Abstract

Fluorescent molecular tomographic image reconstruction usually involves repeatedly solving large-scale matrix equations, which are computationally expensive. In this paper, a method is proposed to reduce the scale of the matrix system. The Jacobian matrix is simplified by deleting the columns or the rows whose values are smaller than a threshold. Furthermore, the measurement data are divided into two groups and are used for iteration of image reconstruction in turn. The simplified system is then solved in the wavelet domain to further accelerate the process of solving the inverse problem. Simulation results demonstrate that the proposed method can significantly speed up the reconstruction process.

© 2013 Optical Society of America

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References

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  1. Z. Xue, D. Han, and J. Tian, “Fast and robust reconstruction approach for sparse fluorescence tomography based on adaptive matching pursuit,” Proc. SPIE 8311, 831107 (2011).
    [CrossRef]
  2. M. Hassan and B. A. Klaunberg, “Biomedical applications of fluorescence imaging in vivo,” Comput. Med. 54, 635–644 (2004).
  3. V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8, 1–33 (2006).
    [CrossRef]
  4. F. Fedele, J. P. Laible, and M. J. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187, 597–619 (2003).
    [CrossRef]
  5. G. Zacharakis, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Fluorescent protein tomography scanner for small animal imaging,” IEEE Trans. Med. Imaging 24, 878–885 (2005).
    [CrossRef]
  6. X. Liu, X. Guo, F. Liu, Y. Zhang, H. Zhang, G. Hu, and J. Bai, “Imaging of indocyanine green perfusion in mouse liver with fluorescence diffuse optical tomography,” IEEE Trans. Biomed. Eng. 58, 2139–2143 (2011).
    [CrossRef]
  7. J. Haller, D. Hyde, N. Deliolanis, R. Kleine, M. Niedre, and V. Ntziachristos, “Visualization of pulmonary inflammation using noninvasive fluorescence molecular imaging,” J. Appl. Physiol. 104, 795–802 (2008).
    [CrossRef]
  8. 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. USA 101, 12294–12299 (2004).
    [CrossRef]
  9. A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh, “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Opt. Express 15, 6696–6716 (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. 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]
  17. M. J. Eppstein, F. Fedele, J. Laible, C. Zhang, A. Godavarty, and E. M. Sevick-Muraca, “A comparison of exact and approximate adjoint sensitivities in fluorescence tomography,” IEEE Trans. Med. Imaging 22, 1215–1223 (2003).
    [CrossRef]
  18. N. Ducros, “A time-domain wavelet-based approach for fluorescence diffuse optical tomography,” Med. Phys. 37, 2890–2900 (2010).
    [CrossRef]
  19. N. Ducros, C. D’andrea, G. Valentini, T. Rudge, S. Arridge, and A. Bassi, “Full-wavelet approach for fluorescence diffuse optical tomography with structured illumination,” Opt. Lett. 35, 3676–3678 (2010).
    [CrossRef]
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  21. L. Li and L. Qu, “Haar wavelet transform for gear fault diagnosis,” Auto. Eng. 25, 510–513 (2003).

2012 (1)

2011 (2)

Z. Xue, D. Han, and J. Tian, “Fast and robust reconstruction approach for sparse fluorescence tomography based on adaptive matching pursuit,” Proc. SPIE 8311, 831107 (2011).
[CrossRef]

X. Liu, X. Guo, F. Liu, Y. Zhang, H. Zhang, G. Hu, and J. Bai, “Imaging of indocyanine green perfusion in mouse liver with fluorescence diffuse optical tomography,” IEEE Trans. Biomed. Eng. 58, 2139–2143 (2011).
[CrossRef]

2010 (2)

2009 (2)

2008 (1)

J. Haller, D. Hyde, N. Deliolanis, R. Kleine, M. Niedre, and V. Ntziachristos, “Visualization of pulmonary inflammation using noninvasive fluorescence molecular imaging,” J. Appl. Physiol. 104, 795–802 (2008).
[CrossRef]

2007 (1)

2006 (1)

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

2005 (2)

G. Zacharakis, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Fluorescent protein tomography scanner for small animal imaging,” IEEE Trans. Med. Imaging 24, 878–885 (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]

2004 (2)

M. Hassan and B. A. Klaunberg, “Biomedical applications of fluorescence imaging in vivo,” Comput. Med. 54, 635–644 (2004).

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. USA 101, 12294–12299 (2004).
[CrossRef]

2003 (4)

F. Fedele, J. P. Laible, and M. J. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187, 597–619 (2003).
[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]

M. J. Eppstein, F. Fedele, J. Laible, C. Zhang, A. Godavarty, and E. M. Sevick-Muraca, “A comparison of exact and approximate adjoint sensitivities in fluorescence tomography,” IEEE Trans. Med. Imaging 22, 1215–1223 (2003).
[CrossRef]

L. Li and L. Qu, “Haar wavelet transform for gear fault diagnosis,” Auto. Eng. 25, 510–513 (2003).

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R49 (1999).
[CrossRef]

1989 (1)

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. 11, 674–693 (1989).
[CrossRef]

Arridge, S.

Arridge, S. R.

A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh, “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Opt. Express 15, 6696–6716 (2007).
[CrossRef]

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

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R49 (1999).
[CrossRef]

S. R. Arridge and M. Schweiger, “A general framework for iterative reconstruction algorithms in optical tomography using a finite element method,” in Computational Radiology and Imaging: Therapy and Diagnosis, IMA Volumes in Mathematics and Its Applications (Springer, 1998).

Bai, J.

X. Liu, X. Guo, F. Liu, Y. Zhang, H. Zhang, G. Hu, and J. Bai, “Imaging of indocyanine green perfusion in mouse liver with fluorescence diffuse optical tomography,” IEEE Trans. Biomed. Eng. 58, 2139–2143 (2011).
[CrossRef]

Bassi, A.

Bianco, S. D.

Bogdanov, A.

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. USA 101, 12294–12299 (2004).
[CrossRef]

Choe, R.

Corlu, A.

Cummer, S. A.

D’andrea, C.

Deliolanis, N.

J. Haller, D. Hyde, N. Deliolanis, R. Kleine, M. Niedre, and V. Ntziachristos, “Visualization of pulmonary inflammation using noninvasive fluorescence molecular imaging,” J. Appl. Physiol. 104, 795–802 (2008).
[CrossRef]

Dinten, J. M.

Ducros, N.

Durduran, T.

Eppstein, M. J.

M. J. Eppstein, F. Fedele, J. Laible, C. Zhang, A. Godavarty, and E. M. Sevick-Muraca, “A comparison of exact and approximate adjoint sensitivities in fluorescence tomography,” IEEE Trans. Med. Imaging 22, 1215–1223 (2003).
[CrossRef]

F. Fedele, J. P. Laible, and M. J. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187, 597–619 (2003).
[CrossRef]

Fedele, F.

F. Fedele, J. P. Laible, and M. J. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187, 597–619 (2003).
[CrossRef]

M. J. Eppstein, F. Fedele, J. Laible, C. Zhang, A. Godavarty, and E. M. Sevick-Muraca, “A comparison of exact and approximate adjoint sensitivities in fluorescence tomography,” IEEE Trans. Med. Imaging 22, 1215–1223 (2003).
[CrossRef]

Frassati, A. L.

Georges, D.

Gibson, A. P.

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

Godavarty, A.

M. J. Eppstein, F. Fedele, J. Laible, C. Zhang, A. Godavarty, and E. M. Sevick-Muraca, “A comparison of exact and approximate adjoint sensitivities in fluorescence tomography,” IEEE Trans. Med. Imaging 22, 1215–1223 (2003).
[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]

Graves, E.

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. USA 101, 12294–12299 (2004).
[CrossRef]

Guo, X.

X. Liu, X. Guo, F. Liu, Y. Zhang, H. Zhang, G. Hu, and J. Bai, “Imaging of indocyanine green perfusion in mouse liver with fluorescence diffuse optical tomography,” IEEE Trans. Biomed. Eng. 58, 2139–2143 (2011).
[CrossRef]

Haller, J.

J. Haller, D. Hyde, N. Deliolanis, R. Kleine, M. Niedre, and V. Ntziachristos, “Visualization of pulmonary inflammation using noninvasive fluorescence molecular imaging,” J. Appl. Physiol. 104, 795–802 (2008).
[CrossRef]

Han, D.

Z. Xue, D. Han, and J. Tian, “Fast and robust reconstruction approach for sparse fluorescence tomography based on adaptive matching pursuit,” Proc. SPIE 8311, 831107 (2011).
[CrossRef]

Hassan, M.

M. Hassan and B. A. Klaunberg, “Biomedical applications of fluorescence imaging in vivo,” Comput. Med. 54, 635–644 (2004).

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]

Hu, G.

X. Liu, X. Guo, F. Liu, Y. Zhang, H. Zhang, G. Hu, and J. Bai, “Imaging of indocyanine green perfusion in mouse liver with fluorescence diffuse optical tomography,” IEEE Trans. Biomed. Eng. 58, 2139–2143 (2011).
[CrossRef]

Hyde, D.

J. Haller, D. Hyde, N. Deliolanis, R. Kleine, M. Niedre, and V. Ntziachristos, “Visualization of pulmonary inflammation using noninvasive fluorescence molecular imaging,” J. Appl. Physiol. 104, 795–802 (2008).
[CrossRef]

Josephson, L.

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. USA 101, 12294–12299 (2004).
[CrossRef]

Klaunberg, B. A.

M. Hassan and B. A. Klaunberg, “Biomedical applications of fluorescence imaging in vivo,” Comput. Med. 54, 635–644 (2004).

Kleine, R.

J. Haller, D. Hyde, N. Deliolanis, R. Kleine, M. Niedre, and V. Ntziachristos, “Visualization of pulmonary inflammation using noninvasive fluorescence molecular imaging,” J. Appl. Physiol. 104, 795–802 (2008).
[CrossRef]

Laible, J.

M. J. Eppstein, F. Fedele, J. Laible, C. Zhang, A. Godavarty, and E. M. Sevick-Muraca, “A comparison of exact and approximate adjoint sensitivities in fluorescence tomography,” IEEE Trans. Med. Imaging 22, 1215–1223 (2003).
[CrossRef]

Laible, J. P.

F. Fedele, J. P. Laible, and M. J. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187, 597–619 (2003).
[CrossRef]

Li, L.

L. Li and L. Qu, “Haar wavelet transform for gear fault diagnosis,” Auto. Eng. 25, 510–513 (2003).

Liu, F.

X. Liu, X. Guo, F. Liu, Y. Zhang, H. Zhang, G. Hu, and J. Bai, “Imaging of indocyanine green perfusion in mouse liver with fluorescence diffuse optical tomography,” IEEE Trans. Biomed. Eng. 58, 2139–2143 (2011).
[CrossRef]

Liu, X.

X. Liu, X. Guo, F. Liu, Y. Zhang, H. Zhang, G. Hu, and J. Bai, “Imaging of indocyanine green perfusion in mouse liver with fluorescence diffuse optical tomography,” IEEE Trans. Biomed. Eng. 58, 2139–2143 (2011).
[CrossRef]

Mallat, S. G.

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. 11, 674–693 (1989).
[CrossRef]

Martelli, F.

Niedre, M.

J. Haller, D. Hyde, N. Deliolanis, R. Kleine, M. Niedre, and V. Ntziachristos, “Visualization of pulmonary inflammation using noninvasive fluorescence molecular imaging,” J. Appl. Physiol. 104, 795–802 (2008).
[CrossRef]

Ninni, P. D.

Ntziachristos, V.

J. Haller, D. Hyde, N. Deliolanis, R. Kleine, M. Niedre, and V. Ntziachristos, “Visualization of pulmonary inflammation using noninvasive fluorescence molecular imaging,” J. Appl. Physiol. 104, 795–802 (2008).
[CrossRef]

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

G. Zacharakis, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Fluorescent protein tomography scanner for small animal imaging,” IEEE Trans. Med. Imaging 24, 878–885 (2005).
[CrossRef]

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. USA 101, 12294–12299 (2004).
[CrossRef]

Qu, L.

L. Li and L. Qu, “Haar wavelet transform for gear fault diagnosis,” Auto. Eng. 25, 510–513 (2003).

Ripoll, J.

G. Zacharakis, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Fluorescent protein tomography scanner for small animal imaging,” IEEE Trans. Med. Imaging 24, 878–885 (2005).
[CrossRef]

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. USA 101, 12294–12299 (2004).
[CrossRef]

Rosen, M. A.

Roy, R.

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]

Rudge, T.

Schellenberger, E. A.

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. USA 101, 12294–12299 (2004).
[CrossRef]

Schnall, M. D.

Schweiger, M.

A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh, “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Opt. Express 15, 6696–6716 (2007).
[CrossRef]

S. R. Arridge and M. Schweiger, “A general framework for iterative reconstruction algorithms in optical tomography using a finite element method,” in Computational Radiology and Imaging: Therapy and Diagnosis, IMA Volumes in Mathematics and Its Applications (Springer, 1998).

Sevick-Muraca, E. M.

M. J. Eppstein, F. Fedele, J. Laible, C. Zhang, A. Godavarty, and E. M. Sevick-Muraca, “A comparison of exact and approximate adjoint sensitivities in fluorescence tomography,” IEEE Trans. Med. Imaging 22, 1215–1223 (2003).
[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]

Silva, A. D.

Tian, J.

Z. Xue, D. Han, and J. Tian, “Fast and robust reconstruction approach for sparse fluorescence tomography based on adaptive matching pursuit,” Proc. SPIE 8311, 831107 (2011).
[CrossRef]

Valentini, G.

Weissleder, R.

G. Zacharakis, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Fluorescent protein tomography scanner for small animal imaging,” IEEE Trans. Med. Imaging 24, 878–885 (2005).
[CrossRef]

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. USA 101, 12294–12299 (2004).
[CrossRef]

Xue, Z.

Z. Xue, D. Han, and J. Tian, “Fast and robust reconstruction approach for sparse fluorescence tomography based on adaptive matching pursuit,” Proc. SPIE 8311, 831107 (2011).
[CrossRef]

Yessayan, D.

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. USA 101, 12294–12299 (2004).
[CrossRef]

Yodh, A. G.

Zacharakis, G.

G. Zacharakis, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Fluorescent protein tomography scanner for small animal imaging,” IEEE Trans. Med. Imaging 24, 878–885 (2005).
[CrossRef]

Zhai, Y.

Zhang, C.

M. J. Eppstein, F. Fedele, J. Laible, C. Zhang, A. Godavarty, and E. M. Sevick-Muraca, “A comparison of exact and approximate adjoint sensitivities in fluorescence tomography,” IEEE Trans. Med. Imaging 22, 1215–1223 (2003).
[CrossRef]

Zhang, H.

X. Liu, X. Guo, F. Liu, Y. Zhang, H. Zhang, G. Hu, and J. Bai, “Imaging of indocyanine green perfusion in mouse liver with fluorescence diffuse optical tomography,” IEEE Trans. Biomed. Eng. 58, 2139–2143 (2011).
[CrossRef]

Zhang, Y.

X. Liu, X. Guo, F. Liu, Y. Zhang, H. Zhang, G. Hu, and J. Bai, “Imaging of indocyanine green perfusion in mouse liver with fluorescence diffuse optical tomography,” IEEE Trans. Biomed. Eng. 58, 2139–2143 (2011).
[CrossRef]

Annu. Rev. Biomed. Eng. (1)

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

Appl. Opt. (1)

Auto. Eng. (1)

L. Li and L. Qu, “Haar wavelet transform for gear fault diagnosis,” Auto. Eng. 25, 510–513 (2003).

Biomed. Opt. Express (1)

Comput. Med. (1)

M. Hassan and B. A. Klaunberg, “Biomedical applications of fluorescence imaging in vivo,” Comput. Med. 54, 635–644 (2004).

IEEE Trans. Biomed. Eng. (1)

X. Liu, X. Guo, F. Liu, Y. Zhang, H. Zhang, G. Hu, and J. Bai, “Imaging of indocyanine green perfusion in mouse liver with fluorescence diffuse optical tomography,” IEEE Trans. Biomed. Eng. 58, 2139–2143 (2011).
[CrossRef]

IEEE Trans. Med. Imaging (3)

G. Zacharakis, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Fluorescent protein tomography scanner for small animal imaging,” IEEE Trans. Med. Imaging 24, 878–885 (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]

M. J. Eppstein, F. Fedele, J. Laible, C. Zhang, A. Godavarty, and E. M. Sevick-Muraca, “A comparison of exact and approximate adjoint sensitivities in fluorescence tomography,” IEEE Trans. Med. Imaging 22, 1215–1223 (2003).
[CrossRef]

IEEE Trans. Pattern Anal. (1)

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. 11, 674–693 (1989).
[CrossRef]

Inverse Probl. (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R49 (1999).
[CrossRef]

J. Appl. Physiol. (1)

J. Haller, D. Hyde, N. Deliolanis, R. Kleine, M. Niedre, and V. Ntziachristos, “Visualization of pulmonary inflammation using noninvasive fluorescence molecular imaging,” J. Appl. Physiol. 104, 795–802 (2008).
[CrossRef]

J. Comput. Phys. (1)

F. Fedele, J. P. Laible, and M. J. Eppstein, “Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: theory and vectorized implementation,” J. Comput. Phys. 187, 597–619 (2003).
[CrossRef]

Med. Phys. (1)

N. Ducros, “A time-domain wavelet-based approach for fluorescence diffuse optical tomography,” Med. Phys. 37, 2890–2900 (2010).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Med. Biol. (1)

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

Proc. Natl. Acad. Sci. USA (1)

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. USA 101, 12294–12299 (2004).
[CrossRef]

Proc. SPIE (1)

Z. Xue, D. Han, and J. Tian, “Fast and robust reconstruction approach for sparse fluorescence tomography based on adaptive matching pursuit,” Proc. SPIE 8311, 831107 (2011).
[CrossRef]

Other (1)

S. R. Arridge and M. Schweiger, “A general framework for iterative reconstruction algorithms in optical tomography using a finite element method,” in Computational Radiology and Imaging: Therapy and Diagnosis, IMA Volumes in Mathematics and Its Applications (Springer, 1998).

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Figures (14)

Fig. 1.
Fig. 1.

Scheme of the iteration method based on grouped measurement data: (a) measurement data without grouping, (b) measurement data of red group, and (c) measurement data of black group.

Fig. 2.
Fig. 2.

Simulated phantoms for reconstruction of FMT (a) with one anomaly and (b) with two anomalies.

Fig. 3.
Fig. 3.

Prior images used for (a) one-anomaly phantom and (b) two-anomaly phantom.

Fig. 4.
Fig. 4.

Adaptively refined meshes for reconstruction of FMT for (a) one-anomaly phantom and (b) two-anomaly phantom.

Fig. 5.
Fig. 5.

Distributions of SUMs and PROPORTIONs.

Fig. 6.
Fig. 6.

Reconstructed results of absorption coefficient μaef (a) without the condition for PROPORTION and (b) with the condition for PROPORTION.

Fig. 7.
Fig. 7.

Reconstructed results of absorption coefficient μaef for phantom with one anomaly based on (a) method without simplified matrix system and (b) proposed method.

Fig. 8.
Fig. 8.

Reconstructed results of absorption coefficient μaef for phantom with two anomalies based on (a) method without simplified matrix system and (b) proposed method.

Fig. 9.
Fig. 9.

Reconstructed results of absorption coefficient μaef based on (a) simplification of the Jacobian matrix, (b) combined simplification of the Jacobian matrix and grouped measurement data, and (c) proposed algorithm.

Fig. 10.
Fig. 10.

Reconstructed results of absorption coefficient μaef for phantom of two anomalies with the value of c being (a) 0.05, (b) 0.1, and (c) 0.2, respectively.

Fig. 11.
Fig. 11.

Simulated phantom for 3D reconstruction. The phantom of radius 10 mm and height 40 mm with a uniform background of μaef=0.005mm1, which is positioned at x=10mm, y=0mm, and z=20mm. The small cylindrical anomaly has a radius of 2 mm and height 6 mm with μaef=0.01mm1.The anomaly is positioned at x=5mm, y=0mm, and z=20mm. The dashed curves represent the measurement planes, at z=15mm, z=20mm, z=25mm.

Fig. 12.
Fig. 12.

3D mesh for image reconstruction.

Fig. 13.
Fig. 13.

Reconstructed images using the proposed algorithm, which are 2D cross sections through the reconstructed 3D volume. The right-hand side corresponds to the top of the cylinder (z=40mm) and the left corresponds to the bottom of the cylinder (z=0mm), with each slice representing a 10 mm increment.

Fig. 14.
Fig. 14.

Reconstructed images using the method without simplified matrix system, which are 2D cross sections through the reconstructed 3D volume. The right-hand side corresponds to the top of the cylinder (z=40mm), and the left corresponds to the bottom of the cylinder (z=0mm), with each slice representing a 10 mm increment.

Tables (7)

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Table 1. Optical and Fluorescent Properties of One-Anomaly Phantom

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Table 2. Optical and Fluorescent Properties of Two-Anomaly Phantom

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Table 3. Performance Comparison of Reconstruction Methods for Phantom with One Anomaly

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Table 4. Performance Comparison of Reconstruction Methods for Phantom with Two Anomalies

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Table 5. Performance Comparison of Reconstruction Methods for Three Techniques

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Table 6. Impact of the Threshold on the Reconstruction for Phantom with Two Anomalies

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Table 7. Performance Comparison of 3D Reconstruction Methods

Equations (40)

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·(DeΦe)+keΦe=Qe,
·(DmΦm)+kmΦm=ϕμaef1iωτΦe,
ke,m=μae,mi+μae,mf+iωc,
De,m=13(μae,mi+μae,mf+μse,m)
AeΦe=Qe,
AmΦm=Qm.
x=F1(y),
Δx=(JTJ+λI)1JTΔy,
J=[y1x1y1xNyMx1yMxN].
SUM=i=1M|Jij|<a,
j=1N|Jij|<a.
PROPORTION=maxi=1M|Jij|i=1M|Jij|<k.
KΔx=b
K^Δx^=b^,
Δx^N×1=[A1ΔxN/2×1D1ΔxN/2×1],b^N×1=[A1bN/2×1D1bN/2×1].
K^N×N=[A1KN/2×N/2D11KN/2×N/2D12KN/2×N/2D13KN/2×N/2].
ψ(x)=12(yF(x))T(yF(x)),
MSE=i=1N{1N(xcalxact)i2},
a=c×i=1Mj=1N|Jij|,
Δx=(Δx1Δx2ΔxiΔxN)T(ΔxRN)
J=(J1J2JiJN)(JRM×N)
[(J1TJ2TJiTJNT)·(J1J2JiJN)+λI]·(Δx1Δx2ΔxiΔxN)=(J1TJ2TJiTJNT)·Δy.
(J1TJ1+λJ1TJ2J1TJiJ1TJNJ2TJ1J2TJ2+λJ2TJiJ2TJNJiTJ1JiTJ2JiTJi+λJiTJNJNTJ1JNTJ2JNTJiJNTJN+λ)·(Δx1Δx2ΔxiΔxN)=(J1T·ΔyJ2T·ΔyJiT·ΔyJNT·Δy),
(JiTJ1JiTJ2JiTJi+λJiTJN)·Δx=JiT·Δy.
Δxi=JiT(ΔyΔx1J1Δx2J2Δxi1Ji1Δxi+1Ji+1ΔxNJN)JiTJi+λ.
limJi0Δxi=limJi0JiT(ΔyΔx1J1Δx2J2Δxi1Ji1Δxi+1Ji+1ΔxNJN)JiTJi+λ=0.
(J1TJΔxJ2TJΔxJiTJΔxJNTJΔx)+λI·(Δx1Δx2ΔxiΔxN)=(J1TΔyJ2TΔyJiTΔyJNTΔy).
limJi0[(J1TJΔxJ2TJΔxJiTJΔxJNTJΔx)+λI·(Δx1Δx2ΔxiΔxN)]=limJi0(J1TΔyJ2TΔyJiTΔyJNTΔy).
limJi0[(J1TJΔxJ2TJΔxJi1TJΔx0Ji+1TJΔxJNTJΔx)+λI·(Δx1Δx2Δxi10Δxi+1ΔxN)]=limJi0(J1TΔyJ2TΔyJi1TΔy0Ji+1TΔyJNTΔy).
limJi0[(J1TJΔxJ2TJΔxJi1TJΔxJi+1TJΔxJNTJΔx)+λI·(Δx1Δx2Δxi1Δxi+1ΔxN)]=limJi0(J1TΔyJ2TΔyJi1TΔyJi+1TΔyJNTΔy).
limJi0[(J1TJ2TJi1TJi+1TJNT)·(J1Δx1+J2Δx2++JiΔxi+JNΔxN)+λI·(Δx1Δx2Δxi1Δxi+1ΔxN)]=limJi0(J1TΔyJ2TΔyJi1TΔyJi+1TΔyJNTΔy).
limJi0[(J1TJ2TJi1TJi+1TJNT)(J1Δx1+J2Δx2++Ji1Δxi1+Ji+1Δxi+1JNΔxN)+λI·(Δx1Δx2Δxi1Δxi+1ΔxN)]=limJi0(J1TΔyJ2TΔyJi1TΔyJi+1TΔyJNTΔy).
limJi0[(J1TJ2TJi1TJi+1TJNT)·(J1J2Ji1Ji+1JN)+λI]·(Δx1Δx2Δxi1Δxi+1ΔxN)=limJi0(J1TJ2TJi1TJi+1TJNT)·Δy.
Δy=(Δy1Δy2ΔyiΔyM)T(ΔyRM)
J=(R1TR2TRiTRMT)T(JRM×N)
[(R1TR2TRiTRMT)·(R1R2RiRM)+λI]·Δx=(R1TR2TRiTRMT)·(Δy1Δy2ΔyiΔyM).
[(R1TR1+R2TR2+RiTRi+RMTRM)+λI]·Δx=Δy1R1T+Δy2R2T++ΔyiRiT+ΔyMRMT.
limRi0[(R1TR1+R2TR2+RiTRi+RMTRM)+λI]·Δx=limRi0(Δy1R1T+Δy2R2T++ΔyiRiT+ΔyMRMT).
limRi0[(R1TR1+R2TR2+Ri1TRi1+Ri+1TRi+1RMTRM)+λI]·Δx=limRi0(Δy1R1T+Δy2R2T++Δyi1Ri1T+Δyi+1Ri+1TΔyMRMT).
limRi0[(R1TR2TRi1TRi+1TRMT)·(R1R2Ri1Ri+1RM)+λI]·Δx=limRi0(R1TR2TRi1TRi+1TRMT)·(Δy1Δy2Δyi1Δyi+1ΔyM).

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