Abstract

Reconstruction in diffuse optical tomography (DOT) necessitates solving the diffusion equation, which is nonlinear with respect to the parameters that have to be reconstructed. Currently applied solving methods are based on the linearization of the equation. For spectral three-dimensional reconstruction, the emerging equation system is too large for direct inversion, but the application of iterative methods is feasible. Computational effort and speed of convergence of these iterative methods are crucial since they determine the computation time of the reconstruction. In this paper, the iterative methods algebraic reconstruction technique (ART) and conjugated gradients (CGs) as well as a new modified ART method are investigated for spectral DOT reconstruction. The aim of the modified ART scheme is to speed up the convergence by considering the specific conditions of spectral reconstruction. As a result, it converges much faster to favorable results than conventional ART and CG methods.

© 2008 Optical Society of America

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2007 (3)

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

B. Brendel and T. Nielsen, “Wavelength optimization in multispectral diffuse optical tomography considering uncertainties in absorption spectra,” Proc. SPIE 6629, 66290A (2007).
[CrossRef]

W. Bangerth, R. Hartmann, and G. Kanschat, “deal.II--a general-purpose object-oriented finite element library,” ACM Trans. Math. Softw. 33, 24 (2007).
[CrossRef]

2005 (4)

X. Wang, B. W. Pogue, S. Jiang, X. Song, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 0517041-0517048 (2005).
[CrossRef]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44, 2082-2093 (2005).
[CrossRef] [PubMed]

B. Brooksby, S. Srinivasan, S. Jiang, H. Deghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30, 1968-1970 (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]

2004 (2)

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29, 256-258 (2004).
[CrossRef] [PubMed]

B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

2003 (1)

2001 (2)

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420-4425 (2001).
[CrossRef] [PubMed]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry for finite-element image reconstruction,” Appl. Opt. 40, 588-600 (2001).
[CrossRef]

1999 (4)

S. B. Colak, M. B. van der Mark, G. W 't Hooft, J. H. Hoogenraad, E. S. van der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143-1158(1999).
[CrossRef]

M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699-1717 (1999).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, and P. M. Schlag, “Development of a time-domain optical mammograph and first in vivo applications,” Appl. Opt. 38, 2927-2943(1999).
[CrossRef]

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

1998 (1)

1993 (1)

S. R. Arridge and M. Schweiger, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef] [PubMed]

1988 (1)

Y. Censor, “Parallel application of block-iterative methods in medical imaging and radiation therapy,” Math. Program. 42, 307-325 (1988).
[CrossRef]

1981 (1)

Y. Censor, “Row-action methods for huge and sparse systems and their applications,” SIAM Rev. 23, 444-466 (1981).
[CrossRef]

Arridge, S. R.

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]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44, 2082-2093 (2005).
[CrossRef] [PubMed]

A. Corlu, T. Durduran, R. Choe, M. Schweiger, E. M. C. Hillman, S. R. Arridge, and A. G. Yodh, “Uniqueness and wavelength optimization in continuous-wave multispectral diffuse optical tomography,” Opt. Lett. 28, 2339-2341 (2003).
[CrossRef] [PubMed]

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

M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699-1717 (1999).
[CrossRef] [PubMed]

S. R. Arridge and W. R. B. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882-884(1998).
[CrossRef]

S. R. Arridge and M. Schweiger, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef] [PubMed]

Backer, L.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Bangerth, W.

W. Bangerth, R. Hartmann, and G. Kanschat, “deal.II--a general-purpose object-oriented finite element library,” ACM Trans. Math. Softw. 33, 24 (2007).
[CrossRef]

Barrett, R.

R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
[CrossRef]

Beek, M. v.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Berry, M.

R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
[CrossRef]

Boas, D. A.

Brendel, B.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

B. Brendel and T. Nielsen, “Wavelength optimization in multispectral diffuse optical tomography considering uncertainties in absorption spectra,” Proc. SPIE 6629, 66290A (2007).
[CrossRef]

Brooksby, B.

Butler, J.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420-4425 (2001).
[CrossRef] [PubMed]

Censor, Y.

Y. Censor, “Parallel application of block-iterative methods in medical imaging and radiation therapy,” Math. Program. 42, 307-325 (1988).
[CrossRef]

Y. Censor, “Row-action methods for huge and sparse systems and their applications,” SIAM Rev. 23, 444-466 (1981).
[CrossRef]

Cerussi, A.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420-4425 (2001).
[CrossRef] [PubMed]

Chan, T.

R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
[CrossRef]

Choe, R.

Colak, S. B.

S. B. Colak, M. B. van der Mark, G. W 't Hooft, J. H. Hoogenraad, E. S. van der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143-1158(1999).
[CrossRef]

Corlu, A.

Cubeddu, R.

R. L. P. van Veen, H. J. C. M. Sterenborg, A. Pifferi, A. Torricelli, and R. Cubeddu, “Determination of vis-NIR absorption coefficients of mammalian fat, with time- and spatially resolved diffuse reflectance and transmission spectroscopy,” in Proceedings of Biomedical Topical Meetings (Optical Society of America, 2004), no. SF-5 on CD-ROM.

Culver, J. P.

Deckers, S.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Deghani, H.

B. Brooksby, S. Srinivasan, S. Jiang, H. Deghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30, 1968-1970 (2005).
[CrossRef] [PubMed]

B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

Demmel, J.

R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
[CrossRef]

der Vorst, H. V.

R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
[CrossRef]

Donato, J.

R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
[CrossRef]

Dongarra, J.

R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
[CrossRef]

Durduran, T.

Eijkhout, V.

R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
[CrossRef]

Eker, C.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420-4425 (2001).
[CrossRef] [PubMed]

Espinoza, J.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420-4425 (2001).
[CrossRef] [PubMed]

Feuerabend, A.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Fishkin, J.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420-4425 (2001).
[CrossRef] [PubMed]

Geimer, S.

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] [PubMed]

Grosenick, D.

Habers, R.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Hartmann, R.

W. Bangerth, R. Hartmann, and G. Kanschat, “deal.II--a general-purpose object-oriented finite element library,” ACM Trans. Math. Softw. 33, 24 (2007).
[CrossRef]

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]

Hillman, E. M. C.

Hoogenraad, J. H.

S. B. Colak, M. B. van der Mark, G. W 't Hooft, J. H. Hoogenraad, E. S. van der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143-1158(1999).
[CrossRef]

Hornung, R.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420-4425 (2001).
[CrossRef] [PubMed]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Jiang, S.

B. Brooksby, S. Srinivasan, S. Jiang, H. Deghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30, 1968-1970 (2005).
[CrossRef] [PubMed]

X. Wang, B. W. Pogue, S. Jiang, X. Song, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 0517041-0517048 (2005).
[CrossRef]

B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry for finite-element image reconstruction,” Appl. Opt. 40, 588-600 (2001).
[CrossRef]

Kanschat, G.

W. Bangerth, R. Hartmann, and G. Kanschat, “deal.II--a general-purpose object-oriented finite element library,” ACM Trans. Math. Softw. 33, 24 (2007).
[CrossRef]

Kogel, C.

X. Wang, B. W. Pogue, S. Jiang, X. Song, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 0517041-0517048 (2005).
[CrossRef]

B. Brooksby, S. Srinivasan, S. Jiang, H. Deghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30, 1968-1970 (2005).
[CrossRef] [PubMed]

B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

Köhler, T.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Konecky, S. D.

K. Lee, R. Choe, A. Corlu, S. D. Konecky, T. Durduran, and A. G. Yodh, “Artifact reduction in CW transmission diffuse optical tomography,” presented at the OSA Biomedical Optics Topical Meeting, Florida, 2004.

Kuijpers, F. A.

S. B. Colak, M. B. van der Mark, G. W 't Hooft, J. H. Hoogenraad, E. S. van der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143-1158(1999).
[CrossRef]

Lee, K.

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44, 2082-2093 (2005).
[CrossRef] [PubMed]

K. Lee, R. Choe, A. Corlu, S. D. Konecky, T. Durduran, and A. G. Yodh, “Artifact reduction in CW transmission diffuse optical tomography,” presented at the OSA Biomedical Optics Topical Meeting, Florida, 2004.

Li, A.

Licha, K.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Lionheart, W. R. B.

McBride, T. O.

Meeuwse, J. P.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Miller, E. L.

Moesta, K. T.

Nielsen, T.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

B. Brendel and T. Nielsen, “Wavelength optimization in multispectral diffuse optical tomography considering uncertainties in absorption spectra,” Proc. SPIE 6629, 66290A (2007).
[CrossRef]

Osterberg, U. L.

Paulsen, K. D.

B. Brooksby, S. Srinivasan, S. Jiang, H. Deghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30, 1968-1970 (2005).
[CrossRef] [PubMed]

X. Wang, B. W. Pogue, S. Jiang, X. Song, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 0517041-0517048 (2005).
[CrossRef]

B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry for finite-element image reconstruction,” Appl. Opt. 40, 588-600 (2001).
[CrossRef]

Pessel, M.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Pifferi, A.

R. L. P. van Veen, H. J. C. M. Sterenborg, A. Pifferi, A. Torricelli, and R. Cubeddu, “Determination of vis-NIR absorption coefficients of mammalian fat, with time- and spatially resolved diffuse reflectance and transmission spectroscopy,” in Proceedings of Biomedical Topical Meetings (Optical Society of America, 2004), no. SF-5 on CD-ROM.

Pijkeren, D. v.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Pogue, B. W.

X. Wang, B. W. Pogue, S. Jiang, X. Song, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 0517041-0517048 (2005).
[CrossRef]

B. Brooksby, S. Srinivasan, S. Jiang, H. Deghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30, 1968-1970 (2005).
[CrossRef] [PubMed]

B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry for finite-element image reconstruction,” Appl. Opt. 40, 588-600 (2001).
[CrossRef]

Poplack, S. P.

B. Brooksby, S. Srinivasan, S. Jiang, H. Deghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30, 1968-1970 (2005).
[CrossRef] [PubMed]

X. Wang, B. W. Pogue, S. Jiang, X. Song, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 0517041-0517048 (2005).
[CrossRef]

B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

Pozo, R.

R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
[CrossRef]

Prahl, S.

S. Prahl, “Tabulated molar extinction coefficient for hemoglobin in water,” http://omlc.ogi.edu/spectra/hemoglobin/summary.html.

Rinneberg, H.

Romine, C.

R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
[CrossRef]

Schippers, F.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Schlag, P. M.

Schweiger, M.

Segelstein, D. J.

D. J. Segelstein, “The complex refractive index of water,” Ph.D. thesis (University of Missouri-Kansas City, 1981).

Shah, N.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420-4425 (2001).
[CrossRef] [PubMed]

Soho, S.

B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

Song, X.

X. Wang, B. W. Pogue, S. Jiang, X. Song, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 0517041-0517048 (2005).
[CrossRef]

B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

Srinivasan, S.

B. Brooksby, S. Srinivasan, S. Jiang, H. Deghani, B. W. Pogue, K. D. Paulsen, J. Weaver, C. Kogel, and S. P. Poplack, “Spectral priors improve near-infrared diffuse tomography more than spatial priors,” Opt. Lett. 30, 1968-1970 (2005).
[CrossRef] [PubMed]

B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

Sterenborg, H. J. C. M.

R. L. P. van Veen, H. J. C. M. Sterenborg, A. Pifferi, A. Torricelli, and R. Cubeddu, “Determination of vis-NIR absorption coefficients of mammalian fat, with time- and spatially resolved diffuse reflectance and transmission spectroscopy,” in Proceedings of Biomedical Topical Meetings (Optical Society of America, 2004), no. SF-5 on CD-ROM.

't Hooft, G. W

S. B. Colak, M. B. van der Mark, G. W 't Hooft, J. H. Hoogenraad, E. S. van der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143-1158(1999).
[CrossRef]

Torricelli, A.

R. L. P. van Veen, H. J. C. M. Sterenborg, A. Pifferi, A. Torricelli, and R. Cubeddu, “Determination of vis-NIR absorption coefficients of mammalian fat, with time- and spatially resolved diffuse reflectance and transmission spectroscopy,” in Proceedings of Biomedical Topical Meetings (Optical Society of America, 2004), no. SF-5 on CD-ROM.

Tosteson, T. D.

B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

Tromberg, B.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420-4425 (2001).
[CrossRef] [PubMed]

v. d. Mark, M.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

v. d. Voort, M.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

van der Linden, E. S.

S. B. Colak, M. B. van der Mark, G. W 't Hooft, J. H. Hoogenraad, E. S. van der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143-1158(1999).
[CrossRef]

van der Mark, M. B.

S. B. Colak, M. B. van der Mark, G. W 't Hooft, J. H. Hoogenraad, E. S. van der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143-1158(1999).
[CrossRef]

van Veen, R. L. P.

R. L. P. van Veen, H. J. C. M. Sterenborg, A. Pifferi, A. Torricelli, and R. Cubeddu, “Determination of vis-NIR absorption coefficients of mammalian fat, with time- and spatially resolved diffuse reflectance and transmission spectroscopy,” in Proceedings of Biomedical Topical Meetings (Optical Society of America, 2004), no. SF-5 on CD-ROM.

Wabnitz, H.

Wang, X.

X. Wang, B. W. Pogue, S. Jiang, X. Song, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 0517041-0517048 (2005).
[CrossRef]

Weaver, J.

Wells, W. A.

X. Wang, B. W. Pogue, S. Jiang, X. Song, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 0517041-0517048 (2005).
[CrossRef]

Yodh, A. G.

Zhang, Q.

Ziegler, A.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

Ziegler, R.

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
[CrossRef]

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S. B. Colak, M. B. van der Mark, G. W 't Hooft, J. H. Hoogenraad, E. S. van der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quantum Electron. 5, 1143-1158(1999).
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B. W. Pogue, S. Jiang, H. Deghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J Biomed. Opt. 9, 541-552 (2004).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

X. Wang, B. W. Pogue, S. Jiang, X. Song, K. D. Paulsen, C. Kogel, S. P. Poplack, and W. A. Wells, “Approximation of Mie scattering parameters in near-infrared tomography of normal breast tissue in vivo,” J. Biomed. Opt. 10, 0517041-0517048 (2005).
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N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420-4425 (2001).
[CrossRef] [PubMed]

Proc. SPIE (2)

T. Nielsen, B. Brendel, T. Köhler, R. Ziegler, A. Ziegler, L. Backer, M. v. Beek, M. v. d. Mark, M. v. d. Voort, R. Habers, K. Licha, M. Pessel, F. Schippers, J. P. Meeuwse, A. Feuerabend, D. v. Pijkeren, and S. Deckers, “Image reconstruction and evaluation of system performance for optical fluorescence tomography,” Proc. SPIE 6431, 643108 (2007).
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R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, 1994).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

D. J. Segelstein, “The complex refractive index of water,” Ph.D. thesis (University of Missouri-Kansas City, 1981).

R. L. P. van Veen, H. J. C. M. Sterenborg, A. Pifferi, A. Torricelli, and R. Cubeddu, “Determination of vis-NIR absorption coefficients of mammalian fat, with time- and spatially resolved diffuse reflectance and transmission spectroscopy,” in Proceedings of Biomedical Topical Meetings (Optical Society of America, 2004), no. SF-5 on CD-ROM.

S. Prahl, “Tabulated molar extinction coefficient for hemoglobin in water,” http://omlc.ogi.edu/spectra/hemoglobin/summary.html.

K. Lee, R. Choe, A. Corlu, S. D. Konecky, T. Durduran, and A. G. Yodh, “Artifact reduction in CW transmission diffuse optical tomography,” presented at the OSA Biomedical Optics Topical Meeting, Florida, 2004.

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Figures (8)

Fig. 1
Fig. 1

Circular 2D phantom ( 10 cm diameter) with five inhomogeneities ( 2 cm diameter). Simulations of this phantom are used to evaluate the reconstruction.

Fig. 2
Fig. 2

FE grid with local refinement at source and detector positions, used for simulations and reconstruction of the 2D phantom.

Fig. 3
Fig. 3

Reconstruction results for the 2D phantom of Fig. 1. Top row: Direct solution by matrix inversion. Bottom rows: Iterative solutions after 2000 iterations of CG, conventional ART, modified ART I, and modified ART II. All iterative methods converge to the direct solution.

Fig. 4
Fig. 4

Reconstruction results for the 2D phantom of Fig. 1. Iterative solutions after five iterations of CG, conventional ART, modified ART I, and modified ART II. Only modified ART II clearly shows the five inhomogeneities with only very weak crosstalk.

Fig. 5
Fig. 5

Logarithmized residual δ res s for the first 500 iterations of ART and the first 250 iterations of CG. For the late iterations, CG performs better. For the first iterations, the ART methods perform better.

Fig. 6
Fig. 6

Logarithmized residual δ res s for the first 50 iterations of ART and the first 25 iterations of CG. Even if CG and ART are compared for the same iteration counts, ART performs better for the first 12 iterations.

Fig. 7
Fig. 7

Image residual δ im s for the first 500 iterations of ART and the first 250 iterations of CG. The ART methods are clearly superior to CG.

Fig. 8
Fig. 8

Reconstruction results for the 2D phantom of Fig. 1 with modified scatter power b. Direct reconstruction assuming a scatter power of 1 for simulations with a scatter power of 0.5 (upper row) and 1.5 (lower row). Only minor crosstalk appears in the chromophore images.

Equations (27)

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

· D Φ + μ a Φ = 1 v S ,
ln Φ br ( x d , x s ) Φ ref ( x d , x s ) = v Ω δ μ a ( x ) G ( x d , x ) G ( x , x s ) G ( x d , x s ) d Ω + v Ω δ D ( x ) G ( x d , x ) · G ( x , x s ) G ( x d , x s ) d Ω .
A a y a + A d y d = b ,
b i = ln Φ br ( x d ( i ) , x s ( i ) ) Φ ref ( x d ( i ) , x s ( i ) ) , A a i j = v w j G ( x d ( i ) , x j ) G ( x j , x s ( i ) ) G ( x d ( i ) , x s ( i ) ) , A d i j = v w j G ( x d ( i ) , x j ) · G ( x j , x s ( i ) ) G ( x d ( i ) , x s ( i ) ) ,
A a l y a l + A d l y d l = b l .
μ a ( λ ) = k = 1 K ϵ k ( λ ) · c k ,
δ μ a ( λ ) = k = 1 K ϵ k ( λ ) · c k k = 1 K ϵ k ( λ ) · c 0 k = k = 1 K ϵ k ( λ ) · δ c k .
μ s ( λ ) = a · ( λ λ 0 ) p .
D ( λ ) = 1 3 a · ( λ λ 0 ) p = a · d ( λ ) ,
δ D ( λ ) = a · d ( λ ) a 0 · d ( λ ) = δ a · d ( λ ) .
( ϵ 1 ( λ 1 ) · A a 1 ϵ K ( λ 1 ) · A a 1 d ( λ 1 ) · A d 1 ϵ 1 ( λ L ) · A a L ϵ K ( λ L ) · A a L d ( λ L ) · A d L ) · ( δ c 1 δ c K δ a ) = ( b 1 b L ) A c · y c = b c .
| A c · y c b c | 2 + η | L · y c | 2 = ! min ,
y c = ( A c T A c + η L T L ) 1 A c T b c .
( A ˜ c | η I ) · ( y ˜ c q ) = b c A art · y art = b c ,
Δ b c i s = b c i j = 1 N c A ˜ c i j · y ˜ c j s η · q i s | Δ b c i s | 2 y ˜ c j s = 2 A ˜ c i j Δ b c i s | Δ b c i s | 2 q i s = 2 η Δ b c i s .
Δ y ˜ c j s = f | Δ b c i s | 2 y ˜ c j s , y ˜ c j s + 1 = y ˜ c j s + r Δ y ˜ c j s , Δ q i s = f | Δ b c i s | 2 q i s , q i s + 1 = q i s + r Δ q i s .
f = 0.5 j = 1 N c a ˜ c i j 2 + η y ˜ c j s + 1 = y ˜ c j s + r a ˜ c i j Δ b c i s j = 1 N c a ˜ c i j 2 + η q i s + 1 = q i s + r η Δ b c i s j = 1 N c a ˜ c i j 2 + η .
Δ b c i s = b c i j = 1 N A ˜ c i j y ˜ c j s η q i ,
| Δ b c i s | 2 y ˜ c j s = 2 A ˜ c i j T Δ b c i s , | Δ b c i s | 2 q i = 2 η Δ b c i s .
Δ y ˜ c j s = f | Δ b c i s | 2 y ˜ c j s , Δ q i = f | Δ b c i s | 2 q i .
| Δ b c i s j = 1 N A ˜ c i j Δ y ˜ c j s η Δ q i | 2 = ! min .
f = 0.5 Δ b c i s T a a T a , a = ( j = 1 N A ˜ c i j A ˜ c i j T + η I ) Δ b c i s .
Δ y ˜ c j s = 2 A ˜ c i j F Δ b c i s , Δ q i s = 2 η F Δ b c i s ,
Δ b c i s 2 ( j = 1 N A ˜ c i j A ˜ c i j T + η I ) F Δ b c i s = ! 0 [ 2 ( j = 1 N A ˜ c i j A ˜ c i j T + η I ) Δ B c i s ] 1 Δ b c i s = f .
( A c T A c + η L T L ) y c = A c T b c .
δ res s = | A c · y c s b c | 2 + η | L · y c s | 2 ,
δ im s = | y c s y c | 2 ,

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