Abstract

We investigated the penalized maximum likelihood estimation of lifetime and amplitude images for fluorescence lifetime imaging microscopy. The proposed method penalizes large variations in the lifetimes and amplitudes in the spatial domain to reduces noise in the images, which is a serious problem in the conventional maximum likelihood estimation method. For an effective optimization of the objective function, we applied an optimization transfer method that is based on a separable surrogate function. Simulations show that the proposed method outperforms the conventional MLE method in terms of the estimation accuracy, and the proposed method yielded less noisy images in real experiments.

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    [CrossRef]
  2. C. W. Chang and M.-A. Mycek, “Enhancing precision in time-domain fluorescence lifetime imaging,” J. Biomed. Opt.15, 056013 (2010).
    [CrossRef] [PubMed]
  3. W. Becker, “Fluorescence lifetime imaging techniques and applications,” J. Microsc.247, 119–136 (2012).
    [CrossRef] [PubMed]
  4. M. Kneen, J. Farinas, Y. Li, and A. Verkman, “Green fluorescent protein as a noninvasive intracellular ph indicator,” Biophys. J.74, 1591–1599 (1998).
    [CrossRef] [PubMed]
  5. P. J. Verveer, A. Squire, and P. I. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J.78, 2127–2137 (2000).
    [CrossRef] [PubMed]
  6. Z. Bajzer, T. M. Therneau, J. C. Sharp, and F. G. Prendergast, “Maximum likelihood method for the analysis of time-resolved fluorescence decay curves,” Eur. Biophys. J.20, 247–262 (1991).
    [CrossRef]
  7. M. Kollner and J. Wolfrum, “How many photons are necessary for fluorescence-lifetime measurements?” Chem. Phys. Lett.200, 199 –204 (1992).
    [CrossRef]
  8. J. Kim and J. Seok, “Statistical properties of amplitude and decay parameter estimators for fluorescence lifetime imaging,” Opt. Express21, 6061–6075 (2013).
    [CrossRef] [PubMed]
  9. H. Cramer, Mathematical Methods of Statistics (PMS-9), Princeton Landmarks in Mathematics and Physics (Princeton University Press, 1999).
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    [CrossRef] [PubMed]
  11. L. P. Watkins and H. Yang, “Information bounds and optimal analysis of dynamic single molecule measurements,” Biophys. J.86, 4015 – 4029 (2004).
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    [CrossRef]
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    [CrossRef] [PubMed]
  15. K. M. Hanson, M. J. Behne, N. P. Barry, T. M. Mauro, E. Gratton, and R. M. Clegg, “Two-photon fluorescence lifetime imaging of the skin stratum corneum ph gradient,” Biophys. J.83, 1682–1690 (2002).
    [CrossRef] [PubMed]
  16. A. Squire and P. I. H. Bastiaens, “Three dimensional image restoration in fluorescence lifetime imaging microscopy,” J. Microsc.193, 36–49 (1999).
    [CrossRef] [PubMed]
  17. D. Sud and M.-A. Mycek, “Image restoration for fluorescence lifetime imaging microscopy (FLIM),” Opt. Express16, 19192–19200 (2008).
    [CrossRef]
  18. M. Heilemann, D. P. Herten, R. Heintzmann, C. Cremer, C. Mller, P. Tinnefeld, K. D. Weston, J. Wolfrum, and M. Sauer, “High-resolution colocalization of single dye molecules by fluorescence lifetime imaging microscopy,” Anal. Chem.74, 3511–3517 (2002).
    [CrossRef] [PubMed]
  19. B. B. Collier and M. J. McShane, “Dynamic windowing algorithm for the fast and accurate determination of luminescence lifetimes,” Anal. Chem.84, 4725–4731 (2012).
    [CrossRef] [PubMed]
  20. E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt.8, 381–390 (2003).
    [CrossRef] [PubMed]
  21. J. Fessler and A. Hero, “Penalized maximum-likelihood image reconstruction using space-alternating generalized em algorithms,” IEEE Trans. Image Process., 4, 1417–1429 (1995).
    [CrossRef] [PubMed]
  22. J.-H. Chang, J. Anderson, and J. Votaw, “Regularized image reconstruction algorithms for positron emission tomography,” IEEE Trans. Med. Imag., 23, 1165 – 1175 (2004).
    [CrossRef]
  23. J. Fessler, “Image reconstruction: Algorithms and analysis,” Online preprint of book in preparation.
  24. A. De Pierro, “A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography,” IEEE Trans. Med. Imag., 14, 132–137 (1995).
    [CrossRef]
  25. P. Huber, Robust Statistics (Wiley, 1974).
  26. J. Fessler and W. Rogers, “Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs,” IEEE Trans. Image Process., 5, 1346–1358 (1996).
    [CrossRef] [PubMed]
  27. H.-J. Lin, P. Herman, and J. R. Lakowicz, “Fluorescence lifetime-resolved ph imaging of living cells,” Cytometry Part A52A, 77–89 (2003).
    [CrossRef]
  28. C. Hille, M. Berg, L. Bressel, D. Munzke, P. Primus, H.-G. Lahmannsraben, and C. Dosche, “Time-domain fluorescence lifetime imaging for intracellular ph sensing in living tissues,” Anal. Bioanal. Chem.391, 1871–1879 (2008).
    [CrossRef] [PubMed]

2013 (1)

2012 (2)

W. Becker, “Fluorescence lifetime imaging techniques and applications,” J. Microsc.247, 119–136 (2012).
[CrossRef] [PubMed]

B. B. Collier and M. J. McShane, “Dynamic windowing algorithm for the fast and accurate determination of luminescence lifetimes,” Anal. Chem.84, 4725–4731 (2012).
[CrossRef] [PubMed]

2010 (1)

C. W. Chang and M.-A. Mycek, “Enhancing precision in time-domain fluorescence lifetime imaging,” J. Biomed. Opt.15, 056013 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (2)

D. Sud and M.-A. Mycek, “Image restoration for fluorescence lifetime imaging microscopy (FLIM),” Opt. Express16, 19192–19200 (2008).
[CrossRef]

C. Hille, M. Berg, L. Bressel, D. Munzke, P. Primus, H.-G. Lahmannsraben, and C. Dosche, “Time-domain fluorescence lifetime imaging for intracellular ph sensing in living tissues,” Anal. Bioanal. Chem.391, 1871–1879 (2008).
[CrossRef] [PubMed]

2004 (3)

S. Pelet, M. J. R. Previte, L. H. Laiho, and P. T. C. So, “A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation.” Biophys. J.87, 2807–2817 (2004).
[CrossRef] [PubMed]

J.-H. Chang, J. Anderson, and J. Votaw, “Regularized image reconstruction algorithms for positron emission tomography,” IEEE Trans. Med. Imag., 23, 1165 – 1175 (2004).
[CrossRef]

L. P. Watkins and H. Yang, “Information bounds and optimal analysis of dynamic single molecule measurements,” Biophys. J.86, 4015 – 4029 (2004).
[CrossRef] [PubMed]

2003 (3)

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt.8, 381–390 (2003).
[CrossRef] [PubMed]

H.-J. Lin, P. Herman, and J. R. Lakowicz, “Fluorescence lifetime-resolved ph imaging of living cells,” Cytometry Part A52A, 77–89 (2003).
[CrossRef]

J. Philip and K. Carlsson, “Theoretical investigation of the signal-to-noise ratio in fluorescence lifetime imaging,” J. Opt. Soc. Am. A20, 368–379 (2003).
[CrossRef]

2002 (3)

H. C. Gerritsen, M. A. H. Asselbergs, A. V. Agronskaia, and W. G. J. H. M. Van Sark, “Fluorescence lifetime imaging in scanning microscopes: acquisition speed, photon economy and lifetime resolution,” J. Microsc.206, 218–224 (2002).
[CrossRef] [PubMed]

K. M. Hanson, M. J. Behne, N. P. Barry, T. M. Mauro, E. Gratton, and R. M. Clegg, “Two-photon fluorescence lifetime imaging of the skin stratum corneum ph gradient,” Biophys. J.83, 1682–1690 (2002).
[CrossRef] [PubMed]

M. Heilemann, D. P. Herten, R. Heintzmann, C. Cremer, C. Mller, P. Tinnefeld, K. D. Weston, J. Wolfrum, and M. Sauer, “High-resolution colocalization of single dye molecules by fluorescence lifetime imaging microscopy,” Anal. Chem.74, 3511–3517 (2002).
[CrossRef] [PubMed]

2000 (1)

P. J. Verveer, A. Squire, and P. I. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J.78, 2127–2137 (2000).
[CrossRef] [PubMed]

1999 (1)

A. Squire and P. I. H. Bastiaens, “Three dimensional image restoration in fluorescence lifetime imaging microscopy,” J. Microsc.193, 36–49 (1999).
[CrossRef] [PubMed]

1998 (1)

M. Kneen, J. Farinas, Y. Li, and A. Verkman, “Green fluorescent protein as a noninvasive intracellular ph indicator,” Biophys. J.74, 1591–1599 (1998).
[CrossRef] [PubMed]

1996 (1)

J. Fessler and W. Rogers, “Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs,” IEEE Trans. Image Process., 5, 1346–1358 (1996).
[CrossRef] [PubMed]

1995 (2)

J. Fessler and A. Hero, “Penalized maximum-likelihood image reconstruction using space-alternating generalized em algorithms,” IEEE Trans. Image Process., 4, 1417–1429 (1995).
[CrossRef] [PubMed]

A. De Pierro, “A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography,” IEEE Trans. Med. Imag., 14, 132–137 (1995).
[CrossRef]

1992 (1)

M. Kollner and J. Wolfrum, “How many photons are necessary for fluorescence-lifetime measurements?” Chem. Phys. Lett.200, 199 –204 (1992).
[CrossRef]

1991 (1)

Z. Bajzer, T. M. Therneau, J. C. Sharp, and F. G. Prendergast, “Maximum likelihood method for the analysis of time-resolved fluorescence decay curves,” Eur. Biophys. J.20, 247–262 (1991).
[CrossRef]

Agronskaia, A. V.

H. C. Gerritsen, M. A. H. Asselbergs, A. V. Agronskaia, and W. G. J. H. M. Van Sark, “Fluorescence lifetime imaging in scanning microscopes: acquisition speed, photon economy and lifetime resolution,” J. Microsc.206, 218–224 (2002).
[CrossRef] [PubMed]

Anderson, J.

J.-H. Chang, J. Anderson, and J. Votaw, “Regularized image reconstruction algorithms for positron emission tomography,” IEEE Trans. Med. Imag., 23, 1165 – 1175 (2004).
[CrossRef]

Asselbergs, M. A. H.

H. C. Gerritsen, M. A. H. Asselbergs, A. V. Agronskaia, and W. G. J. H. M. Van Sark, “Fluorescence lifetime imaging in scanning microscopes: acquisition speed, photon economy and lifetime resolution,” J. Microsc.206, 218–224 (2002).
[CrossRef] [PubMed]

Bajzer, Z.

Z. Bajzer, T. M. Therneau, J. C. Sharp, and F. G. Prendergast, “Maximum likelihood method for the analysis of time-resolved fluorescence decay curves,” Eur. Biophys. J.20, 247–262 (1991).
[CrossRef]

Barry, N.

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt.8, 381–390 (2003).
[CrossRef] [PubMed]

Barry, N. P.

K. M. Hanson, M. J. Behne, N. P. Barry, T. M. Mauro, E. Gratton, and R. M. Clegg, “Two-photon fluorescence lifetime imaging of the skin stratum corneum ph gradient,” Biophys. J.83, 1682–1690 (2002).
[CrossRef] [PubMed]

Bastiaens, P. I.

P. J. Verveer, A. Squire, and P. I. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J.78, 2127–2137 (2000).
[CrossRef] [PubMed]

Bastiaens, P. I. H.

A. Squire and P. I. H. Bastiaens, “Three dimensional image restoration in fluorescence lifetime imaging microscopy,” J. Microsc.193, 36–49 (1999).
[CrossRef] [PubMed]

Becker, W.

W. Becker, “Fluorescence lifetime imaging techniques and applications,” J. Microsc.247, 119–136 (2012).
[CrossRef] [PubMed]

Behne, M. J.

K. M. Hanson, M. J. Behne, N. P. Barry, T. M. Mauro, E. Gratton, and R. M. Clegg, “Two-photon fluorescence lifetime imaging of the skin stratum corneum ph gradient,” Biophys. J.83, 1682–1690 (2002).
[CrossRef] [PubMed]

Berg, M.

C. Hille, M. Berg, L. Bressel, D. Munzke, P. Primus, H.-G. Lahmannsraben, and C. Dosche, “Time-domain fluorescence lifetime imaging for intracellular ph sensing in living tissues,” Anal. Bioanal. Chem.391, 1871–1879 (2008).
[CrossRef] [PubMed]

Bressel, L.

C. Hille, M. Berg, L. Bressel, D. Munzke, P. Primus, H.-G. Lahmannsraben, and C. Dosche, “Time-domain fluorescence lifetime imaging for intracellular ph sensing in living tissues,” Anal. Bioanal. Chem.391, 1871–1879 (2008).
[CrossRef] [PubMed]

Breusegem, S.

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt.8, 381–390 (2003).
[CrossRef] [PubMed]

Carlsson, K.

Chang, C. W.

C. W. Chang and M.-A. Mycek, “Enhancing precision in time-domain fluorescence lifetime imaging,” J. Biomed. Opt.15, 056013 (2010).
[CrossRef] [PubMed]

Chang, J.-H.

J.-H. Chang, J. Anderson, and J. Votaw, “Regularized image reconstruction algorithms for positron emission tomography,” IEEE Trans. Med. Imag., 23, 1165 – 1175 (2004).
[CrossRef]

Clegg, R. M.

K. M. Hanson, M. J. Behne, N. P. Barry, T. M. Mauro, E. Gratton, and R. M. Clegg, “Two-photon fluorescence lifetime imaging of the skin stratum corneum ph gradient,” Biophys. J.83, 1682–1690 (2002).
[CrossRef] [PubMed]

Collier, B. B.

B. B. Collier and M. J. McShane, “Dynamic windowing algorithm for the fast and accurate determination of luminescence lifetimes,” Anal. Chem.84, 4725–4731 (2012).
[CrossRef] [PubMed]

Cramer, H.

H. Cramer, Mathematical Methods of Statistics (PMS-9), Princeton Landmarks in Mathematics and Physics (Princeton University Press, 1999).

Cremer, C.

M. Heilemann, D. P. Herten, R. Heintzmann, C. Cremer, C. Mller, P. Tinnefeld, K. D. Weston, J. Wolfrum, and M. Sauer, “High-resolution colocalization of single dye molecules by fluorescence lifetime imaging microscopy,” Anal. Chem.74, 3511–3517 (2002).
[CrossRef] [PubMed]

De Pierro, A.

A. De Pierro, “A modified expectation maximization algorithm for penalized likelihood estimation in emission tomography,” IEEE Trans. Med. Imag., 14, 132–137 (1995).
[CrossRef]

Dosche, C.

C. Hille, M. Berg, L. Bressel, D. Munzke, P. Primus, H.-G. Lahmannsraben, and C. Dosche, “Time-domain fluorescence lifetime imaging for intracellular ph sensing in living tissues,” Anal. Bioanal. Chem.391, 1871–1879 (2008).
[CrossRef] [PubMed]

Farinas, J.

M. Kneen, J. Farinas, Y. Li, and A. Verkman, “Green fluorescent protein as a noninvasive intracellular ph indicator,” Biophys. J.74, 1591–1599 (1998).
[CrossRef] [PubMed]

Fessler, J.

J. Fessler and W. Rogers, “Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs,” IEEE Trans. Image Process., 5, 1346–1358 (1996).
[CrossRef] [PubMed]

J. Fessler and A. Hero, “Penalized maximum-likelihood image reconstruction using space-alternating generalized em algorithms,” IEEE Trans. Image Process., 4, 1417–1429 (1995).
[CrossRef] [PubMed]

J. Fessler, “Image reconstruction: Algorithms and analysis,” Online preprint of book in preparation.

Gerritsen, H. C.

H. C. Gerritsen, M. A. H. Asselbergs, A. V. Agronskaia, and W. G. J. H. M. Van Sark, “Fluorescence lifetime imaging in scanning microscopes: acquisition speed, photon economy and lifetime resolution,” J. Microsc.206, 218–224 (2002).
[CrossRef] [PubMed]

Gratton, E.

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt.8, 381–390 (2003).
[CrossRef] [PubMed]

K. M. Hanson, M. J. Behne, N. P. Barry, T. M. Mauro, E. Gratton, and R. M. Clegg, “Two-photon fluorescence lifetime imaging of the skin stratum corneum ph gradient,” Biophys. J.83, 1682–1690 (2002).
[CrossRef] [PubMed]

Grecco, H. E.

Hanson, K. M.

K. M. Hanson, M. J. Behne, N. P. Barry, T. M. Mauro, E. Gratton, and R. M. Clegg, “Two-photon fluorescence lifetime imaging of the skin stratum corneum ph gradient,” Biophys. J.83, 1682–1690 (2002).
[CrossRef] [PubMed]

Heilemann, M.

M. Heilemann, D. P. Herten, R. Heintzmann, C. Cremer, C. Mller, P. Tinnefeld, K. D. Weston, J. Wolfrum, and M. Sauer, “High-resolution colocalization of single dye molecules by fluorescence lifetime imaging microscopy,” Anal. Chem.74, 3511–3517 (2002).
[CrossRef] [PubMed]

Heintzmann, R.

M. Heilemann, D. P. Herten, R. Heintzmann, C. Cremer, C. Mller, P. Tinnefeld, K. D. Weston, J. Wolfrum, and M. Sauer, “High-resolution colocalization of single dye molecules by fluorescence lifetime imaging microscopy,” Anal. Chem.74, 3511–3517 (2002).
[CrossRef] [PubMed]

Herman, P.

H.-J. Lin, P. Herman, and J. R. Lakowicz, “Fluorescence lifetime-resolved ph imaging of living cells,” Cytometry Part A52A, 77–89 (2003).
[CrossRef]

Hero, A.

J. Fessler and A. Hero, “Penalized maximum-likelihood image reconstruction using space-alternating generalized em algorithms,” IEEE Trans. Image Process., 4, 1417–1429 (1995).
[CrossRef] [PubMed]

Herten, D. P.

M. Heilemann, D. P. Herten, R. Heintzmann, C. Cremer, C. Mller, P. Tinnefeld, K. D. Weston, J. Wolfrum, and M. Sauer, “High-resolution colocalization of single dye molecules by fluorescence lifetime imaging microscopy,” Anal. Chem.74, 3511–3517 (2002).
[CrossRef] [PubMed]

Hille, C.

C. Hille, M. Berg, L. Bressel, D. Munzke, P. Primus, H.-G. Lahmannsraben, and C. Dosche, “Time-domain fluorescence lifetime imaging for intracellular ph sensing in living tissues,” Anal. Bioanal. Chem.391, 1871–1879 (2008).
[CrossRef] [PubMed]

Huber, P.

P. Huber, Robust Statistics (Wiley, 1974).

Kim, J.

Kneen, M.

M. Kneen, J. Farinas, Y. Li, and A. Verkman, “Green fluorescent protein as a noninvasive intracellular ph indicator,” Biophys. J.74, 1591–1599 (1998).
[CrossRef] [PubMed]

Kollner, M.

M. Kollner and J. Wolfrum, “How many photons are necessary for fluorescence-lifetime measurements?” Chem. Phys. Lett.200, 199 –204 (1992).
[CrossRef]

Lahmannsraben, H.-G.

C. Hille, M. Berg, L. Bressel, D. Munzke, P. Primus, H.-G. Lahmannsraben, and C. Dosche, “Time-domain fluorescence lifetime imaging for intracellular ph sensing in living tissues,” Anal. Bioanal. Chem.391, 1871–1879 (2008).
[CrossRef] [PubMed]

Laiho, L. H.

S. Pelet, M. J. R. Previte, L. H. Laiho, and P. T. C. So, “A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation.” Biophys. J.87, 2807–2817 (2004).
[CrossRef] [PubMed]

Lakowicz, J. R.

H.-J. Lin, P. Herman, and J. R. Lakowicz, “Fluorescence lifetime-resolved ph imaging of living cells,” Cytometry Part A52A, 77–89 (2003).
[CrossRef]

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Kluwer Academic/Plenum, 1999).
[CrossRef]

Li, Y.

M. Kneen, J. Farinas, Y. Li, and A. Verkman, “Green fluorescent protein as a noninvasive intracellular ph indicator,” Biophys. J.74, 1591–1599 (1998).
[CrossRef] [PubMed]

Lin, H.-J.

H.-J. Lin, P. Herman, and J. R. Lakowicz, “Fluorescence lifetime-resolved ph imaging of living cells,” Cytometry Part A52A, 77–89 (2003).
[CrossRef]

Mauro, T. M.

K. M. Hanson, M. J. Behne, N. P. Barry, T. M. Mauro, E. Gratton, and R. M. Clegg, “Two-photon fluorescence lifetime imaging of the skin stratum corneum ph gradient,” Biophys. J.83, 1682–1690 (2002).
[CrossRef] [PubMed]

McShane, M. J.

B. B. Collier and M. J. McShane, “Dynamic windowing algorithm for the fast and accurate determination of luminescence lifetimes,” Anal. Chem.84, 4725–4731 (2012).
[CrossRef] [PubMed]

Mller, C.

M. Heilemann, D. P. Herten, R. Heintzmann, C. Cremer, C. Mller, P. Tinnefeld, K. D. Weston, J. Wolfrum, and M. Sauer, “High-resolution colocalization of single dye molecules by fluorescence lifetime imaging microscopy,” Anal. Chem.74, 3511–3517 (2002).
[CrossRef] [PubMed]

Munzke, D.

C. Hille, M. Berg, L. Bressel, D. Munzke, P. Primus, H.-G. Lahmannsraben, and C. Dosche, “Time-domain fluorescence lifetime imaging for intracellular ph sensing in living tissues,” Anal. Bioanal. Chem.391, 1871–1879 (2008).
[CrossRef] [PubMed]

Mycek, M.-A.

C. W. Chang and M.-A. Mycek, “Enhancing precision in time-domain fluorescence lifetime imaging,” J. Biomed. Opt.15, 056013 (2010).
[CrossRef] [PubMed]

D. Sud and M.-A. Mycek, “Image restoration for fluorescence lifetime imaging microscopy (FLIM),” Opt. Express16, 19192–19200 (2008).
[CrossRef]

Pelet, S.

S. Pelet, M. J. R. Previte, L. H. Laiho, and P. T. C. So, “A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation.” Biophys. J.87, 2807–2817 (2004).
[CrossRef] [PubMed]

Philip, J.

Prendergast, F. G.

Z. Bajzer, T. M. Therneau, J. C. Sharp, and F. G. Prendergast, “Maximum likelihood method for the analysis of time-resolved fluorescence decay curves,” Eur. Biophys. J.20, 247–262 (1991).
[CrossRef]

Previte, M. J. R.

S. Pelet, M. J. R. Previte, L. H. Laiho, and P. T. C. So, “A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation.” Biophys. J.87, 2807–2817 (2004).
[CrossRef] [PubMed]

Primus, P.

C. Hille, M. Berg, L. Bressel, D. Munzke, P. Primus, H.-G. Lahmannsraben, and C. Dosche, “Time-domain fluorescence lifetime imaging for intracellular ph sensing in living tissues,” Anal. Bioanal. Chem.391, 1871–1879 (2008).
[CrossRef] [PubMed]

Roda-Navarro, P.

Rogers, W.

J. Fessler and W. Rogers, “Spatial resolution properties of penalized-likelihood image reconstruction: space-invariant tomographs,” IEEE Trans. Image Process., 5, 1346–1358 (1996).
[CrossRef] [PubMed]

Ruan, Q.

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt.8, 381–390 (2003).
[CrossRef] [PubMed]

Sauer, M.

M. Heilemann, D. P. Herten, R. Heintzmann, C. Cremer, C. Mller, P. Tinnefeld, K. D. Weston, J. Wolfrum, and M. Sauer, “High-resolution colocalization of single dye molecules by fluorescence lifetime imaging microscopy,” Anal. Chem.74, 3511–3517 (2002).
[CrossRef] [PubMed]

Seok, J.

Sharp, J. C.

Z. Bajzer, T. M. Therneau, J. C. Sharp, and F. G. Prendergast, “Maximum likelihood method for the analysis of time-resolved fluorescence decay curves,” Eur. Biophys. J.20, 247–262 (1991).
[CrossRef]

So, P. T. C.

S. Pelet, M. J. R. Previte, L. H. Laiho, and P. T. C. So, “A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation.” Biophys. J.87, 2807–2817 (2004).
[CrossRef] [PubMed]

Squire, A.

P. J. Verveer, A. Squire, and P. I. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J.78, 2127–2137 (2000).
[CrossRef] [PubMed]

A. Squire and P. I. H. Bastiaens, “Three dimensional image restoration in fluorescence lifetime imaging microscopy,” J. Microsc.193, 36–49 (1999).
[CrossRef] [PubMed]

Sud, D.

Sutin, J.

E. Gratton, S. Breusegem, J. Sutin, Q. Ruan, and N. Barry, “Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods,” J. Biomed. Opt.8, 381–390 (2003).
[CrossRef] [PubMed]

Therneau, T. M.

Z. Bajzer, T. M. Therneau, J. C. Sharp, and F. G. Prendergast, “Maximum likelihood method for the analysis of time-resolved fluorescence decay curves,” Eur. Biophys. J.20, 247–262 (1991).
[CrossRef]

Tinnefeld, P.

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Figures (8)

Fig. 1
Fig. 1

Estimated lifetime and amplitude images obtained with MLE: (a) τ1, (b) τ2, (c) A1, and (d) A2.

Fig. 2
Fig. 2

Estimated lifetime and amplitude images obtained with PMLEQ: (a) τ1, (b) τ2, (c) A1, and (d) A2.

Fig. 3
Fig. 3

Estimated lifetime and amplitude images obtained with PMLETV: (a) τ1, (b) τ2, (c) A1, and (d) A2.

Fig. 4
Fig. 4

Estimated lifetime and amplitude images obtained using MLE with binning of 3×3 window: (a) τ1, (b) τ2, (c) A1, and (d) A2.

Fig. 5
Fig. 5

Estimated lifetime and amplitude images from the polymer: (a) MLE from high photon counts, (b) MLE from low photon count, (c) PMLEQ from low photon counts, and (d) PMLETV from low photon counts.

Fig. 6
Fig. 6

Estimated lifetime and amplitude images from the HeLa cell using the MLE: (a) τ1, (b) τ2, (c) A1, (d) A2.

Fig. 7
Fig. 7

Estimated lifetime and amplitude images from the HeLa cell using the PMLEQ: (a) τ1, (b) τ2, (c) A1, and (d) A2.

Fig. 8
Fig. 8

Estimated lifetime and amplitude images from the HeLa cell using the PMLETV: (a) τ1, (b) τ2, (c) A1, and (d) A2.

Tables (4)

Tables Icon

Table 1 True values of the lifetimes, amplitudes and the average photon counts in the synthetic image (the lifetime is expressed in units of nanoseconds)

Tables Icon

Table 2 Bias and STD of the estimated lifetimes and amplitudes in the ellipse, square, and circle

Tables Icon

Table 3 Correlation between the true and estimated images

Tables Icon

Table 4 Average computation time in seconds

Equations (24)

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g ( t k , x i , y j ) = Poisson { λ ( t k ; θ i , j ) } , k = 0 , 1 , . , K 1 ,
λ ( t k ; θ i , j ) = h ( t k ) * f ( t k ; θ i , j ) .
f ( t ; θ i , j ) = p = 0 P 1 A p ( x i , y j ) e t τ p ( x i , y j ) ,
θ i , j = [ A 0 ( x i , y j ) , A 1 ( x i , y j ) , . . , A P 1 ( x i , y j ) , τ 0 ( x i , y j ) , Δ τ 1 ( x i , y j ) , . . , Δ τ P 1 ( x i , y j ) ] .
τ p ( x i , y j ) = τ 0 ( x i , y j ) + p = 1 P 1 Δ τ p ( x i , y j ) , p = 1 , 2 , . . , P 1 .
Θ = { θ i , j | ( i , j ) C } ,
L ( Θ ; g ) = ( i , j ) C L i , j ( θ i , j ; g i j ) ,
L i , j ( θ i , j ; g i j ) = k = 0 K 1 λ ( t k ; θ i , j ) + g ( t k , x i , y j ) log λ ( t k ; θ i , j ) log g ( t k , x i , y j ) ! .
Θ ^ = argmax Θ 0 L ( Θ ; g ) .
θ ^ i , j = argmax θ i , j > 0 L i , j ( θ i , j ; g i , j ) , ( i , j ) C .
Φ ( Θ ; g ) = L ( Θ ; g ) + β R ( Θ ) ,
R ( Θ ) = p = 0 2 P 1 ( i , j ) C ψ ( [ D i j h Θ ] p ) + ψ ( [ D i j v Θ ] p ) ,
ψ ( [ D i j h Θ ] p ) = { ϕ ( [ θ i + 1 , j θ i , j ] p ) , if ( i + 1 , j ) C 0 , otherwise ,
ψ ( [ D i j v Θ ] p ) = { ϕ ( [ θ i , j + 1 θ i , j ] p ) , if ( i , j + 1 ) C 0 , otherwise ,
ϕ ( x ) = x 2 + ε 2 ,
Φ s ( θ ; θ k ) Φ ( θ ) ,
Φ s ( θ k ; θ k ) = Φ ( θ k ) .
θ k + 1 = argmin θ Φ s ( θ ; θ k ) .
ϕ ( [ θ i + 1 , j θ i , j ] p ) q ( [ D i j h Θ ] p ; [ D i j h Θ k ] p ) = q ( 1 2 { 2 [ θ i + 1 , j θ i + 1 , j k ] p } + 1 2 { 2 [ θ i , j θ i , j k ] p } + [ D i j h Θ k ] p ; [ D i j h Θ k ] p ) 1 2 q ( 2 [ θ i + 1 , j θ i + 1 , j k ] p + [ D i j h Θ k ] p ; [ D i j h Θ k ] p ) + 1 2 q ( 2 [ θ i , j θ i , j k ] p + [ D i j h Θ k ] p ; [ D i j h Θ k ] p ) ,
( i , j ) C ψ ( [ D i j h Θ ] p ) ( i , j ) C R h ( [ θ i , j ] p ; Θ p k ) ,
R h ( [ θ i , j ] p ; Θ k ) = { 1 2 q ( 2 [ θ i , j θ i , j k ] p + [ D i 1 , j h Θ k ] p ; [ D i 1 , j h Θ k ] p ) + 1 2 q ( 2 [ θ i , j θ i , j k ] p + [ D i , j h Θ k ] p ; [ D i , j h Θ k ] p ) , ( i 1 , j ) C , ( i + 1 , j ) C 1 2 q ( 2 [ θ i , j θ i , j k ] p + [ D i 1 , j h Θ k ] p ; [ D i 1 , j h Θ k ] p ) , ( i 1 , j ) C , ( i + 1 , j ) C 1 2 q ( 2 [ θ i , j θ i , j k ] p + [ D i , j h Θ k ] p ; [ D i , j h Θ k ] p ) , ( i 1 , j ) C , ( i + 1 , j ) C 0 , ( i + 1 , j ) C , ( i 1 , j ) C .
R ( Θ ) R s ( Θ ; Θ k ) = ( i , j C ) R h v ( θ i , j ; Θ k ) ,
R h v ( θ i , j ; Θ k ) = p = 0 2 P 1 R h ( [ θ i , j ] p ; Θ k ) + R v ( [ θ i , j ] p ; Θ k ) .
θ i , j k + 1 = argmin θ i , j > 0 L i j ( θ i , j ; g i , j ) + β R s ( θ i , j ; Θ k ) .

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