Abstract

A common difficulty for the traditional methods of fluorescent molecular tomographic (FMT) reconstruction is that only a small amount of measurements can be used to recover the image comprised of a large number of pixels. This difficulty not only leads to expensive computational cost but also likely results in an unstable solution prone to be affected by the noise in the measurement data. In this paper, we propose a region-based method for reducing the unknowns, where the target areas are determined by searching for the nearest neighbor nodes. In this method, the Hessian matrix of the second-order derivatives is incorporated to speed up the optimization process. An iteration strategy of multi-wavelength measurement is introduced to further improve the accuracy of inverse solutions. Simulation results demonstrate that the proposed approach can significantly speed up the reconstruction process and improve the image quality of FMT.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  26. C. Panagiotou, S. Somayajula, A. P. Gibson, M. Schweiger, R. M. Leahy, and S. R. Arridge, “Information theoretic regularization in diffuse optical tomography,” J. Opt. Soc. Am. A 26, 1277–1290 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]

2010 (1)

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[CrossRef]

2009 (6)

Y. Zhai and S. A. Cummer, “Fast tomographic reconstruction strategy for diffuse optical tomography,” Opt. Express 17, 5285–5297 (2009).
[CrossRef] [PubMed]

C. Panagiotou, S. Somayajula, A. P. Gibson, M. Schweiger, R. M. Leahy, and S. R. Arridge, “Information theoretic regularization in diffuse optical tomography,” J. Opt. Soc. Am. A 26, 1277–1290 (2009).
[CrossRef]

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 1–59 (2009).
[CrossRef]

S. Walrand, F. Jamar, and S. Pauwels, “Improved solution for ill-posed linear systems using a constrained optimization ruled by a penalty: evaluation in nuclear medicine tomography,” Inverse Probl. 25, 1–17 (2009).
[CrossRef]

C. Balas, “Review of biomedical optical imaging—a powerful, non-invasive, non-ionizing technology for improving in vivo diagnosis,” Meas. Sci. Technol. 20, 1–12 (2009).
[CrossRef]

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett. 94, 251107–251107-3 (2009).
[CrossRef]

2008 (1)

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

2007 (2)

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. Transf. 104, 24–39 (2007).
[CrossRef]

A. Adler, T. Dai, and W. R. B. Lionheart, “Temporal image reconstruction in electrical impedance tomography,” Physiol. Meas 28, S1–S11 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (7)

R. Roy, A. B. Thompson, A. Godavarty, and E. M. Sevick-Muraca, “Tomographic fluorescence imaging in tissue phantoms: a novel reconstruction algorithm and imaging geometry,” IEEE Trans. Med. Imaging 24, 137–154 (2005).
[CrossRef] [PubMed]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377–1386 (2005).
[CrossRef] [PubMed]

A. B. Milstein, K. J. Webb, and C. A. Bouman, “Estimation of kinetic model parameters in fluorescence optical diffusion tomography,” J. Opt. Soc. Am. A 22, 1357–1368 (2005).
[CrossRef]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef] [PubMed]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345 (2005).
[CrossRef]

F. Fedele, M. J. Eppstein, J. P. Laible, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence photon migration by the boundary element method,” J. Comput. Phys. 210, 1–24 (2005).
[CrossRef]

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

2004 (2)

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9, 1046–1062 (2004).
[CrossRef] [PubMed]

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12, 5402–5417 (2004).
[CrossRef] [PubMed]

2003 (2)

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media,” IEEE Trans. Med. Imaging 22, 824–836 (2003).
[CrossRef] [PubMed]

A. D. Klose and A. H. Hielscher, “Quasi-Newton methods in optical tomographic image reconstruction,” Inverse Probl. 19, 387–409 (2003).
[CrossRef]

2000 (1)

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model of the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

1999 (2)

M. E. Kilmer, E. L. Miller, D. A. Boas, D. H. Brooks, C. A. DiMarzio, and R. J. Gaudette, “Direct object localization and characterization from diffuse photon density wave data,”Proc SPIE 3597, 45–54 (1999).
[CrossRef]

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, and J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

1988 (1)

J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, Wiley Series in Probability and Statistics (Wiley, 1988).

Abdoulaev, G. S.

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9, 1046–1062 (2004).
[CrossRef] [PubMed]

Adler, A.

A. Adler, T. Dai, and W. R. B. Lionheart, “Temporal image reconstruction in electrical impedance tomography,” Physiol. Meas 28, S1–S11 (2007).
[CrossRef] [PubMed]

Ale, A.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[CrossRef]

Andersson-Engels, S.

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett. 94, 251107–251107-3 (2009).
[CrossRef]

Arridge, S. R.

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 1–59 (2009).
[CrossRef]

C. Panagiotou, S. Somayajula, A. P. Gibson, M. Schweiger, R. M. Leahy, and S. R. Arridge, “Information theoretic regularization in diffuse optical tomography,” J. Opt. Soc. Am. A 26, 1277–1290 (2009).
[CrossRef]

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

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

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model of the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, and J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

Axelsson, J.

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett. 94, 251107–251107-3 (2009).
[CrossRef]

Bading, J. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef] [PubMed]

Balas, C.

C. Balas, “Review of biomedical optical imaging—a powerful, non-invasive, non-ionizing technology for improving in vivo diagnosis,” Meas. Sci. Technol. 20, 1–12 (2009).
[CrossRef]

Bangerth, W.

Bluestone, A. Y.

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9, 1046–1062 (2004).
[CrossRef] [PubMed]

Boas, D. A.

M. E. Kilmer, E. L. Miller, D. A. Boas, D. H. Brooks, C. A. DiMarzio, and R. J. Gaudette, “Direct object localization and characterization from diffuse photon density wave data,”Proc SPIE 3597, 45–54 (1999).
[CrossRef]

Bouman, C. A.

Brooks, D. H.

M. E. Kilmer, E. L. Miller, D. A. Boas, D. H. Brooks, C. A. DiMarzio, and R. J. Gaudette, “Direct object localization and characterization from diffuse photon density wave data,”Proc SPIE 3597, 45–54 (1999).
[CrossRef]

Charette, A.

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. Transf. 104, 24–39 (2007).
[CrossRef]

Chaudhari, A. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef] [PubMed]

Cherry, S. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef] [PubMed]

Conti, P. S.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef] [PubMed]

Cummer, S. A.

Dai, T.

A. Adler, T. Dai, and W. R. B. Lionheart, “Temporal image reconstruction in electrical impedance tomography,” Physiol. Meas 28, S1–S11 (2007).
[CrossRef] [PubMed]

Darvas, F.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef] [PubMed]

Dehghani, H.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model of the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

DiMarzio, C. A.

M. E. Kilmer, E. L. Miller, D. A. Boas, D. H. Brooks, C. A. DiMarzio, and R. J. Gaudette, “Direct object localization and characterization from diffuse photon density wave data,”Proc SPIE 3597, 45–54 (1999).
[CrossRef]

Eppstein, M. J.

F. Fedele, M. J. Eppstein, J. P. Laible, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence photon migration by the boundary element method,” J. Comput. Phys. 210, 1–24 (2005).
[CrossRef]

Fedele, F.

F. Fedele, M. J. Eppstein, J. P. Laible, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence photon migration by the boundary element method,” J. Comput. Phys. 210, 1–24 (2005).
[CrossRef]

Freyer, M.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[CrossRef]

Gao, F.

Gaudette, R. J.

M. E. Kilmer, E. L. Miller, D. A. Boas, D. H. Brooks, C. A. DiMarzio, and R. J. Gaudette, “Direct object localization and characterization from diffuse photon density wave data,”Proc SPIE 3597, 45–54 (1999).
[CrossRef]

Gibson, A. P.

Godavarty, A.

R. Roy, A. B. Thompson, A. Godavarty, and E. M. Sevick-Muraca, “Tomographic fluorescence imaging in tissue phantoms: a novel reconstruction algorithm and imaging geometry,” IEEE Trans. Med. Imaging 24, 137–154 (2005).
[CrossRef] [PubMed]

F. Fedele, M. J. Eppstein, J. P. Laible, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence photon migration by the boundary element method,” J. Comput. Phys. 210, 1–24 (2005).
[CrossRef]

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media,” IEEE Trans. Med. Imaging 22, 824–836 (2003).
[CrossRef] [PubMed]

Hebden, J. C.

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

Hielscher, A. H.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345 (2005).
[CrossRef]

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9, 1046–1062 (2004).
[CrossRef] [PubMed]

A. D. Klose and A. H. Hielscher, “Quasi-Newton methods in optical tomographic image reconstruction,” Inverse Probl. 19, 387–409 (2003).
[CrossRef]

Jamar, F.

S. Walrand, F. Jamar, and S. Pauwels, “Improved solution for ill-posed linear systems using a constrained optimization ruled by a penalty: evaluation in nuclear medicine tomography,” Inverse Probl. 25, 1–17 (2009).
[CrossRef]

Joshi, A.

Kaipio, J. P.

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, and J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

Kilmer, M. E.

M. E. Kilmer, E. L. Miller, D. A. Boas, D. H. Brooks, C. A. DiMarzio, and R. J. Gaudette, “Direct object localization and characterization from diffuse photon density wave data,”Proc SPIE 3597, 45–54 (1999).
[CrossRef]

Kim, H. K.

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. Transf. 104, 24–39 (2007).
[CrossRef]

Klose, A. D.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345 (2005).
[CrossRef]

A. D. Klose and A. H. Hielscher, “Quasi-Newton methods in optical tomographic image reconstruction,” Inverse Probl. 19, 387–409 (2003).
[CrossRef]

Kolehmainen, V.

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, and J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

Laible, J. P.

F. Fedele, M. J. Eppstein, J. P. Laible, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence photon migration by the boundary element method,” J. Comput. Phys. 210, 1–24 (2005).
[CrossRef]

Lasker, J.

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9, 1046–1062 (2004).
[CrossRef] [PubMed]

Leahy, R. M.

C. Panagiotou, S. Somayajula, A. P. Gibson, M. Schweiger, R. M. Leahy, and S. R. Arridge, “Information theoretic regularization in diffuse optical tomography,” J. Opt. Soc. Am. A 26, 1277–1290 (2009).
[CrossRef]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef] [PubMed]

Lionheart, W. R. B.

A. Adler, T. Dai, and W. R. B. Lionheart, “Temporal image reconstruction in electrical impedance tomography,” Physiol. Meas 28, S1–S11 (2007).
[CrossRef] [PubMed]

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, and J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

Magnus, J. R.

J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, Wiley Series in Probability and Statistics (Wiley, 1988).

Miller, E. L.

M. E. Kilmer, E. L. Miller, D. A. Boas, D. H. Brooks, C. A. DiMarzio, and R. J. Gaudette, “Direct object localization and characterization from diffuse photon density wave data,”Proc SPIE 3597, 45–54 (1999).
[CrossRef]

Milstein, A. B.

Moats, R. A.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef] [PubMed]

Neudecker, H.

J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, Wiley Series in Probability and Statistics (Wiley, 1988).

Ntziachristos, V.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[CrossRef]

V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8, 1–33 (2006).
[CrossRef] [PubMed]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377–1386 (2005).
[CrossRef] [PubMed]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345 (2005).
[CrossRef]

Okada, E.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model of the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

Panagiotou, C.

Pauwels, S.

S. Walrand, F. Jamar, and S. Pauwels, “Improved solution for ill-posed linear systems using a constrained optimization ruled by a penalty: evaluation in nuclear medicine tomography,” Inverse Probl. 25, 1–17 (2009).
[CrossRef]

Ripoll, J.

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377–1386 (2005).
[CrossRef] [PubMed]

Roy, R.

R. Roy, A. B. Thompson, A. Godavarty, and E. M. Sevick-Muraca, “Tomographic fluorescence imaging in tissue phantoms: a novel reconstruction algorithm and imaging geometry,” IEEE Trans. Med. Imaging 24, 137–154 (2005).
[CrossRef] [PubMed]

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media,” IEEE Trans. Med. Imaging 22, 824–836 (2003).
[CrossRef] [PubMed]

Sarantopoulos, A.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[CrossRef]

Schotland, J. C.

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 1–59 (2009).
[CrossRef]

Schulz, R. B.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[CrossRef]

Schweiger, M.

C. Panagiotou, S. Somayajula, A. P. Gibson, M. Schweiger, R. M. Leahy, and S. R. Arridge, “Information theoretic regularization in diffuse optical tomography,” J. Opt. Soc. Am. A 26, 1277–1290 (2009).
[CrossRef]

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model of the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

Sevick-Muraca, E. M.

F. Fedele, M. J. Eppstein, J. P. Laible, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence photon migration by the boundary element method,” J. Comput. Phys. 210, 1–24 (2005).
[CrossRef]

R. Roy, A. B. Thompson, A. Godavarty, and E. M. Sevick-Muraca, “Tomographic fluorescence imaging in tissue phantoms: a novel reconstruction algorithm and imaging geometry,” IEEE Trans. Med. Imaging 24, 137–154 (2005).
[CrossRef] [PubMed]

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12, 5402–5417 (2004).
[CrossRef] [PubMed]

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media,” IEEE Trans. Med. Imaging 22, 824–836 (2003).
[CrossRef] [PubMed]

Smith, D. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef] [PubMed]

Soehngen, E.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[CrossRef]

Somayajula, S.

Soubret, A.

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377–1386 (2005).
[CrossRef] [PubMed]

Stewart, M.

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9, 1046–1062 (2004).
[CrossRef] [PubMed]

Tanikawa, Y.

Tarvainen, T.

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

Thompson, A. B.

R. Roy, A. B. Thompson, A. Godavarty, and E. M. Sevick-Muraca, “Tomographic fluorescence imaging in tissue phantoms: a novel reconstruction algorithm and imaging geometry,” IEEE Trans. Med. Imaging 24, 137–154 (2005).
[CrossRef] [PubMed]

Vauhkonen, M.

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

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, and J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

Walrand, S.

S. Walrand, F. Jamar, and S. Pauwels, “Improved solution for ill-posed linear systems using a constrained optimization ruled by a penalty: evaluation in nuclear medicine tomography,” Inverse Probl. 25, 1–17 (2009).
[CrossRef]

Webb, K. J.

Xu, C. T.

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett. 94, 251107–251107-3 (2009).
[CrossRef]

Yamada, Y.

Zhai, Y.

Zhao, H.

Zientkowska, M.

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[CrossRef]

Annu. Rev. Biomed. Eng. (1)

V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8, 1–33 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

C. T. Xu, J. Axelsson, and S. Andersson-Engels, “Fluorescence diffuse optical tomography using upconverting nanoparticles,” Appl. Phys. Lett. 94, 251107–251107-3 (2009).
[CrossRef]

IEEE Trans. Med. Imaging (4)

R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29, 465–473 (2010).
[CrossRef]

R. Roy, A. B. Thompson, A. Godavarty, and E. M. Sevick-Muraca, “Tomographic fluorescence imaging in tissue phantoms: a novel reconstruction algorithm and imaging geometry,” IEEE Trans. Med. Imaging 24, 137–154 (2005).
[CrossRef] [PubMed]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377–1386 (2005).
[CrossRef] [PubMed]

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media,” IEEE Trans. Med. Imaging 22, 824–836 (2003).
[CrossRef] [PubMed]

Inverse Probl. (4)

S. Walrand, F. Jamar, and S. Pauwels, “Improved solution for ill-posed linear systems using a constrained optimization ruled by a penalty: evaluation in nuclear medicine tomography,” Inverse Probl. 25, 1–17 (2009).
[CrossRef]

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 1–59 (2009).
[CrossRef]

A. D. Klose and A. H. Hielscher, “Quasi-Newton methods in optical tomographic image reconstruction,” Inverse Probl. 19, 387–409 (2003).
[CrossRef]

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, and J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

J. Biomed. Opt. (1)

A. Y. Bluestone, M. Stewart, J. Lasker, G. S. Abdoulaev, A. H. Hielscher, “Three-dimensional optical tomographic brain imaging in small animals, part 1: hypercapnia,” J. Biomed. Opt. 9, 1046–1062 (2004).
[CrossRef] [PubMed]

J. Comput. Phys. (2)

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345 (2005).
[CrossRef]

F. Fedele, M. J. Eppstein, J. P. Laible, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence photon migration by the boundary element method,” J. Comput. Phys. 210, 1–24 (2005).
[CrossRef]

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

J. Quant. Spectrosc. Radiat. Transf. (2)

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. Transf. 104, 24–39 (2007).
[CrossRef]

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

Meas. Sci. Technol. (1)

C. Balas, “Review of biomedical optical imaging—a powerful, non-invasive, non-ionizing technology for improving in vivo diagnosis,” Meas. Sci. Technol. 20, 1–12 (2009).
[CrossRef]

Med. Phys. (1)

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model of the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef] [PubMed]

Opt. Express (3)

Phys. Med. Biol. (2)

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, “Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging,” Phys. Med. Biol. 50, 5421–5441 (2005).
[CrossRef] [PubMed]

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

Physiol. Meas (1)

A. Adler, T. Dai, and W. R. B. Lionheart, “Temporal image reconstruction in electrical impedance tomography,” Physiol. Meas 28, S1–S11 (2007).
[CrossRef] [PubMed]

Proc SPIE (1)

M. E. Kilmer, E. L. Miller, D. A. Boas, D. H. Brooks, C. A. DiMarzio, and R. J. Gaudette, “Direct object localization and characterization from diffuse photon density wave data,”Proc SPIE 3597, 45–54 (1999).
[CrossRef]

Other (1)

J. R. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, Wiley Series in Probability and Statistics (Wiley, 1988).

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Figures (12)

Fig. 1
Fig. 1

Schematic illustration of the process of target area growth. (a) Existing target nodes that have been found, (b) the nearest neighbor nodes of the existing target nodes, and (c) the candidate node with the minimum cost is attached as the target node.

Fig. 2
Fig. 2

Flow diagram for the multi-wavelength measurement scheme.

Fig. 3
Fig. 3

Simulated phantoms for FMT of single target phantom.

Fig. 4
Fig. 4

Model of prior image of single target phantom.

Fig. 5
Fig. 5

Adaptively refined grid of single target phantom.

Fig. 6
Fig. 6

Reconstructed image of absorption coefficient due to fluorophore μ a x f of single target phantom. (a) Proposed algorithm and (b) traditional method.

Fig. 7
Fig. 7

Reconstructed image of absorption coefficient due to fluorophore μ a x f of single target phantom. (a) With excitation light measurement, (b) with emission light measurement, and (c) with multi-wavelength measurement.

Fig. 8
Fig. 8

Simulated phantoms for FMT of double target phantom.

Fig. 9
Fig. 9

Model of prior image of double target phantom.

Fig. 10
Fig. 10

Adaptively refined grid of double target phantom.

Fig. 11
Fig. 11

Reconstructed image of absorption coefficient due to fluorophore μ a x f of double target phanton. (a) Proposed algorithm, and (b) traditional method.

Fig. 12
Fig. 12

Reconstructed image of absorption coefficient due to fluorophore μ a x f of double target phantom. (a) With excitation light measurement, (b) with emission light measurement, and (c) with multi-wavelength measurement.

Tables (7)

Tables Icon

Table 1 Optical and Fluorescent Properties of Single Target Phantom

Tables Icon

Table 2 Performance Comparison for Algorithms of Single Target Phantom

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Table 3 Performance Comparison for Reconstructed Results of Single Target Phantom Based on Different Kinds of Measurement

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Table 4 Optical and Fluorescent Properties of Double Target Phantom

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Table 5 Performance Comparison for Algorithms of Double Target Phantom

Tables Icon

Table 6 Performance Comparison for Reconstructed Results of Double Target Phantom Based on Different Kinds of Measurement

Tables Icon

Table 7 Impact of ε on the Reconstruction Process

Equations (25)

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

( D x Φ x ) + k x Φ x = S x on Ω ,
( D m Φ m ) + k m Φ m = S m = φ μ a x f 1 + i ω τ 1 + ( ω τ ) 2 Φ x on Ω .
D x , m = 1 3 ( μ a x , m i + μ a x , m f + μ s x , m ) ,
k x , m = i ω c + μ a x , m i + μ a x , m f ,
n ( D x Φ x ) + b x Φ x = 0 on Ω ,
n ( D m Φ m ) + b m Φ m = 0 on Ω ,
A x Φ x = S x ,
A m Φ m = S m ,
A i j = Ω D x , m ϕ i ϕ j d Ω + Ω k x , m ϕ i ϕ j d Ω + Ω b x , m ϕ i ϕ j d s ,
S i = Ω S x , m ϕ i d Ω .
y = F ( x ) ,
y = F ( x 0 ) + F ( x 0 ) ( x x 0 ) + 1 2 ! F ( x 0 ) ( x x 0 ) 2 + + 1 n ! F ( n ) ( x 0 ) ( x x 0 ) n + ,
y = F ( x 0 ) + F ( x 0 ) ( x x 0 ) .
Δ x = ( J T J + λ I ) 1 J T Δ y ,
Δ x = J T ( J J T + λ I ) 1 Δ y .
x = arg min x ψ ( x ) = y F ( x ) 2 + λ x 2 ,
ψ ( x + Δ x ) = ψ ( x ) + [ ψ ( x ) ] T Δ x + 1 2 Δ x T H Δ x ,
ψ ( x ) = [ ψ ( x ) x 1 ψ ( x ) x 2 ψ ( x ) x N ] T .
H = [ 2 ψ x 1 2 2 ψ x 1 x 2 2 ψ x 1 x N 2 ψ x 2 x 1 2 ψ x 2 2 2 ψ x 2 x N 2 ψ x N x 1 2 ψ x N x 2 2 ψ x N 2 ] .
H Δ x = ψ ( x ) .
b k = min i = 1 , 2 , , N p i c k ,
p i c k = ( x p i x c k ) 2 + ( y p i y c k ) 2 ,
D ( X ) = E { [ X E ( X ) ] 2 } ,
MSE = 1 N i = 1 N ( p ̃ i p i ) 2 ,
r i = ( p i p ̃ i ) p ̃ i × 100 % , i = 1 , 2 , , N ,

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