2016, 10(1): 227-246. doi: 10.3934/ipi.2016.10.227

Approximate marginalization of absorption and scattering in fluorescence diffuse optical tomography

1. 

Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland

2. 

Department of Computer Science, University College London, Gower Street, London WC1E 6BT, United Kingdom

3. 

Department of Mathematics, University of Auckland, Private Bag 92019, Auckland Mail Centre, Auckland 1142

4. 

Center for Nanoscience and Technology, Istituto Italiano di Tecnologia, Dept of Physics, Politecnico di Milano, 20133 Milan, Italy

5. 

University of Eastern Finland, Department of Applied Physics, P.O.Box 1627, 70211 Kuopio

Received  October 2014 Revised  March 2015 Published  February 2016

In fluorescence diffuse optical tomography (fDOT), the reconstruction of the fluorophore concentration inside the target body is usually carried out using a normalized Born approximation model where the measured fluorescent emission data is scaled by measured excitation data. One of the benefits of the model is that it can tolerate inaccuracy in the absorption and scattering distributions that are used in the construction of the forward model to some extent. In this paper, we employ the recently proposed Bayesian approximation error approach to fDOT for compensating for the modeling errors caused by the inaccurately known optical properties of the target in combination with the normalized Born approximation model. The approach is evaluated using a simulated test case with different amount of error in the optical properties. The results show that the Bayesian approximation error approach improves the tolerance of fDOT imaging against modeling errors caused by inaccurately known absorption and scattering of the target.
Citation: Meghdoot Mozumder, Tanja Tarvainen, Simon Arridge, Jari P. Kaipio, Cosimo D'Andrea, Ville Kolehmainen. Approximate marginalization of absorption and scattering in fluorescence diffuse optical tomography. Inverse Problems & Imaging, 2016, 10 (1) : 227-246. doi: 10.3934/ipi.2016.10.227
References:
[1]

S. R. Arridge, Optical tomography in medical imaging,, Inv. Probl., 15 (1999). doi: 10.1088/0266-5611/15/2/022.

[2]

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen and M. Vauhkonen, Approximation errors and model reduction with an application in optical diffusion tomography,, Inv. Probl., 22 (2006), 175. doi: 10.1088/0266-5611/22/1/010.

[3]

D. Calvetti, J. P. Kaipio and E. Somersalo, Aristotelian prior boundary conditions,, Int. J. Math., 1 (2006), 63.

[4]

D. Calvetti and E. Somersalo, An Introduction to Bayesian Scientific Computing Ten Lectures on Subjective Computing,, Springer, (2007).

[5]

W. F. Cheong, S. A. Prahl and A. J. Welch, A review of the optical properties of biological tissues,, IEEE J. Quant. Electron., 26 (1990), 2166. doi: 10.1109/3.64354.

[6]

A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. Arridge, M. D. Schnall and A. G. Yodh, Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,, Opt. Exp., 15 (2007). doi: 10.1364/OE.15.006696.

[7]

T. Correia, N. Ducros, C. D'Andrea, M. Schweiger and S. Arridge, Quantitative fluorescence diffuse optical tomography in the presence of heterogeneities,, Opt. Lett., 38 (2013), 1903. doi: 10.1364/OL.38.001903.

[8]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, D. N. Pattanayak, B. Chance and A. G. Yodh, Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,, Med. Phys., 30 (2003), 235. doi: 10.1118/1.1534109.

[9]

S. C. Davis, K. S. Samkoe, J. A. O'Hara, S. L. Gibbs-Strauss, H. L. Payne, P. J. Hoopes, K. D. Paulsen and B. W. Pogue, MRI-coupled fluorescence tomography quantifies EGFR activity in brain tumors,, Acad. Radiol., 17 (2010), 271. doi: 10.1016/j.acra.2009.11.001.

[10]

B. Dogdas, D. Stout, A. Chatziioannou and R. M. Leahy, Digimouse: A 3D whole body mouse atlas from ct and cryosection data,, Phys. Med. Biol., 52 (2007), 577. doi: 10.1088/0031-9155/52/3/003.

[11]

S. J. Erickson, S. L. Martinez, J. DeCerce, A. Romero, L. Caldera and A. Godavarty, Three-dimensional fluorescence tomography of human breast tissues in vivo using a hand-held optical imager,, Phys. Med. Biol., 58 (2013).

[12]

Q. Fang, Digimouse atlas FEM mesh,, , ().

[13]

E. E. Graves, J. Ripoll, R. Weissleder and V. Ntziachristos, A submillimeter resolution fluorescence molecular imaging system for small animal imaging,, Med. Phys., 30 (2003), 901. doi: 10.1118/1.1568977.

[14]

J. Heino and E. Somersalo, A modelling error approach for the estimation of optical absorption in the presence of anisotropies,, Phys. Med. Biol., 49 (2004), 4785. doi: 10.1088/0031-9155/49/20/009.

[15]

J. Heino, E. Somersalo and J. Kaipio, Compensation for geometric mismodelling by anisotropies in optical tomography,, Opt. Express, 13 (2005), 296. doi: 10.1364/OPEX.13.000296.

[16]

J. Huttunen and J. Kaipio, Approximation errors in nostationary inverse problems,, Inv. Probl. Imag., 1 (2007), 77. doi: 10.3934/ipi.2007.1.77.

[17]

J. Huttunen and J. Kaipio, Approximation error analysis in nonlinear state estimation with an application to state-space identification,, Inv. Probl., 23 (2007), 2141. doi: 10.1088/0266-5611/23/5/019.

[18]

A. Ishimaru, Wave Propagation and Scattering in Random Media,, Academic, (1997). doi: 10.1109/9780470547045.

[19]

S. L. Jacques, Optical properties of biological tissues: A review,, Phys. Med. Biol., 58 (2013). doi: 10.1088/0031-9155/58/11/R37.

[20]

J. Kaipio and V. Kolehmainen, Approximate marginalization over modelling errors and uncertainites in inverse problems,, in Bayesian Theory and Applications (eds. P. Damien, (2013), 644. doi: 10.1093/acprof:oso/9780199695607.003.0032.

[21]

J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems,, Springer, (2005).

[22]

J. Kaipio and E. Somersalo, Statistical inverse problems: Discretization, model reduction and inverse crimes,, J. Comput. Appl. Math., 198 (2007), 493. doi: 10.1016/j.cam.2005.09.027.

[23]

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J. M. Dinten, P. Peltié, J. L. Coll and P. Rizo, In vivo mice lung tumor follow-up with fluorescence diffuse optical tomography,, J. Biomed. Opt., 13 (2008). doi: 10.1117/1.2884505.

[24]

V. Kolehmainen, M. Schweiger, I. Nissilä, T. Tarvainen, S. R. Arridge and J. P. Kaipio, Approximation errors and model reduction in three-dimensional diffuse optical tomography,, J. Opt. Soc. Am. A., 26 (2009), 2257. doi: 10.1364/JOSAA.26.002257.

[25]

V. Kolehmainen, T. Tarvainen, S. R. Arridge and J. P. Kaipio, Marginalization of uninteresting distributed parameters in inverse problems - application to diffuse optical tomography,, Int. J. Uncertainty Quantification, 1 (2011), 1. doi: 10.1615/Int.J.UncertaintyQuantification.v1.i1.10.

[26]

V. Kolehmainen, A. Vanne, S. Siltanen, S. Jarvenpaa, J. Kaipio, M. Lassas and M. Kalke, Parallelized bayesian inversion for three-dimensional dental x-ray imaging,, IEEE Trans. Med. Imag., 25 (2006), 218. doi: 10.1109/TMI.2005.862662.

[27]

A. Lehikoinen, S. Finsterle, A. Voutilainen, L. M. Heikkinen, M. Vauhkonen and J. P. Kaipio, Approximation errors and truncation of computational domains with application to geophysical tomography,, Inv. Probl. Imag., 1 (2007), 371. doi: 10.3934/ipi.2007.1.371.

[28]

C. Lieberman, K. Willcox and O. Ghattas, Parameter and state model reduction for large-scale statistical inverse problems,, SIAM J. Sci. Comput., 32 (2010), 2523. doi: 10.1137/090775622.

[29]

Y. Lin, H. Yan, O. Nalcioglu and G. Gulsen, Quantitative fluorescence tomography with functional and structural a priori information,, Appl. Opt., 48 (2009), 1328. doi: 10.1364/AO.48.001328.

[30]

A. Martin, J. Aguirre, A. Sarasa-Renedo, D. Tsoukatou, A. Garofalakis, H. Meyer, C. Mamalaki, J. Ripoll and A. M. Planas, Imaging changes in lymphoid organs in vivo after brain ischemia with three-dimensional fluorescence molecular tomography in transgenic mice expressing green fluorescent protein in T lymphocytes,, Mol. Imag., 7 (2008).

[31]

M. Mozumder, T. Tarvainen, S. R. Arridge, J. Kaipio and V. Kolehmainen, Compensation of optode sensitivity and position errors in diffuse optical tomography using the approximation error approach,, Biomed. Opt. Express, 4 (2013), 2015. doi: 10.1364/BOE.4.002015.

[32]

M. Mozumder, T. Tarvainen, J. P. Kaipio, S. R. Arridge and V. Kolehmainen, Compensation of modeling errors due to unknown domain boundary in diffuse optical tomography,, J. Opt. Soc. Am. A, 31 (2014), 1847. doi: 10.1364/JOSAA.31.001847.

[33]

A. Nissinen, L. Heikkinen and J. Kaipio, Approximation errors in electrical impedance tomography - an experimental study,, Meas. Sci. Technol., 19 (2008).

[34]

A. Nissinen, L. M. Heikkinen, V. Kolehmainen and J. P. Kaipio, Compensation of errors due to discretization, domain truncation and unknown contact impedances in electrical impedance tomography,, Meas. Sci. Technol., 20 (2009). doi: 10.1088/0957-0233/20/10/105504.

[35]

V. Ntziachristos, J. Ripoll, L. V. Wang and R. Weissleder, Looking and listening to light: The evolution of whole-body photonic imaging,, Nat. Biotech., 23 (2005), 313. doi: 10.1038/nbt1074.

[36]

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson and R. Weissleder, Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,, Proc. Natl. Acad. Sci. U.S.A., 101 (2004), 12294. doi: 10.1073/pnas.0401137101.

[37]

V. Ntziachristos, C. H. Tung, C. Bremer and R. Weissleder, Fluorescence molecular tomography resolves protease activity in vivo,, Nat. Med., 8 (2002), 757. doi: 10.1038/nm729.

[38]

V. Ntziachristos and R. Weissleder, Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,, Opt. Lett., 26 (2001), 893. doi: 10.1364/OL.26.000893.

[39]

S. Patwardhan, S. Bloch, S. Achilefu and J. Culver, Time-dependent whole-body fluorescence tomography of probe bio-distributions in mice,, Opt. Express, 13 (2005), 2564. doi: 10.1364/OPEX.13.002564.

[40]

S. Pursiainen, Two-stage reconstruction of a circular anomaly in electrical impedance tomography,, Inv. Probl., 22 (2006), 1689. doi: 10.1088/0266-5611/22/5/010.

[41]

T. J. Rudge, V. Y. Soloviev and S. R. Arridge, Fast image reconstruction in fluoresence optical tomography using data compression,, Opt. Lett., 35 (2010), 763. doi: 10.1364/OL.35.000763.

[42]

H. Rue and L. Held, Gaussian Markov Random Fields: Theory and Applications,, Monographs on Statistics and Applied Probability, (2005). doi: 10.1201/9780203492024.

[43]

R. Schulz, J. Ripoll and V. Ntziachristos, Experimental fluorescence tomography of tissues with noncontact measurements,, IEEE Trans. Med. Imag., 23 (2004), 492. doi: 10.1109/TMI.2004.825633.

[44]

M. Schweiger, S. R. Arridge and I. Nissilä, Gauss-Newton method for image reconstruction in diffuse optical tomography,, Phys. Med. Biol., 50 (2005), 2365. doi: 10.1088/0031-9155/50/10/013.

[45]

A. Seppanen, A. Voutilainen and J. P. Kaipio, State estimation in process tomography - reconstruction of velocity fields using eit,, Inv. Probl., 25 (2009). doi: 10.1088/0266-5611/25/8/085009.

[46]

H. Shih and V. Ntziachristos, In vivo characterization of Her-2/neu carcinogenesis in mice using fluorescence molecular tomography,, Proc. Biomed. Opt., (2006). doi: 10.1364/BIO.2006.TuC1.

[47]

M. Solomon, B. R. White, R. E. Nothdruft, W. Akers, G. Sudlow, A. T. Eggebrecht, S. Achilefu and J. P. Culver, Video-rate fluorescence diffuse optical tomography for in vivo sentinel lymph node imaging,, Biomed. Opt. Express, 2 (2011), 3267. doi: 10.1364/BOE.2.003267.

[48]

V. Y. Soloviev, C. D'Andrea, G. Valentini, R. Cubeddu and S. R. Arridge, Combined reconstruction of fluorescent and optical parameters using time-resolved data,, Appl. Opt., 48 (2009), 28. doi: 10.1364/AO.48.000028.

[49]

Y. Tan and H. Jiang, Diffuse optical tomography guided quantitative fluorescence molecular tomography,, Appl. Opt., 47 (2008), 2011. doi: 10.1364/AO.47.002011.

[50]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. R. Arridge and J. P. Kaipio, An approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,, Inv. Probl., 26 (2010). doi: 10.1088/0266-5611/26/1/015005.

[51]

S. V. D. Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. V. D. Voort, R. Nachabe, M. Mark, M. Beek, L. Bakker, L. Fels, S. Elias, P. Luijten and W. Mali, A novel fluorescent imaging agent for diffuse optical tomography of the breast: First clinical experience in patients,, Mol. Imag. Biol., 12 (2010), 343.

show all references

References:
[1]

S. R. Arridge, Optical tomography in medical imaging,, Inv. Probl., 15 (1999). doi: 10.1088/0266-5611/15/2/022.

[2]

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen and M. Vauhkonen, Approximation errors and model reduction with an application in optical diffusion tomography,, Inv. Probl., 22 (2006), 175. doi: 10.1088/0266-5611/22/1/010.

[3]

D. Calvetti, J. P. Kaipio and E. Somersalo, Aristotelian prior boundary conditions,, Int. J. Math., 1 (2006), 63.

[4]

D. Calvetti and E. Somersalo, An Introduction to Bayesian Scientific Computing Ten Lectures on Subjective Computing,, Springer, (2007).

[5]

W. F. Cheong, S. A. Prahl and A. J. Welch, A review of the optical properties of biological tissues,, IEEE J. Quant. Electron., 26 (1990), 2166. doi: 10.1109/3.64354.

[6]

A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. Arridge, M. D. Schnall and A. G. Yodh, Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,, Opt. Exp., 15 (2007). doi: 10.1364/OE.15.006696.

[7]

T. Correia, N. Ducros, C. D'Andrea, M. Schweiger and S. Arridge, Quantitative fluorescence diffuse optical tomography in the presence of heterogeneities,, Opt. Lett., 38 (2013), 1903. doi: 10.1364/OL.38.001903.

[8]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, D. N. Pattanayak, B. Chance and A. G. Yodh, Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,, Med. Phys., 30 (2003), 235. doi: 10.1118/1.1534109.

[9]

S. C. Davis, K. S. Samkoe, J. A. O'Hara, S. L. Gibbs-Strauss, H. L. Payne, P. J. Hoopes, K. D. Paulsen and B. W. Pogue, MRI-coupled fluorescence tomography quantifies EGFR activity in brain tumors,, Acad. Radiol., 17 (2010), 271. doi: 10.1016/j.acra.2009.11.001.

[10]

B. Dogdas, D. Stout, A. Chatziioannou and R. M. Leahy, Digimouse: A 3D whole body mouse atlas from ct and cryosection data,, Phys. Med. Biol., 52 (2007), 577. doi: 10.1088/0031-9155/52/3/003.

[11]

S. J. Erickson, S. L. Martinez, J. DeCerce, A. Romero, L. Caldera and A. Godavarty, Three-dimensional fluorescence tomography of human breast tissues in vivo using a hand-held optical imager,, Phys. Med. Biol., 58 (2013).

[12]

Q. Fang, Digimouse atlas FEM mesh,, , ().

[13]

E. E. Graves, J. Ripoll, R. Weissleder and V. Ntziachristos, A submillimeter resolution fluorescence molecular imaging system for small animal imaging,, Med. Phys., 30 (2003), 901. doi: 10.1118/1.1568977.

[14]

J. Heino and E. Somersalo, A modelling error approach for the estimation of optical absorption in the presence of anisotropies,, Phys. Med. Biol., 49 (2004), 4785. doi: 10.1088/0031-9155/49/20/009.

[15]

J. Heino, E. Somersalo and J. Kaipio, Compensation for geometric mismodelling by anisotropies in optical tomography,, Opt. Express, 13 (2005), 296. doi: 10.1364/OPEX.13.000296.

[16]

J. Huttunen and J. Kaipio, Approximation errors in nostationary inverse problems,, Inv. Probl. Imag., 1 (2007), 77. doi: 10.3934/ipi.2007.1.77.

[17]

J. Huttunen and J. Kaipio, Approximation error analysis in nonlinear state estimation with an application to state-space identification,, Inv. Probl., 23 (2007), 2141. doi: 10.1088/0266-5611/23/5/019.

[18]

A. Ishimaru, Wave Propagation and Scattering in Random Media,, Academic, (1997). doi: 10.1109/9780470547045.

[19]

S. L. Jacques, Optical properties of biological tissues: A review,, Phys. Med. Biol., 58 (2013). doi: 10.1088/0031-9155/58/11/R37.

[20]

J. Kaipio and V. Kolehmainen, Approximate marginalization over modelling errors and uncertainites in inverse problems,, in Bayesian Theory and Applications (eds. P. Damien, (2013), 644. doi: 10.1093/acprof:oso/9780199695607.003.0032.

[21]

J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems,, Springer, (2005).

[22]

J. Kaipio and E. Somersalo, Statistical inverse problems: Discretization, model reduction and inverse crimes,, J. Comput. Appl. Math., 198 (2007), 493. doi: 10.1016/j.cam.2005.09.027.

[23]

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J. M. Dinten, P. Peltié, J. L. Coll and P. Rizo, In vivo mice lung tumor follow-up with fluorescence diffuse optical tomography,, J. Biomed. Opt., 13 (2008). doi: 10.1117/1.2884505.

[24]

V. Kolehmainen, M. Schweiger, I. Nissilä, T. Tarvainen, S. R. Arridge and J. P. Kaipio, Approximation errors and model reduction in three-dimensional diffuse optical tomography,, J. Opt. Soc. Am. A., 26 (2009), 2257. doi: 10.1364/JOSAA.26.002257.

[25]

V. Kolehmainen, T. Tarvainen, S. R. Arridge and J. P. Kaipio, Marginalization of uninteresting distributed parameters in inverse problems - application to diffuse optical tomography,, Int. J. Uncertainty Quantification, 1 (2011), 1. doi: 10.1615/Int.J.UncertaintyQuantification.v1.i1.10.

[26]

V. Kolehmainen, A. Vanne, S. Siltanen, S. Jarvenpaa, J. Kaipio, M. Lassas and M. Kalke, Parallelized bayesian inversion for three-dimensional dental x-ray imaging,, IEEE Trans. Med. Imag., 25 (2006), 218. doi: 10.1109/TMI.2005.862662.

[27]

A. Lehikoinen, S. Finsterle, A. Voutilainen, L. M. Heikkinen, M. Vauhkonen and J. P. Kaipio, Approximation errors and truncation of computational domains with application to geophysical tomography,, Inv. Probl. Imag., 1 (2007), 371. doi: 10.3934/ipi.2007.1.371.

[28]

C. Lieberman, K. Willcox and O. Ghattas, Parameter and state model reduction for large-scale statistical inverse problems,, SIAM J. Sci. Comput., 32 (2010), 2523. doi: 10.1137/090775622.

[29]

Y. Lin, H. Yan, O. Nalcioglu and G. Gulsen, Quantitative fluorescence tomography with functional and structural a priori information,, Appl. Opt., 48 (2009), 1328. doi: 10.1364/AO.48.001328.

[30]

A. Martin, J. Aguirre, A. Sarasa-Renedo, D. Tsoukatou, A. Garofalakis, H. Meyer, C. Mamalaki, J. Ripoll and A. M. Planas, Imaging changes in lymphoid organs in vivo after brain ischemia with three-dimensional fluorescence molecular tomography in transgenic mice expressing green fluorescent protein in T lymphocytes,, Mol. Imag., 7 (2008).

[31]

M. Mozumder, T. Tarvainen, S. R. Arridge, J. Kaipio and V. Kolehmainen, Compensation of optode sensitivity and position errors in diffuse optical tomography using the approximation error approach,, Biomed. Opt. Express, 4 (2013), 2015. doi: 10.1364/BOE.4.002015.

[32]

M. Mozumder, T. Tarvainen, J. P. Kaipio, S. R. Arridge and V. Kolehmainen, Compensation of modeling errors due to unknown domain boundary in diffuse optical tomography,, J. Opt. Soc. Am. A, 31 (2014), 1847. doi: 10.1364/JOSAA.31.001847.

[33]

A. Nissinen, L. Heikkinen and J. Kaipio, Approximation errors in electrical impedance tomography - an experimental study,, Meas. Sci. Technol., 19 (2008).

[34]

A. Nissinen, L. M. Heikkinen, V. Kolehmainen and J. P. Kaipio, Compensation of errors due to discretization, domain truncation and unknown contact impedances in electrical impedance tomography,, Meas. Sci. Technol., 20 (2009). doi: 10.1088/0957-0233/20/10/105504.

[35]

V. Ntziachristos, J. Ripoll, L. V. Wang and R. Weissleder, Looking and listening to light: The evolution of whole-body photonic imaging,, Nat. Biotech., 23 (2005), 313. doi: 10.1038/nbt1074.

[36]

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson and R. Weissleder, Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,, Proc. Natl. Acad. Sci. U.S.A., 101 (2004), 12294. doi: 10.1073/pnas.0401137101.

[37]

V. Ntziachristos, C. H. Tung, C. Bremer and R. Weissleder, Fluorescence molecular tomography resolves protease activity in vivo,, Nat. Med., 8 (2002), 757. doi: 10.1038/nm729.

[38]

V. Ntziachristos and R. Weissleder, Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,, Opt. Lett., 26 (2001), 893. doi: 10.1364/OL.26.000893.

[39]

S. Patwardhan, S. Bloch, S. Achilefu and J. Culver, Time-dependent whole-body fluorescence tomography of probe bio-distributions in mice,, Opt. Express, 13 (2005), 2564. doi: 10.1364/OPEX.13.002564.

[40]

S. Pursiainen, Two-stage reconstruction of a circular anomaly in electrical impedance tomography,, Inv. Probl., 22 (2006), 1689. doi: 10.1088/0266-5611/22/5/010.

[41]

T. J. Rudge, V. Y. Soloviev and S. R. Arridge, Fast image reconstruction in fluoresence optical tomography using data compression,, Opt. Lett., 35 (2010), 763. doi: 10.1364/OL.35.000763.

[42]

H. Rue and L. Held, Gaussian Markov Random Fields: Theory and Applications,, Monographs on Statistics and Applied Probability, (2005). doi: 10.1201/9780203492024.

[43]

R. Schulz, J. Ripoll and V. Ntziachristos, Experimental fluorescence tomography of tissues with noncontact measurements,, IEEE Trans. Med. Imag., 23 (2004), 492. doi: 10.1109/TMI.2004.825633.

[44]

M. Schweiger, S. R. Arridge and I. Nissilä, Gauss-Newton method for image reconstruction in diffuse optical tomography,, Phys. Med. Biol., 50 (2005), 2365. doi: 10.1088/0031-9155/50/10/013.

[45]

A. Seppanen, A. Voutilainen and J. P. Kaipio, State estimation in process tomography - reconstruction of velocity fields using eit,, Inv. Probl., 25 (2009). doi: 10.1088/0266-5611/25/8/085009.

[46]

H. Shih and V. Ntziachristos, In vivo characterization of Her-2/neu carcinogenesis in mice using fluorescence molecular tomography,, Proc. Biomed. Opt., (2006). doi: 10.1364/BIO.2006.TuC1.

[47]

M. Solomon, B. R. White, R. E. Nothdruft, W. Akers, G. Sudlow, A. T. Eggebrecht, S. Achilefu and J. P. Culver, Video-rate fluorescence diffuse optical tomography for in vivo sentinel lymph node imaging,, Biomed. Opt. Express, 2 (2011), 3267. doi: 10.1364/BOE.2.003267.

[48]

V. Y. Soloviev, C. D'Andrea, G. Valentini, R. Cubeddu and S. R. Arridge, Combined reconstruction of fluorescent and optical parameters using time-resolved data,, Appl. Opt., 48 (2009), 28. doi: 10.1364/AO.48.000028.

[49]

Y. Tan and H. Jiang, Diffuse optical tomography guided quantitative fluorescence molecular tomography,, Appl. Opt., 47 (2008), 2011. doi: 10.1364/AO.47.002011.

[50]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. R. Arridge and J. P. Kaipio, An approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,, Inv. Probl., 26 (2010). doi: 10.1088/0266-5611/26/1/015005.

[51]

S. V. D. Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. V. D. Voort, R. Nachabe, M. Mark, M. Beek, L. Bakker, L. Fels, S. Elias, P. Luijten and W. Mali, A novel fluorescent imaging agent for diffuse optical tomography of the breast: First clinical experience in patients,, Mol. Imag. Biol., 12 (2010), 343.

[1]

Herbert Egger, Manuel Freiberger, Matthias Schlottbom. On forward and inverse models in fluorescence diffuse optical tomography. Inverse Problems & Imaging, 2010, 4 (3) : 411-427. doi: 10.3934/ipi.2010.4.411

[2]

Shui-Nee Chow, Ke Yin, Hao-Min Zhou, Ali Behrooz. Solving inverse source problems by the Orthogonal Solution and Kernel Correction Algorithm (OSKCA) with applications in fluorescence tomography. Inverse Problems & Imaging, 2014, 8 (1) : 79-102. doi: 10.3934/ipi.2014.8.79

[3]

Tim Kreutzmann, Andreas Rieder. Geometric reconstruction in bioluminescence tomography. Inverse Problems & Imaging, 2014, 8 (1) : 173-197. doi: 10.3934/ipi.2014.8.173

[4]

Lacramioara Grecu, Constantin Popa. Constrained SART algorithm for inverse problems in image reconstruction. Inverse Problems & Imaging, 2013, 7 (1) : 199-216. doi: 10.3934/ipi.2013.7.199

[5]

Adriana González, Laurent Jacques, Christophe De Vleeschouwer, Philippe Antoine. Compressive optical deflectometric tomography: A constrained total-variation minimization approach. Inverse Problems & Imaging, 2014, 8 (2) : 421-457. doi: 10.3934/ipi.2014.8.421

[6]

Daniela Calvetti, Paul J. Hadwin, Janne M. J. Huttunen, Jari P. Kaipio, Erkki Somersalo. Artificial boundary conditions and domain truncation in electrical impedance tomography. Part II: Stochastic extension of the boundary map. Inverse Problems & Imaging, 2015, 9 (3) : 767-789. doi: 10.3934/ipi.2015.9.767

[7]

Daniela Calvetti, Paul J. Hadwin, Janne M. J. Huttunen, David Isaacson, Jari P. Kaipio, Debra McGivney, Erkki Somersalo, Joseph Volzer. Artificial boundary conditions and domain truncation in electrical impedance tomography. Part I: Theory and preliminary results. Inverse Problems & Imaging, 2015, 9 (3) : 749-766. doi: 10.3934/ipi.2015.9.749

[8]

Masoumeh Dashti, Stephen Harris, Andrew Stuart. Besov priors for Bayesian inverse problems. Inverse Problems & Imaging, 2012, 6 (2) : 183-200. doi: 10.3934/ipi.2012.6.183

[9]

Hiroshi Isozaki. Inverse boundary value problems in the horosphere - A link between hyperbolic geometry and electrical impedance tomography. Inverse Problems & Imaging, 2007, 1 (1) : 107-134. doi: 10.3934/ipi.2007.1.107

[10]

Tan Bui-Thanh, Quoc P. Nguyen. FEM-based discretization-invariant MCMC methods for PDE-constrained Bayesian inverse problems. Inverse Problems & Imaging, 2016, 10 (4) : 943-975. doi: 10.3934/ipi.2016028

[11]

Leonid Kunyansky. Fast reconstruction algorithms for the thermoacoustic tomography in certain domains with cylindrical or spherical symmetries. Inverse Problems & Imaging, 2012, 6 (1) : 111-131. doi: 10.3934/ipi.2012.6.111

[12]

Guillaume Bal, Ian Langmore, Youssef Marzouk. Bayesian inverse problems with Monte Carlo forward models. Inverse Problems & Imaging, 2013, 7 (1) : 81-105. doi: 10.3934/ipi.2013.7.81

[13]

Lassi Roininen, Janne M. J. Huttunen, Sari Lasanen. Whittle-Matérn priors for Bayesian statistical inversion with applications in electrical impedance tomography. Inverse Problems & Imaging, 2014, 8 (2) : 561-586. doi: 10.3934/ipi.2014.8.561

[14]

Henrik Garde, Kim Knudsen. 3D reconstruction for partial data electrical impedance tomography using a sparsity prior. Conference Publications, 2015, 2015 (special) : 495-504. doi: 10.3934/proc.2015.0495

[15]

Tan Bui-Thanh, Omar Ghattas. A scalable algorithm for MAP estimators in Bayesian inverse problems with Besov priors. Inverse Problems & Imaging, 2015, 9 (1) : 27-53. doi: 10.3934/ipi.2015.9.27

[16]

Kui Lin, Shuai Lu, Peter Mathé. Oracle-type posterior contraction rates in Bayesian inverse problems. Inverse Problems & Imaging, 2015, 9 (3) : 895-915. doi: 10.3934/ipi.2015.9.895

[17]

Mila Nikolova. Model distortions in Bayesian MAP reconstruction. Inverse Problems & Imaging, 2007, 1 (2) : 399-422. doi: 10.3934/ipi.2007.1.399

[18]

Plamen Stefanov, Wenxiang Cong, Ge Wang. Modulated luminescence tomography. Inverse Problems & Imaging, 2015, 9 (2) : 579-589. doi: 10.3934/ipi.2015.9.579

[19]

Fabrice Delbary, Rainer Kress. Electrical impedance tomography using a point electrode inverse scheme for complete electrode data. Inverse Problems & Imaging, 2011, 5 (2) : 355-369. doi: 10.3934/ipi.2011.5.355

[20]

Martin Hanke, William Rundell. On rational approximation methods for inverse source problems. Inverse Problems & Imaging, 2011, 5 (1) : 185-202. doi: 10.3934/ipi.2011.5.185

2016 Impact Factor: 1.094

Metrics

  • PDF downloads (2)
  • HTML views (0)
  • Cited by (1)

[Back to Top]