhomogeneous medium using MAP-based estimation,” Math. Probl. Eng. 2015, 1–9 (2015).

Qiao, Y. B.

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “An efficient and robust reconstruction method for optical tomography with the time-domain radiative transfer equation,” Opt. Lasers Eng. 78, 155–164 (2016).
[Crossref]

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation,” Opt. Commun. 351, 75–84 (2015).
[Crossref]

H. Qi, Y. B. Qiao, S. C. Sun, Y. C. Yao, and L. M. Ruan, “Image reconstruction of two-dimensional highly scattering inhomogeneous medium using MAP-based estimation,” Math. Probl. Eng. 2015, 1–9 (2015).

Quan, H.

Rasmussen, J. C.

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[Crossref] [PubMed]

Ren, K.

K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28(4), 1463–1489 (2006).
[Crossref]

Roy, R.

Ruan, L. M.

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “An efficient and robust reconstruction method for optical tomography with the time-domain radiative transfer equation,” Opt. Lasers Eng. 78, 155–164 (2016).
[Crossref]

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation,” Opt. Commun. 351, 75–84 (2015).
[Crossref]

H. Qi, Y. B. Qiao, S. C. Sun, Y. C. Yao, and L. M. Ruan, “Image reconstruction of two-dimensional highly scattering inhomogeneous medium using MAP-based estimation,” Math. Probl. Eng. 2015, 1–9 (2015).

Saquib, S. S.

S. S. Saquib, K. M. Hanson, and G. S. Cunningham, “Model-based image reconstruction from time-resolved diffusion data,” Proc. SPIE 3034, 369–380 (1997).
[Crossref]

Schittkowski, K.

K. Schittkowski, “The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function,” Numer. Math. 38(1), 83–114 (1982).
[Crossref]

Sevick-Muraca, E. M.

Sielschott, H.

T. Dierkes, O. Dorn, F. Natterer, V. Palamodov, and H. Sielschott, “Fréchet derivatives for some bilinear inverse problems,” SIAM J. Appl. Math. 62(6), 2092–2113 (2002).
[Crossref]

Sun, S. C.

H. Qi, Y. B. Qiao, S. C. Sun, Y. C. Yao, and L. M. Ruan, “Image reconstruction of two-dimensional highly scattering inhomogeneous medium using MAP-based estimation,” Math. Probl. Eng. 2015, 1–9 (2015).

Tan, H. P.

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “An efficient and robust reconstruction method for optical tomography with the time-domain radiative transfer equation,” Opt. Lasers Eng. 78, 155–164 (2016).
[Crossref]

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation,” Opt. Commun. 351, 75–84 (2015).
[Crossref]

Tarvainen, T.

T. Tarvainen, B. T. Cox, J. P. Kaipio, and S. R. Arridge, “Reconstructing absorption and scattering distributions in quantitative photoacoustic tomography,” Inverse Probl. 28(8), 1067–1079 (2012).
[Crossref]

Vishwanath, K.

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009).
[Crossref] [PubMed]

Wang, S. M.

B. Zhang, C. L. Xu, and S. M. Wang, “An inverse method for flue gas shielded metal surface temperature measurement based on infrared radiation,” Meas. Sci. Technol. 27(7), 074002 (2016).
[Crossref]

Wareing, T. A.

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[Crossref] [PubMed]

Webb, K. J.

Xu, C. L.

B. Zhang, C. L. Xu, and S. M. Wang, “An inverse method for flue gas shielded metal surface temperature measurement based on infrared radiation,” Meas. Sci. Technol. 27(7), 074002 (2016).
[Crossref]

Yao, Y. C.

H. Qi, Y. B. Qiao, S. C. Sun, Y. C. Yao, and L. M. Ruan, “Image reconstruction of two-dimensional highly scattering inhomogeneous medium using MAP-based estimation,” Math. Probl. Eng. 2015, 1–9 (2015).

Ye, J. C.

Zhang, B.

B. Zhang, C. L. Xu, and S. M. Wang, “An inverse method for flue gas shielded metal surface temperature measurement based on infrared radiation,” Meas. Sci. Technol. 27(7), 074002 (2016).
[Crossref]

Zirak, R.

R. Zirak and M. Khademi, “An efficient method for model refinement in diffuse optical tomography,” Opt. Commun. 279(2), 273–284 (2007).
[Crossref]

Appl. Opt. (2)

Astrophys. J. (1)

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

Combust. Flame (1)

R. Hernández and J. Ballester, “Flame imaging as a diagnostic tool for industrial combustion,” Combust. Flame 155(3), 509–528 (2008).
[Crossref]

Comput. Med. Imaging Graph. (1)

J. Guan, S. Fang, and C. Guo, “Optical tomography reconstruction algorithm based on the radiative transfer equation considering refractive index: Part 2. Inverse model,” Comput. Med. Imaging Graph. 37(3), 256–262 (2013).
[Crossref] [PubMed]

IEEE Trans. Med. Imaging (1)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[Crossref] [PubMed]

Int. J. Heat Mass Tran. (1)

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, ““Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Tran. 49(11), 1820–1832 (2006).
[Crossref]

Inverse Probl. (4)

H. K. Kim and A. H. Hielscher, “A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer,” Inverse Probl. 25(1), 711–723 (2009).
[Crossref]

O. Dorn, “A transport-backtransport method for optical tomography,” Inverse Probl. 14(5), 1107–1130 (1998).
[Crossref]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
[Crossref]

T. Tarvainen, B. T. Cox, J. P. Kaipio, and S. R. Arridge, “Reconstructing absorption and scattering distributions in quantitative photoacoustic tomography,” Inverse Probl. 28(8), 1067–1079 (2012).
[Crossref]

J. Electron. Imaging (1)

S. A. Gassan and H. H. Andreas, “Three-dimensional optical tomography with the equation of radiative transfer,” J. Electron. Imaging 12(4), 594–601 (2003).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

R. Elaloufi, R. Carminati, and J. J. Greffet, “Time-dependent transport through scattering media: from radiative transfer to diffusion,” J. Opt. A, Pure Appl. Opt. 4(5), S103–S108 (2002).
[Crossref]

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

J. Quant. Spectrosc. Ra. (4)

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous galerkin formulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Ra. 113(10), 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. Ra. 104(1), 24–39 (2007).
[Crossref]

J. Boulanger and A. Charette, “Numerical developments for Short-Pulsed near Infra-red laser spectroscopy. Part II: inverse treatment,” J. Quant. Spectrosc. Ra. 91(3), 297–318 (2005).
[Crossref]

A. D. Klose and A. H. Hielscher, “Optical tomography using the time-independent equation of radiative transfer—Part 2: inverse model,” J. Quant. Spectrosc. Ra. 72(5), 715–732 (2002).
[Crossref]

J. Quant. Spectrosc. Radiat. Transf. (1)

A. D. Klose, “The forward and inverse problem in tissue optics based on the radiative transfer equation: a brief review,” J. Quant. Spectrosc. Radiat. Transf. 111(11), 1852–1853 (2010).
[Crossref] [PubMed]

J. Quant. Spectrosco Ra. (2)

A. Charette, J. Boulanger, and H. K. Kim, “An overview on recent radiation transport algorithm development for optical tomography imaging,” J. Quant. Spectrosco Ra. 109(17–18), 2743–2766 (2008).
[Crossref]

M. Marin, F. Asllanaj, and D. Maillet, “Sensitivity analysis to optical properties of biological tissues subjected to a short-pulsed laser using the time-dependent radiative transfer equation,” J. Quant. Spectrosco Ra. 133, 117–127 (2014).
[Crossref]

Math. Probl. Eng. (1)

H. Qi, Y. B. Qiao, S. C. Sun, Y. C. Yao, and L. M. Ruan, “Image reconstruction of two-dimensional highly scattering inhomogeneous medium using MAP-based estimation,” Math. Probl. Eng. 2015, 1–9 (2015).

Math. Program. (1)

M. Fukushima, “A successive quadratic programming algorithm with global and superlinear convergence properties,” Math. Program. 35(3), 253–264 (1986).
[Crossref]

Meas. Sci. Technol. (1)

B. Zhang, C. L. Xu, and S. M. Wang, “An inverse method for flue gas shielded metal surface temperature measurement based on infrared radiation,” Meas. Sci. Technol. 27(7), 074002 (2016).
[Crossref]

Med. Phys. (1)

A. D. Klose and A. H. Hielscher, “Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26(8), 1698–1707 (1999).
[Crossref] [PubMed]

Nonlinear Program (1)

M. J. D. Powell, “The convergence of variable metric methods for non-linearly constrained optimization calculations,” Nonlinear Program 3(2), 27–63 (1978).

Numer. Math. (1)

K. Schittkowski, “The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function,” Numer. Math. 38(1), 83–114 (1982).
[Crossref]

Opt. Commun. (2)

R. Zirak and M. Khademi, “An efficient method for model refinement in diffuse optical tomography,” Opt. Commun. 279(2), 273–284 (2007).
[Crossref]

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “Multi-start iterative reconstruction of the radiative parameter distributions in participating media based on the transient radiative transfer equation,” Opt. Commun. 351, 75–84 (2015).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (2)

E. Jonathan, “Non-contact and non-destructive testing of silicon V-grooves: a non-medical application of optical coherence tomography (OCT),” Opt. Lasers Eng. 44(11), 1117–1131 (2006).
[Crossref]

Y. B. Qiao, H. Qi, Q. Chen, L. M. Ruan, and H. P. Tan, “An efficient and robust reconstruction method for optical tomography with the time-domain radiative transfer equation,” Opt. Lasers Eng. 78, 155–164 (2016).
[Crossref]

Phys. Med. Biol. (2)

A. Joshi, J. C. Rasmussen, E. M. Sevick-Muraca, T. A. Wareing, and J. McGhee, “Radiative transport-based frequency-domain fluorescence tomography,” Phys. Med. Biol. 53(8), 2069–2088 (2008).
[Crossref] [PubMed]

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54(8), 2493–2509 (2009).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

P. Ben-Abdallah, S. A. Biehs, and K. Joulain, “Many-body radiative heat transfer theory,” Phys. Rev. Lett. 107(11), 114301 (2011).
[Crossref] [PubMed]

Proc. SPIE (1)

S. S. Saquib, K. M. Hanson, and G. S. Cunningham, “Model-based image reconstruction from time-resolved diffusion data,” Proc. SPIE 3034, 369–380 (1997).
[Crossref]

SIAM J. Appl. Math. (1)

T. Dierkes, O. Dorn, F. Natterer, V. Palamodov, and H. Sielschott, “Fréchet derivatives for some bilinear inverse problems,” SIAM J. Appl. Math. 62(6), 2092–2113 (2002).
[Crossref]

SIAM J. Sci. Comput. (1)

K. Ren, G. Bal, and A. H. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28(4), 1463–1489 (2006).
[Crossref]

Other (3)

J. Heino, Approaches for Modelling and Reconstruction in Optical Tomography in the Presence of Anisotropies (Helsinki University of Technology, 2005).

M. F. Modest, Radiative Heat Transfer (Academic, 2003).

P. C. Hansen, “The L-curve and its use in the numerical treatment of inverse problems,” in Computational Inverse Problems in Electrocardiology, P. Johnston, ed. (WIT Press, 1999), pp. 119–142.

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Figures (10)

Fig. 1
Fig. 1 Schematic of the model with optical fibers.
Fig. 2
Fig. 2 L-curve for the scale parameter.
Fig. 3
Fig. 3 Reconstructed results of the Test 1 using the SQP algorithm. The real distributions are on the left column, the reconstructed distributions without regularization are on the middle column and the reconstructed distributions with regularization are on the right column.
Fig. 4
Fig. 4 The reconstruction results using the CG method.
Fig. 5
Fig. 5 The cross-section of the reconstruction results at y = 1.0cm and y = 3.0cm.
Fig. 6
Fig. 6 Reconstructed results with measurement errors. The results with 10% measurement error are on the left column and the results with 20% measurement error are on the right column.
Fig. 7
Fig. 7 Reconstructed results of the media with circle inclusions. The real distributions are on the left column and the reconstructed distributions are on the right column.
Fig. 8
Fig. 8 Reconstructed results of the media with oval inclusions. The real distributions are on the left column and the reconstructed distributions are on the right column.
Fig. 9
Fig. 9 Reconstructed results of the scattering-domain media. The results of Test 2 are on the top row and the results of Test 3 are on the bottom row.
Fig. 10
Fig. 10 Reconstructed results of Test 4.

Tables (5)

Tables Icon

Table 1 Absorption and scattering coefficients in the medium of Test 1.

Tables Icon

Table 2 Comparison of the reconstruction using the SQP and CG.

Tables Icon

Table 3 The NRMSE of the reconstructed results with measurement errors.

Tables Icon

Table 4 Absorption and scattering coefficients of the highly scattering media.

Tables Icon

Table 5 Absorption and scattering coefficients of Test 4.

Equations (42)

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

1 c I( r,Ω,t ) t +ΩI( r,Ω,t )=β( r )I( r,Ω,t )+ μ s ( r ) 4π 4π I( r, Ω ,t )Φ( Ω ,Ω )d Ω
Φ( Ω ,Ω )= 1 g 2 [ 1+ g 2 2g( Ω Ω ) ] 3 2
Φ( Ω ,Ω )= 1 g 2 1+ g 2 2g( Ω Ω )
I( r,Ω,t )= I c ( r,Ω,t )+ I d ( r,Ω,t )
1 c I c ( r,Ω,t ) t +Ω I c ( r,Ω,t )=β( r ) I c ( r,Ω,t )
1 c I d ( r,Ω,t ) t +Ω· I d ( r,Ω,t )= β( r ) I d ( r,Ω,t )+ μ s ( r ) 4π 4π I d ( r, Ω ,t )Φ( Ω ,Ω )d Ω + S c ( r,Ω,t )
I c ( r,Ω,t )= I in exp[ 0 s 0 β( r )dr ][ H( ct s 0 )H( ctc t p s 0 ) ]δ( Ω Ω 0 )
S c ( r,Ω,t )= μ s ( r ) 4π I in exp[ 0 s 0 β( r )dr ][ H( ct s 0 )H( ctc t p s 0 ) ]Φ( Ω 0 ,Ω )
P( r,t )= Ωn>0 I( r,Ω,t )ΩndΩ
1 c I k ( r,t ) t + ξ k I k ( r,t ) x + η k I k ( r,t ) y = β( r ) I k ( r,t )+ μ s ( r ) 4π k =1 K w k I k ( r,t )Φ( Ω k , Ω k ) + S c ( r,t )
I k,i,j n = S c i,j + μ s 4π w k Φ k, k I k ,i,j n1 + I k,i,j n1 / ( cΔt ) +( ξ k / Δx ) I k,i1,j n +( η k / Δy ) I k,i,j1 n 1/ ( cΔt ) + ξ k / Δx + η k / Δy +( μ a + μ s )
F(x)= 1 2 s d n [ M s,d n P s,d n ( x ) ] 2 / ( M s,d n ) 2
minimize F(x) subjectto c i (x)=0 i=1,2,, m e c i (x)0 i= m e +1,,m
min 1 2 d k T B k d k + g T d k s.t. c i + c i T d k =0 i=1,2, m e c i + c i T d k 0 i= m e +1,,m
L( x,λ )=F( x ) i=1 m λ i c i ( x )
B k+1 = B k + ( y ˜ k y ˜ k T ) / ( y ˜ k T s k ) ( B k s k s k T B k ) / s k T B k s k
θ={ 1 s k T y k β s k T B k s k ( 1β ) s k T B k s k / [ s k T B k s k s k T y k ] s k T y k <β s k T B k s k
y k = x L( x k+1 , λ k+1 ) x L( x k , λ k+1 )
F r ( x )=F( x )+r{ i=1 m e max[ 0, c i ( x ) ] + i=1 m e | c i ( x ) | }
r={ max( | λ i k+1 | )+ρ r<max( | λ i k+1 | ) r else }
F r ( x k+1 )< F r ( x k )+σ a k F ¯ r [ ( x k , d k )( F r x k ) ]
F ¯ r ( x k , d k )=f( x k )+ g kT d+ 1 2 d T B k d+r[ i=1 m e | c i k + c i k d | + i= m e +1 m | min( 0, c i x k + c i x k T d ) | ]
min 1 2 d ^ k T B k d ^ k + p kT d ^ k s.t. c i + h i kT d ^ k =0 i=1,2, m e c i + h i kT d ^ k 0 i= m e +1,,m
p k = g k + 1 2 i=1 m λ i k+1 [ c i ( x k + d ^ k ) c i ( x k ) ]
h i k = c i k + 1 2 d ^ k [ c i ( x k + d ^ k ) c i ( x k ) ]
F r [ x k + a k d k + ( a k ) 2 ( d ^ k d k ) ]< F r ( x k )+σ a k [ F ¯ r ( x k , d k ) F r ( x k ) ]
F r ( x k + a k d k ) F r ( x k )+σ a k F ¯ r [ ( x k , d k )( F r x k ) ]
max[ | c i x k + h i kT d k c i ( x k + d k ) | ]<σmax[ | c i x k + c i x kT d k c i ( x k + d k ) | ]
[ F r ( x k ) F r ( x k+1 ) ] / ( ρ+| F r ( x k+1 ) | ) ε
F(x)= 1 2 s d n [ M s,d n P s,d n ( x ) ] 2 / ( M s,d n ) 2 + s λ s ( r,Ω,t ) T D 4π × { [ 1 c t +Ω+β( r ) ] I d μ s ( r ) 4π 4π I d Φ( Ω ,Ω )d Ω S c }dΩdrdt
ΔF=F( x+Δx )F( x )= s d n ( P s,d n ( x ) M s,d n )Δ P s,d n / ( M s,d n ) 2 + s T D 4π λ s { [ 1 c t +Ω+β( r ) ]Δ I d μ s ( r ) 4π 4π Δ I d Φ( Ω ,Ω )d Ω }dΩdrdt + s T D 4π λ s [ Δβ( r ) I d Δ μ s ( r ) 4π 4π I d Φ( Ω ,Ω )d Ω ]dΩdrdt
s d n P s,d n ( x ) M s,d n ( M s,d n ) 2 Δ P s,d n + s T D 4π λ s × { [ 1 c t +Ω+β( r ) ]Δ I d μ s ( r ) 4π 4π Δ I d Φ( Ω ,Ω )d Ω }dΩdrdt=0
ΔF= D F x Δx= s T D 4π λ s [ Δβ( r ) I d Δ μ s ( r ) 4π 4π I d Φ( Ω ,Ω )d Ω ]dΩdrdt
F[ μ a ( r ) ]= s T 4π λ s ( r,Ω,t ) I d dΩdt
F[ μ s ( r ) ]= s T 4π λ s ( r,Ω,t )[ I d 1 4π 4π I d Φ( Ω ,Ω )d Ω ]dΩdt
λ s ( d,Ω,t )= ( P s,d n ( x ) M s,d n ) / ( M s,d n ) 2 forΩn>0
1 c t λ s Ω λ s =β( r ) λ s + μ s ( r ) 4π 4π λ s ( r, Ω ,t )Φ( Ω ,Ω )d Ω + S λ
1 c t λ s +Ω λ s =β( r ) λ s + μ s ( r ) 4π 4π λ s Φ( Ω ,Ω )d Ω + S λ
F( x )= 1 2 s d n [ M s,d n P s,d n ( x ) ] 2 / ( M s,d n ) 2 +ψ(x)
ψ(x)= 1 p σ p {s,r}N b sr | x s x r | p
NRMSE= i N ( x i x ˜ i ) 2 / i N x i 2
M s,d n = M ˜ s,d n +ran d n σ s,d n

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