Abstract

This paper is a theoretical exploration of spatial resolution in diffuse fluorescence tomography. It is demonstrated that, given a fixed imaging geometry, one cannot—relative to standard techniques such as Tikhonov regularization and truncated singular value decomposition—improve the spatial resolution of the optical reconstructions via increasing the node density of the mesh considered for modeling light transport. Using techniques from linear algebra, it is shown that, as one increases the number of nodes beyond the number of measurements, information is lost by the forward model. It is demonstrated that this information cannot be recovered using various common reconstruction techniques. Evidence is provided showing that this phenomenon is related to the smoothing properties of the elliptic forward model that is used in the diffusion approximation to light transport in tissue. This argues for reconstruction techniques that are sensitive to boundaries, such as L1-reconstruction and the use of priors, as well as the natural approach of building a measurement geometry that reflects the desired image resolution.

© 2012 Optical Society of America

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2011 (3)

2010 (3)

2009 (3)

D. S. Kepshire, N. Mincu, M. Hutchins, J. Guber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, doi:10.1063/1.3109903, 043701 (2009).
[CrossRef]

H. Dehghani, M. Eames, P. Yalavarthy, S. Davis, S. Srinivasan, C. Carpenter, B. Pogue, and K. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Eng. 25, 711–732 (2009).
[CrossRef]

F. Leblond, H. Dehghani, D. Kepshire, and B. W. Pogue, “Early-photon fluorescence tomography: spatial resolution improvements and noise stability considerations,” J. Opt. Soc. Am. A 26, 1444–1457 (2009).
[CrossRef]

2008 (2)

2006 (2)

2005 (2)

Z. M. Wang, G. Y. Panasyuk, V. A. Markel, and J. C. Schotland, “Experimental demonstration of an analytic method for image reconstruction in optical diffusion tomography with large data sets,” Opt. Lett. 30, 3338–3340 (2005).
[CrossRef]

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

2002 (3)

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[CrossRef]

C. H. Contag and B. D. Ross, “It’s not just about anatomy: in vivo bioluminescence imaging as an eyepiece into biology,” J. Magn. Reson. Imaging 16, 378–387 (2002).
[CrossRef]

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
[CrossRef]

2001 (3)

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. USA 98, 4420–4425 (2001).
[CrossRef]

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).

1999 (1)

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

1998 (1)

1997 (2)

1995 (1)

K. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef]

1993 (1)

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

1983 (2)

Arridge, S. R.

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

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 J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef]

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

Bachmann, M. H.

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
[CrossRef]

Boas, D. A.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

Bremer, C.

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[CrossRef]

Brukilacchio, T. J.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

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. USA 98, 4420–4425 (2001).
[CrossRef]

Carpenter, C.

H. Dehghani, M. Eames, P. Yalavarthy, S. Davis, S. Srinivasan, C. Carpenter, B. Pogue, and K. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Eng. 25, 711–732 (2009).
[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. USA 98, 4420–4425 (2001).
[CrossRef]

Chaves, T.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

Chen, A.

Chen, J.

Chorlton, M.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

Contag, C. H.

C. H. Contag and B. D. Ross, “It’s not just about anatomy: in vivo bioluminescence imaging as an eyepiece into biology,” J. Magn. Reson. Imaging 16, 378–387 (2002).
[CrossRef]

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
[CrossRef]

Culver, J. P.

Davis, S.

F. Leblond, S. Davis, P. Valdés, and B. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

H. Dehghani, M. Eames, P. Yalavarthy, S. Davis, S. Srinivasan, C. Carpenter, B. Pogue, and K. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Eng. 25, 711–732 (2009).
[CrossRef]

Davis, S. C.

Dehghani, H.

K. M. Tichauer, R. W. Holt, F. El-Gussein, Q. Zhu, H. Dehghani, F. Leblond, and B. W. Pogue, “Imaging workflow and optical data calibration for CT-guided whole-body time-domain fluorescence tomography,” Biomed. Opt. Express 2, 3021–3036 (2011).
[CrossRef]

Q. Zhu, H. Dehghani, K. M. Tichauer, R. W. Holt, K. Vishwanath, F. Leblond, and B. W. Pogue, “A three-dimensional finite element model and image reconstruction algorithm for time-domain fluorescence imaging in highly scattering media,” Phys. Med. Biol. 56, 7419–7434 (2011).
[CrossRef]

D. S. Kepshire, N. Mincu, M. Hutchins, J. Guber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, doi:10.1063/1.3109903, 043701 (2009).
[CrossRef]

H. Dehghani, M. Eames, P. Yalavarthy, S. Davis, S. Srinivasan, C. Carpenter, B. Pogue, and K. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Eng. 25, 711–732 (2009).
[CrossRef]

F. Leblond, H. Dehghani, D. Kepshire, and B. W. Pogue, “Early-photon fluorescence tomography: spatial resolution improvements and noise stability considerations,” J. Opt. Soc. Am. A 26, 1444–1457 (2009).
[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).
[CrossRef]

P. Yalavarthy, H. Dehghani, B. Pogue, and K. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[CrossRef]

Delpy, D. T.

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

Eames, M.

H. Dehghani, M. Eames, P. Yalavarthy, S. Davis, S. Srinivasan, C. Carpenter, B. Pogue, and K. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Eng. 25, 711–732 (2009).
[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. USA 98, 4420–4425 (2001).
[CrossRef]

El-Ghussein, F.

El-Gussein, F.

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. USA 98, 4420–4425 (2001).
[CrossRef]

Ferwada, H. A.

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. USA 98, 4420–4425 (2001).
[CrossRef]

Friedberg, S.

S. Friedberg, A. Insel, and L. Spence, Linear Algebra, 4th ed. (Prentice Hall, 2003).

Golub, G.

G. Golub and C. F. van Loan, Matrix Calculations (Johns Hopkins University, 1989).

Groenhuis, R. A. J.

Guber, J.

D. S. Kepshire, N. Mincu, M. Hutchins, J. Guber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, doi:10.1063/1.3109903, 043701 (2009).
[CrossRef]

Hansen, P. C.

P. C. Hansen, Discrete Inverse Problems: Insight and Algorithms (SIAM, 2010).

Hebden, J. C.

S. R. Arridge and J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef]

Hillman, E.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

Hiraoka, M.

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

Holboke, M. J.

Holt, R. W.

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. USA 98, 4420–4425 (2001).
[CrossRef]

Hutchins, M.

D. S. Kepshire, N. Mincu, M. Hutchins, J. Guber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, doi:10.1063/1.3109903, 043701 (2009).
[CrossRef]

Hypnarowski, J.

D. S. Kepshire, N. Mincu, M. Hutchins, J. Guber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, doi:10.1063/1.3109903, 043701 (2009).
[CrossRef]

Insel, A.

S. Friedberg, A. Insel, and L. Spence, Linear Algebra, 4th ed. (Prentice Hall, 2003).

Intes, X.

Jacques, S. L.

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13, 041302 (2008).
[CrossRef]

Jiang, H.

K. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef]

Jiang, S.

Kaipio, J.

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

Kepshire, D.

Kepshire, D. S.

D. S. Kepshire, N. Mincu, M. Hutchins, J. Guber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, doi:10.1063/1.3109903, 043701 (2009).
[CrossRef]

Khayat, M.

D. S. Kepshire, N. Mincu, M. Hutchins, J. Guber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, doi:10.1063/1.3109903, 043701 (2009).
[CrossRef]

Konecky, S. D.

Kopans, D. B.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

Leblond, F.

K. M. Tichauer, R. W. Holt, F. El-Gussein, Q. Zhu, H. Dehghani, F. Leblond, and B. W. Pogue, “Imaging workflow and optical data calibration for CT-guided whole-body time-domain fluorescence tomography,” Biomed. Opt. Express 2, 3021–3036 (2011).
[CrossRef]

Q. Zhu, H. Dehghani, K. M. Tichauer, R. W. Holt, K. Vishwanath, F. Leblond, and B. W. Pogue, “A three-dimensional finite element model and image reconstruction algorithm for time-domain fluorescence imaging in highly scattering media,” Phys. Med. Biol. 56, 7419–7434 (2011).
[CrossRef]

F. Leblond, K. M. Tichauer, R. W. Holt, F. El-Ghussein, and B. W. Pogue, “Toward whole-body optical imaging of rats using single-photon counting fluorescence tomography,” Opt. Lett. 36, 3723–3725 (2011).
[CrossRef]

F. Leblond, K. M. Tichauer, and B. W. Pogue, “Singular value decomposition metrics show limitations of detector design in diffuse optical tomography,” Biomed. Opt. Express 1, 1514–1531(2010).
[CrossRef]

F. Leblond, S. Davis, P. Valdés, and B. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

F. Leblond, H. Dehghani, D. Kepshire, and B. W. Pogue, “Early-photon fluorescence tomography: spatial resolution improvements and noise stability considerations,” J. Opt. Soc. Am. A 26, 1444–1457 (2009).
[CrossRef]

D. S. Kepshire, N. Mincu, M. Hutchins, J. Guber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, doi:10.1063/1.3109903, 043701 (2009).
[CrossRef]

Lee, K.

Lesage, F.

Li, A.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

Lionheart, W. R. B.

Markel, V.

Markel, V. A.

McBride, T. O.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Mincu, N.

D. S. Kepshire, N. Mincu, M. Hutchins, J. Guber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, doi:10.1063/1.3109903, 043701 (2009).
[CrossRef]

Moore, R. H.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

Ntziachristos, V.

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[CrossRef]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).

Osterberg, U. L.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Osterman, K. S.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Paithankar, D.

Panasyuk, G. Y.

Patterson, M.

Patterson, M. S.

Paulsen, K.

H. Dehghani, M. Eames, P. Yalavarthy, S. Davis, S. Srinivasan, C. Carpenter, B. Pogue, and K. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Eng. 25, 711–732 (2009).
[CrossRef]

P. Yalavarthy, H. Dehghani, B. Pogue, and K. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[CrossRef]

K. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef]

Paulsen, K. D.

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).
[CrossRef]

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Pogue, B.

F. Leblond, S. Davis, P. Valdés, and B. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

H. Dehghani, M. Eames, P. Yalavarthy, S. Davis, S. Srinivasan, C. Carpenter, B. Pogue, and K. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Eng. 25, 711–732 (2009).
[CrossRef]

P. Yalavarthy, H. Dehghani, B. Pogue, and K. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[CrossRef]

D. Paithankar, A. Chen, B. Pogue, M. Patterson, and E. Sevick-Muraca, “Imaging of fluorescent yield and lifetime from multiply scattered light reemitted from random media,” Appl. Opt. 36, 2260–2272 (1997).
[CrossRef]

Pogue, B. W.

F. Leblond, K. M. Tichauer, R. W. Holt, F. El-Ghussein, and B. W. Pogue, “Toward whole-body optical imaging of rats using single-photon counting fluorescence tomography,” Opt. Lett. 36, 3723–3725 (2011).
[CrossRef]

Q. Zhu, H. Dehghani, K. M. Tichauer, R. W. Holt, K. Vishwanath, F. Leblond, and B. W. Pogue, “A three-dimensional finite element model and image reconstruction algorithm for time-domain fluorescence imaging in highly scattering media,” Phys. Med. Biol. 56, 7419–7434 (2011).
[CrossRef]

K. M. Tichauer, R. W. Holt, F. El-Gussein, Q. Zhu, H. Dehghani, F. Leblond, and B. W. Pogue, “Imaging workflow and optical data calibration for CT-guided whole-body time-domain fluorescence tomography,” Biomed. Opt. Express 2, 3021–3036 (2011).
[CrossRef]

F. Leblond, K. M. Tichauer, and B. W. Pogue, “Singular value decomposition metrics show limitations of detector design in diffuse optical tomography,” Biomed. Opt. Express 1, 1514–1531(2010).
[CrossRef]

D. S. Kepshire, N. Mincu, M. Hutchins, J. Guber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, doi:10.1063/1.3109903, 043701 (2009).
[CrossRef]

F. Leblond, H. Dehghani, D. Kepshire, and B. W. Pogue, “Early-photon fluorescence tomography: spatial resolution improvements and noise stability considerations,” J. Opt. Soc. Am. A 26, 1444–1457 (2009).
[CrossRef]

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13, 041302 (2008).
[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).
[CrossRef]

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Poplack, S. P.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Rafferty, E.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

Ross, B. D.

C. H. Contag and B. D. Ross, “It’s not just about anatomy: in vivo bioluminescence imaging as an eyepiece into biology,” J. Magn. Reson. Imaging 16, 378–387 (2002).
[CrossRef]

Schotland, J. C.

Schweiger, M.

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

Sevick-Muraca, E.

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. USA 98, 4420–4425 (2001).
[CrossRef]

Somersalo, E.

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

Spence, L.

S. Friedberg, A. Insel, and L. Spence, Linear Algebra, 4th ed. (Prentice Hall, 2003).

Srinivasan, S.

H. Dehghani, M. Eames, P. Yalavarthy, S. Davis, S. Srinivasan, C. Carpenter, B. Pogue, and K. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Eng. 25, 711–732 (2009).
[CrossRef]

Stott, J. J.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

Ten Bosch, J. J.

Tichauer, K. M.

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. USA 98, 4420–4425 (2001).
[CrossRef]

Tung, C. H.

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[CrossRef]

Valdés, P.

F. Leblond, S. Davis, P. Valdés, and B. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

van Loan, C. F.

G. Golub and C. F. van Loan, Matrix Calculations (Johns Hopkins University, 1989).

Venugopal, V.

Vishwanath, K.

Q. Zhu, H. Dehghani, K. M. Tichauer, R. W. Holt, K. Vishwanath, F. Leblond, and B. W. Pogue, “A three-dimensional finite element model and image reconstruction algorithm for time-domain fluorescence imaging in highly scattering media,” Phys. Med. Biol. 56, 7419–7434 (2011).
[CrossRef]

Wang, Z. M.

Weissleder, R.

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[CrossRef]

Wells, W. A.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Wu, T.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

Yalavarthy, P.

H. Dehghani, M. Eames, P. Yalavarthy, S. Davis, S. Srinivasan, C. Carpenter, B. Pogue, and K. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Eng. 25, 711–732 (2009).
[CrossRef]

P. Yalavarthy, H. Dehghani, B. Pogue, and K. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[CrossRef]

Yodh, A. G.

Zhang, Q.

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

Zhu, Q.

K. M. Tichauer, R. W. Holt, F. El-Gussein, Q. Zhu, H. Dehghani, F. Leblond, and B. W. Pogue, “Imaging workflow and optical data calibration for CT-guided whole-body time-domain fluorescence tomography,” Biomed. Opt. Express 2, 3021–3036 (2011).
[CrossRef]

Q. Zhu, H. Dehghani, K. M. Tichauer, R. W. Holt, K. Vishwanath, F. Leblond, and B. W. Pogue, “A three-dimensional finite element model and image reconstruction algorithm for time-domain fluorescence imaging in highly scattering media,” Phys. Med. Biol. 56, 7419–7434 (2011).
[CrossRef]

Annu. Rev. Biomed. Eng. (1)

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
[CrossRef]

Appl. Opt. (3)

Biomed. Opt. Express (2)

Commun. Numer. Meth. Eng. (1)

H. Dehghani, M. Eames, P. Yalavarthy, S. Davis, S. Srinivasan, C. Carpenter, B. Pogue, and K. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Meth. Eng. 25, 711–732 (2009).
[CrossRef]

Inverse Probl. (1)

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

J. Biomed. Opt. (2)

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13, 041302 (2008).
[CrossRef]

Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10, 024033 (2005).
[CrossRef]

J. Magn. Reson. Imaging (1)

C. H. Contag and B. D. Ross, “It’s not just about anatomy: in vivo bioluminescence imaging as an eyepiece into biology,” J. Magn. Reson. Imaging 16, 378–387 (2002).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Photochem. Photobiol. B (1)

F. Leblond, S. Davis, P. Valdés, and B. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

Med. Phys. (2)

K. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef]

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

Nat. Med. (1)

V. Ntziachristos, C. H. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–761 (2002).
[CrossRef]

Opt. Express (2)

Opt. Lett. (6)

Phys. Med. Biol. (2)

Q. Zhu, H. Dehghani, K. M. Tichauer, R. W. Holt, K. Vishwanath, F. Leblond, and B. W. Pogue, “A three-dimensional finite element model and image reconstruction algorithm for time-domain fluorescence imaging in highly scattering media,” Phys. Med. Biol. 56, 7419–7434 (2011).
[CrossRef]

S. R. Arridge and J. C. Hebden, “Optical imaging in medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef]

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

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. USA 98, 4420–4425 (2001).
[CrossRef]

Radiology (1)

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiology 218, 261–266 (2001).

Rev. Sci. Instrum. (1)

D. S. Kepshire, N. Mincu, M. Hutchins, J. Guber, H. Dehghani, J. Hypnarowski, F. Leblond, M. Khayat, and B. W. Pogue, “A microcomputed tomography guided fluorescence tomography system for small animal molecular imaging,” Rev. Sci. Instrum. 80, doi:10.1063/1.3109903, 043701 (2009).
[CrossRef]

Other (4)

S. Friedberg, A. Insel, and L. Spence, Linear Algebra, 4th ed. (Prentice Hall, 2003).

G. Golub and C. F. van Loan, Matrix Calculations (Johns Hopkins University, 1989).

P. C. Hansen, Discrete Inverse Problems: Insight and Algorithms (SIAM, 2010).

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

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Figures (4)

Fig. 1.
Fig. 1.

Image reconstruction and information loss for an imaging geometry with 32 sources and 5 detectors. The top row shows the true solutions, the middle row shows the reconstructed images using the maximal number of SVD modes, and the bottom row presents the information that is lost through regularization. The images are shown for an increasing spatial resolution from left to right.

Fig. 2.
Fig. 2.

Image reconstruction and information loss for an imaging geometry with 128 sources and 5 detectors. The top row shows the true solutions, the middle row shows the reconstructed images using the maximal number of SVD modes, and the bottom row presents the information that is lost through regularization. The images are shown for an increasing spatial resolution from left to right.

Fig. 3.
Fig. 3.

Reconstruction error versus node density for all detection geometries considered. The error decreases as the number of measurement increases, while the error typically increases with the number of nodes.

Fig. 4.
Fig. 4.

Reconstruction error as a function of smoothness of the optical properties vector. A value of 1 indicates that no smoothing has been applied (and thus the optical properties vector exhibits sharp edges), whereas a value of 10 indicates the largest amount of smoothing that has been applied.

Equations (29)

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

·κ(r)Φ(r,ω)+(μa(r)+iωcm(r))Φ(r,ω)=S(r,ω),
Φ(r,ω)+2Bκ(r)Φ(r,ω)ν|Ω=0,
·κx(r)Φx(r,ω)(μa,x(r)+iωcn(r))Φx(r,ω)+Sx(r,ω)=0,
·κm(r)Φm(r,ω)(μa,m(r)+iωcn(r))Φm(r,ω)+Sm(r,ω)=0,
Sm(r,ω)=Qfμa,f1iωτΦx(r,ω).
Φm(r,ω)=Ωd3rGm(r,r,ω)Qfμa,f(r)1iωτΦx(r,ω),
Φm(rk,ω)=Φm,k(ω)=i=1NvΔViGm(rk,ri,ω)Qfμa,f(ri)1iωτΦx(ri,ω),
Φm,k(ω)=i=1Nvakiμa,fi,
aki=Gm(rk,ri,ω)Qfμa,f(ri)1iωτΦx(rk,ω).
Ker(A)={vRNv:Av=0}.
Ker(A)={wRNv:v,w=0for allvker(A)}.
RNv=Ker(A)Ker(A).
Ran(A)={wRNm:there existsvRNvwithAv=w}.
Nv=dimensionKer(A)+Rank(A).
error=μa,fμa,freconμa,f=μa,fkernelμa,f
μLS=minμ:Aμ=yμ2;
(ATA+αI)μ=AT(ymeas),
μα=argmin{Aμymeas2+αμ2}.
μα=1α(ATymeasATAμα)=1α(AT(ymeasAμα)).
A=UΣVT
σ1σ2σNm0.
μp=i=1p1σiymeas,uivi,
ATAμ=ATPymeas+AT(IP)(ymeas)=ATymeas
T(μ)=μ+β(ATymeasATAμ)
ATuj=σjvj.
ATuj=i=1NvATuj,vivi=i=1pATuj,vivi+i=p+1Nv<ATuj,vi>vi=i=1puj,Avivi+i=p+1Nv<uj,Avi>vi=i=1pδ(i,j)σivi+0=σjvj.
Ai=(1011001001).
A6=(101010010101).
{(1,0,1,0,0,0),(0,0,1,0,1,0),(0,1,0,1,0,0),(0,0,0,1,0,1),},

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