Abstract

We apply reparameterization and the maximum likelihood method to a specific fluorescence-mediated tomography problem where the solution is known a priori to be extremely sparse (i.e., all image values are zero except for one). Our algorithm performs significantly better than a standard image reconstruction method, particularly for deep-seated targets, and achieves close to 150 μm accuracy in a 3 mm diameter cross-sectional area with only 12 measurements. Moreover, results do not depend on the selection of a regularization parameter or other ad hoc values, and since reconstructions can be computed very quickly, the algorithm is also suitable for real-time implementation.

© 2013 Optical Society of America

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  1. C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (3)

E. Zettergren, D. Vickers, J. M. Runnels, S. K. Murthy, C. P. Lin, and M. Niedre, J. Biomed. Opt. 17, 037001 (2012).
[CrossRef]

E. Zettergren, T. Swamy, J. Runnels, C. P. Lin, and M. Niedre, Phys. Med. Biol. 57, 4627 (2012).
[CrossRef]

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

2009 (1)

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

2008 (1)

J. B. Smerage and D. F. Hayes, Cancer Invest. 26, 109 (2008).
[CrossRef]

2007 (1)

2006 (1)

D. C. Comsa, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 51, 3733 (2006).
[CrossRef]

2005 (1)

2004 (1)

Adibi, A.

Ahn, S.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

Bouman, C. A.

Celso, C. Lo

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

Cherry, S. R.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

Comsa, D. C.

D. C. Comsa, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 51, 3733 (2006).
[CrossRef]

Cote, D.

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

Dutta, J.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

Eftekhar, A. A.

Farrell, T. J.

D. C. Comsa, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 51, 3733 (2006).
[CrossRef]

Fleming, H. E.

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

Fujisaki, J.

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

Georgakoudi, I.

Hayes, D. F.

J. B. Smerage and D. F. Hayes, Cancer Invest. 26, 109 (2008).
[CrossRef]

Huang, J.

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).

Kennedy, M. D.

Leahy, R. M.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

Li, C.

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

Lin, C. P.

E. Zettergren, T. Swamy, J. Runnels, C. P. Lin, and M. Niedre, Phys. Med. Biol. 57, 4627 (2012).
[CrossRef]

E. Zettergren, D. Vickers, J. M. Runnels, S. K. Murthy, C. P. Lin, and M. Niedre, J. Biomed. Opt. 17, 037001 (2012).
[CrossRef]

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

J. Novak, I. Georgakoudi, X. Wei, A. Prossin, and C. P. Lin, Opt. Lett. 29, 77 (2004).
[CrossRef]

E. Zettergren, D. Vickers, J. Runnels, C. P. Lin, and M. J. Niedre, Proceedings of the IEEE Engineering in Medicine and Biololgy Society, 2011 Annual International Conference of the IEEE (IEEE, 2011), p. 486.

Low, P. S.

Miake-Lye, S.

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

Milstein, A. B.

Mohajerani, P.

Murthy, S. K.

E. Zettergren, D. Vickers, J. M. Runnels, S. K. Murthy, C. P. Lin, and M. Niedre, J. Biomed. Opt. 17, 037001 (2012).
[CrossRef]

Niedre, M.

E. Zettergren, D. Vickers, J. M. Runnels, S. K. Murthy, C. P. Lin, and M. Niedre, J. Biomed. Opt. 17, 037001 (2012).
[CrossRef]

E. Zettergren, T. Swamy, J. Runnels, C. P. Lin, and M. Niedre, Phys. Med. Biol. 57, 4627 (2012).
[CrossRef]

Niedre, M. J.

E. Zettergren, D. Vickers, J. Runnels, C. P. Lin, and M. J. Niedre, Proceedings of the IEEE Engineering in Medicine and Biololgy Society, 2011 Annual International Conference of the IEEE (IEEE, 2011), p. 486.

Novak, J.

Patterson, M. S.

D. C. Comsa, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 51, 3733 (2006).
[CrossRef]

Prossin, A.

Rowe, D. W.

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

Runnels, J.

E. Zettergren, T. Swamy, J. Runnels, C. P. Lin, and M. Niedre, Phys. Med. Biol. 57, 4627 (2012).
[CrossRef]

E. Zettergren, D. Vickers, J. Runnels, C. P. Lin, and M. J. Niedre, Proceedings of the IEEE Engineering in Medicine and Biololgy Society, 2011 Annual International Conference of the IEEE (IEEE, 2011), p. 486.

Runnels, J. M.

E. Zettergren, D. Vickers, J. M. Runnels, S. K. Murthy, C. P. Lin, and M. Niedre, J. Biomed. Opt. 17, 037001 (2012).
[CrossRef]

Scadden, D. T.

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

Smerage, J. B.

J. B. Smerage and D. F. Hayes, Cancer Invest. 26, 109 (2008).
[CrossRef]

Swamy, T.

E. Zettergren, T. Swamy, J. Runnels, C. P. Lin, and M. Niedre, Phys. Med. Biol. 57, 4627 (2012).
[CrossRef]

Vickers, D.

E. Zettergren, D. Vickers, J. M. Runnels, S. K. Murthy, C. P. Lin, and M. Niedre, J. Biomed. Opt. 17, 037001 (2012).
[CrossRef]

E. Zettergren, D. Vickers, J. Runnels, C. P. Lin, and M. J. Niedre, Proceedings of the IEEE Engineering in Medicine and Biololgy Society, 2011 Annual International Conference of the IEEE (IEEE, 2011), p. 486.

Webb, K. J.

Wei, X.

Wu, J. W.

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

Zettergren, E.

E. Zettergren, D. Vickers, J. M. Runnels, S. K. Murthy, C. P. Lin, and M. Niedre, J. Biomed. Opt. 17, 037001 (2012).
[CrossRef]

E. Zettergren, T. Swamy, J. Runnels, C. P. Lin, and M. Niedre, Phys. Med. Biol. 57, 4627 (2012).
[CrossRef]

E. Zettergren, D. Vickers, J. Runnels, C. P. Lin, and M. J. Niedre, Proceedings of the IEEE Engineering in Medicine and Biololgy Society, 2011 Annual International Conference of the IEEE (IEEE, 2011), p. 486.

Zhao, C. X.

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

Appl. Opt. (2)

Cancer Invest. (1)

J. B. Smerage and D. F. Hayes, Cancer Invest. 26, 109 (2008).
[CrossRef]

J. Biomed. Opt. (1)

E. Zettergren, D. Vickers, J. M. Runnels, S. K. Murthy, C. P. Lin, and M. Niedre, J. Biomed. Opt. 17, 037001 (2012).
[CrossRef]

Nature (1)

C. Lo Celso, H. E. Fleming, J. W. Wu, C. X. Zhao, S. Miake-Lye, J. Fujisaki, D. Cote, D. W. Rowe, C. P. Lin, and D. T. Scadden, Nature 457, 92 (2009).
[CrossRef]

Opt. Lett. (1)

Phys. Med. Biol. (3)

E. Zettergren, T. Swamy, J. Runnels, C. P. Lin, and M. Niedre, Phys. Med. Biol. 57, 4627 (2012).
[CrossRef]

J. Dutta, S. Ahn, C. Li, S. R. Cherry, and R. M. Leahy, Phys. Med. Biol. 57, 1459 (2012).
[CrossRef]

D. C. Comsa, T. J. Farrell, and M. S. Patterson, Phys. Med. Biol. 51, 3733 (2006).
[CrossRef]

Other (2)

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, 1993).

E. Zettergren, D. Vickers, J. Runnels, C. P. Lin, and M. J. Niedre, Proceedings of the IEEE Engineering in Medicine and Biololgy Society, 2011 Annual International Conference of the IEEE (IEEE, 2011), p. 486.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic of DFFC with (b) photograph of detector ring and phantom in center; lasers and detectors labeled. (c) Sample data for microspheres (3 of 12 channels shown); one spike circled to highlight interchannel differences. The background was subtracted from each data set and an offset added for display purposes.

Fig. 2.
Fig. 2.

(a) Photograph of phantom cross section with shallow tube. (b) Previous r-ART result. (c) ML surface; dot indicates position of peak. (d)–(f) Same as (a)–(c) but for deep tube.

Fig. 3.
Fig. 3.

(a)–(d) Two-dimensional histograms of microsphere positions obtained with ML method; left insets show close-ups for (a) and (c). Circumference of phantom and the inner wall of tube is overlayed in light blue.

Equations (3)

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yN(ηWe(r),R),
η^(r)=e(r)TWTR1ye(r)TWTR1We(r),
r^=argmaxr|e(r)TWTR1y|2e(r)TWTR1We(r),

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