Abstract

We investigate a fast optimization method for determining the minimizer of the negative Poisson likelihood function for the global analysis of fluorescence lifetime microscopy. Using the alternating optimization strategy, we iteratively solve a non-convex optimization problem to estimate the lifetime parameters and a convex optimization problem to estimate the concentration parameters. We effectively determine the minimizer of the non-convex optimization using the Gauss-Newton method and that of the convex optimization by applying the optimization transfer strategy, which is based on the convex inequality. In the simulation studies, the proposed method was able to determine the minimizer of the objective function significantly faster than the conventional simultaneous optimization method.

© 2014 Optical Society of America

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References

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  1. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Kluwer Academic/Plenum, 1999).
    [Crossref]
  2. J. Kim, J. Seok, H. Lee, and M. Lee, “Penalized maximum likelihood estimation of lifetime and amplitude images from multi-exponentially decaying fluorescence signals,” Opt. Express 21, 20240–20253 (2013).
    [Crossref] [PubMed]
  3. 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]
  4. C. W. Chang and M.-A. Mycek, “Total variation versus wavelet-based methods for image denoising in fluorescence lifetime imaging microscopy,” J. Biophotonics 5, 449–457 (2012).
    [Crossref] [PubMed]
  5. C. W. Chang and M.-A. Mycek, “Enhancing precision in time-domain fluorescence lifetime imaging,” J. Biomed. Opt. 15, 056013 (2010).
    [Crossref] [PubMed]
  6. J. Salmon, C.-A. Deledalle, R. Willett, and Z. Harmany, “Poisson noise reduction with non-local PCA,” in proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2012), pp. 1109–1112.
  7. R. Giryes and M. Elad, “Sparsity based poisson denoising,” in proceedings of IEEE Convention of Electrical Electronics Engineers in Israel (IEEE, 2012), pp. 1–5.
  8. V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proceedings of the National Academy of Sciences 109, E1679–E1687 (2012).
    [Crossref]
  9. H. E. Grecco, P. Roda-Navarro, and P. J. Verveer, “Global analysis of time correlated single photon counting FRER-FLIM data,” Opt. Express 17, 6493–6508 (2009).
    [Crossref] [PubMed]
  10. 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]
  11. J. Kim and J. Seok, “Statistical properties of amplitude and decay parameter estimators for fluorescence lifetime imaging,” Opt. Express 21, 6061–6075 (2013).
    [Crossref] [PubMed]
  12. S. C. Warren, A. Margineanu, D. Alibhai, D. J. Kelly, C. Talbot, Y. Alexandrov, I. Munro, M. Katan, C. Dunsby, and P. M. W. French, “Rapid global fitting of large fluorescence lifetime imaging microscopy datasets,” PLoS ONE 8, e70687 (2013).
    [Crossref] [PubMed]
  13. J. Fessler, E. Ficaro, N. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imag. 16, 166–175 (1997).
    [Crossref]
  14. J. Fessler, “Image reconstruction: Algorithms and analysis,” Online preprint of book in preparation.
  15. K. Lange, Optimization, Springer Texts in Statistics (Springer, 2004).
    [Crossref]
  16. U. Niesen, D. Shah, and G. W. Wornell, “Adaptive alternating minimization algorithms,” IEEE Trans. Inf. Theory 55, 1423–1429 (2009).
    [Crossref]
  17. Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci.248–272 (2008).
    [Crossref]
  18. M. Figueiredo and J. Bioucas-Dias, “Restoration of poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19, 3133–3145 (2010).
    [Crossref] [PubMed]
  19. A. Jezierska, C. Chaux, J.-C. Pesquet, H. Talbot, and G. Engler, “An EM approach for time-variant poisson-gaussian model parameter estimation,” IEEE Trans. Signal Process. 62, 17–30 (2014).
    [Crossref]
  20. C. W. Chang and M.-A. Mycek, “Precise fluorophore lifetime mapping in live-cell, multi-photon excitation microscopy,” Opt. Express 18, 8688–8696 (2010).
    [Crossref] [PubMed]
  21. P. Roudot, C. Kervrann, F. Waharte, and J. Boulanger, “Lifetime map reconstruction in frequency-domain fluorescence lifetime imaging microscopy,” in proceedings of IEEE International Conference on Image Processing, (IEEE, 2012), pp. 2537–2540.
  22. P. Roudot, C. Kervrann, J. Boulanger, and F. Waharte, “Noise modeling for intensified camera in fluorescence imaging: Application to image denoising,” in proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2013), pp. 600–603.
  23. W. H. Press, Numerical recipes : the art of scientific computing, 3rd ed. (Cambridge University, 2007).
  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. J. Moré and D. Sorensen, “Computing a trust region step,” SIAM J. Sci. Comput. 4, 553–572 (1983).
    [Crossref]
  26. M. A. Branch, T. F. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” SIAM J. Sci. Comput. 21, 1–23 (1999).
    [Crossref]
  27. R. Byrd, R. Schnabel, and G. Shultz, “Approximate solution of the trust region problem by minimization over two-dimensional subspaces,” Math. Program. 40, 247–263 (1988).
    [Crossref]

2014 (1)

A. Jezierska, C. Chaux, J.-C. Pesquet, H. Talbot, and G. Engler, “An EM approach for time-variant poisson-gaussian model parameter estimation,” IEEE Trans. Signal Process. 62, 17–30 (2014).
[Crossref]

2013 (3)

2012 (2)

C. W. Chang and M.-A. Mycek, “Total variation versus wavelet-based methods for image denoising in fluorescence lifetime imaging microscopy,” J. Biophotonics 5, 449–457 (2012).
[Crossref] [PubMed]

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proceedings of the National Academy of Sciences 109, E1679–E1687 (2012).
[Crossref]

2010 (3)

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

M. Figueiredo and J. Bioucas-Dias, “Restoration of poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19, 3133–3145 (2010).
[Crossref] [PubMed]

C. W. Chang and M.-A. Mycek, “Precise fluorophore lifetime mapping in live-cell, multi-photon excitation microscopy,” Opt. Express 18, 8688–8696 (2010).
[Crossref] [PubMed]

2009 (2)

U. Niesen, D. Shah, and G. W. Wornell, “Adaptive alternating minimization algorithms,” IEEE Trans. Inf. Theory 55, 1423–1429 (2009).
[Crossref]

H. E. Grecco, P. Roda-Navarro, and P. J. Verveer, “Global analysis of time correlated single photon counting FRER-FLIM data,” Opt. Express 17, 6493–6508 (2009).
[Crossref] [PubMed]

2004 (1)

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]

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)

M. A. Branch, T. F. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” SIAM J. Sci. Comput. 21, 1–23 (1999).
[Crossref]

1997 (1)

J. Fessler, E. Ficaro, N. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imag. 16, 166–175 (1997).
[Crossref]

1995 (1)

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

1988 (1)

R. Byrd, R. Schnabel, and G. Shultz, “Approximate solution of the trust region problem by minimization over two-dimensional subspaces,” Math. Program. 40, 247–263 (1988).
[Crossref]

1983 (1)

J. Moré and D. Sorensen, “Computing a trust region step,” SIAM J. Sci. Comput. 4, 553–572 (1983).
[Crossref]

Alexandrov, Y.

S. C. Warren, A. Margineanu, D. Alibhai, D. J. Kelly, C. Talbot, Y. Alexandrov, I. Munro, M. Katan, C. Dunsby, and P. M. W. French, “Rapid global fitting of large fluorescence lifetime imaging microscopy datasets,” PLoS ONE 8, e70687 (2013).
[Crossref] [PubMed]

Alibhai, D.

S. C. Warren, A. Margineanu, D. Alibhai, D. J. Kelly, C. Talbot, Y. Alexandrov, I. Munro, M. Katan, C. Dunsby, and P. M. W. French, “Rapid global fitting of large fluorescence lifetime imaging microscopy datasets,” PLoS ONE 8, e70687 (2013).
[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]

Bioucas-Dias, J.

M. Figueiredo and J. Bioucas-Dias, “Restoration of poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19, 3133–3145 (2010).
[Crossref] [PubMed]

Bobin, J.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proceedings of the National Academy of Sciences 109, E1679–E1687 (2012).
[Crossref]

Boulanger, J.

P. Roudot, C. Kervrann, F. Waharte, and J. Boulanger, “Lifetime map reconstruction in frequency-domain fluorescence lifetime imaging microscopy,” in proceedings of IEEE International Conference on Image Processing, (IEEE, 2012), pp. 2537–2540.

P. Roudot, C. Kervrann, J. Boulanger, and F. Waharte, “Noise modeling for intensified camera in fluorescence imaging: Application to image denoising,” in proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2013), pp. 600–603.

Branch, M. A.

M. A. Branch, T. F. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” SIAM J. Sci. Comput. 21, 1–23 (1999).
[Crossref]

Byrd, R.

R. Byrd, R. Schnabel, and G. Shultz, “Approximate solution of the trust region problem by minimization over two-dimensional subspaces,” Math. Program. 40, 247–263 (1988).
[Crossref]

Candes, E.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proceedings of the National Academy of Sciences 109, E1679–E1687 (2012).
[Crossref]

Chahid, M.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proceedings of the National Academy of Sciences 109, E1679–E1687 (2012).
[Crossref]

Chang, C. W.

C. W. Chang and M.-A. Mycek, “Total variation versus wavelet-based methods for image denoising in fluorescence lifetime imaging microscopy,” J. Biophotonics 5, 449–457 (2012).
[Crossref] [PubMed]

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

C. W. Chang and M.-A. Mycek, “Precise fluorophore lifetime mapping in live-cell, multi-photon excitation microscopy,” Opt. Express 18, 8688–8696 (2010).
[Crossref] [PubMed]

Chaux, C.

A. Jezierska, C. Chaux, J.-C. Pesquet, H. Talbot, and G. Engler, “An EM approach for time-variant poisson-gaussian model parameter estimation,” IEEE Trans. Signal Process. 62, 17–30 (2014).
[Crossref]

Clinthorne, N.

J. Fessler, E. Ficaro, N. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imag. 16, 166–175 (1997).
[Crossref]

Coleman, T. F.

M. A. Branch, T. F. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” SIAM J. Sci. Comput. 21, 1–23 (1999).
[Crossref]

Dahan, M.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proceedings of the National Academy of Sciences 109, E1679–E1687 (2012).
[Crossref]

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]

Deledalle, C.-A.

J. Salmon, C.-A. Deledalle, R. Willett, and Z. Harmany, “Poisson noise reduction with non-local PCA,” in proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2012), pp. 1109–1112.

Dunsby, C.

S. C. Warren, A. Margineanu, D. Alibhai, D. J. Kelly, C. Talbot, Y. Alexandrov, I. Munro, M. Katan, C. Dunsby, and P. M. W. French, “Rapid global fitting of large fluorescence lifetime imaging microscopy datasets,” PLoS ONE 8, e70687 (2013).
[Crossref] [PubMed]

Elad, M.

R. Giryes and M. Elad, “Sparsity based poisson denoising,” in proceedings of IEEE Convention of Electrical Electronics Engineers in Israel (IEEE, 2012), pp. 1–5.

Engler, G.

A. Jezierska, C. Chaux, J.-C. Pesquet, H. Talbot, and G. Engler, “An EM approach for time-variant poisson-gaussian model parameter estimation,” IEEE Trans. Signal Process. 62, 17–30 (2014).
[Crossref]

Fessler, J.

J. Fessler, E. Ficaro, N. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imag. 16, 166–175 (1997).
[Crossref]

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

Ficaro, E.

J. Fessler, E. Ficaro, N. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imag. 16, 166–175 (1997).
[Crossref]

Figueiredo, M.

M. Figueiredo and J. Bioucas-Dias, “Restoration of poissonian images using alternating direction optimization,” IEEE Trans. Image Process. 19, 3133–3145 (2010).
[Crossref] [PubMed]

French, P. M. W.

S. C. Warren, A. Margineanu, D. Alibhai, D. J. Kelly, C. Talbot, Y. Alexandrov, I. Munro, M. Katan, C. Dunsby, and P. M. W. French, “Rapid global fitting of large fluorescence lifetime imaging microscopy datasets,” PLoS ONE 8, e70687 (2013).
[Crossref] [PubMed]

Giryes, R.

R. Giryes and M. Elad, “Sparsity based poisson denoising,” in proceedings of IEEE Convention of Electrical Electronics Engineers in Israel (IEEE, 2012), pp. 1–5.

Grecco, H. E.

Harmany, Z.

J. Salmon, C.-A. Deledalle, R. Willett, and Z. Harmany, “Poisson noise reduction with non-local PCA,” in proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2012), pp. 1109–1112.

Jezierska, A.

A. Jezierska, C. Chaux, J.-C. Pesquet, H. Talbot, and G. Engler, “An EM approach for time-variant poisson-gaussian model parameter estimation,” IEEE Trans. Signal Process. 62, 17–30 (2014).
[Crossref]

Katan, M.

S. C. Warren, A. Margineanu, D. Alibhai, D. J. Kelly, C. Talbot, Y. Alexandrov, I. Munro, M. Katan, C. Dunsby, and P. M. W. French, “Rapid global fitting of large fluorescence lifetime imaging microscopy datasets,” PLoS ONE 8, e70687 (2013).
[Crossref] [PubMed]

Kelly, D. J.

S. C. Warren, A. Margineanu, D. Alibhai, D. J. Kelly, C. Talbot, Y. Alexandrov, I. Munro, M. Katan, C. Dunsby, and P. M. W. French, “Rapid global fitting of large fluorescence lifetime imaging microscopy datasets,” PLoS ONE 8, e70687 (2013).
[Crossref] [PubMed]

Kervrann, C.

P. Roudot, C. Kervrann, J. Boulanger, and F. Waharte, “Noise modeling for intensified camera in fluorescence imaging: Application to image denoising,” in proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2013), pp. 600–603.

P. Roudot, C. Kervrann, F. Waharte, and J. Boulanger, “Lifetime map reconstruction in frequency-domain fluorescence lifetime imaging microscopy,” in proceedings of IEEE International Conference on Image Processing, (IEEE, 2012), pp. 2537–2540.

Kim, J.

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.

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

Lange, K.

J. Fessler, E. Ficaro, N. Clinthorne, and K. Lange, “Grouped-coordinate ascent algorithms for penalized-likelihood transmission image reconstruction,” IEEE Trans. Med. Imag. 16, 166–175 (1997).
[Crossref]

K. Lange, Optimization, Springer Texts in Statistics (Springer, 2004).
[Crossref]

Lee, H.

Lee, M.

Li, Y.

M. A. Branch, T. F. Coleman, and Y. Li, “A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems,” SIAM J. Sci. Comput. 21, 1–23 (1999).
[Crossref]

Margineanu, A.

S. C. Warren, A. Margineanu, D. Alibhai, D. J. Kelly, C. Talbot, Y. Alexandrov, I. Munro, M. Katan, C. Dunsby, and P. M. W. French, “Rapid global fitting of large fluorescence lifetime imaging microscopy datasets,” PLoS ONE 8, e70687 (2013).
[Crossref] [PubMed]

Moré, J.

J. Moré and D. Sorensen, “Computing a trust region step,” SIAM J. Sci. Comput. 4, 553–572 (1983).
[Crossref]

Mousavi, H. S.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proceedings of the National Academy of Sciences 109, E1679–E1687 (2012).
[Crossref]

Munro, I.

S. C. Warren, A. Margineanu, D. Alibhai, D. J. Kelly, C. Talbot, Y. Alexandrov, I. Munro, M. Katan, C. Dunsby, and P. M. W. French, “Rapid global fitting of large fluorescence lifetime imaging microscopy datasets,” PLoS ONE 8, e70687 (2013).
[Crossref] [PubMed]

Mycek, M.-A.

C. W. Chang and M.-A. Mycek, “Total variation versus wavelet-based methods for image denoising in fluorescence lifetime imaging microscopy,” J. Biophotonics 5, 449–457 (2012).
[Crossref] [PubMed]

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

C. W. Chang and M.-A. Mycek, “Precise fluorophore lifetime mapping in live-cell, multi-photon excitation microscopy,” Opt. Express 18, 8688–8696 (2010).
[Crossref] [PubMed]

Niesen, U.

U. Niesen, D. Shah, and G. W. Wornell, “Adaptive alternating minimization algorithms,” IEEE Trans. Inf. Theory 55, 1423–1429 (2009).
[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]

Pesquet, J.-C.

A. Jezierska, C. Chaux, J.-C. Pesquet, H. Talbot, and G. Engler, “An EM approach for time-variant poisson-gaussian model parameter estimation,” IEEE Trans. Signal Process. 62, 17–30 (2014).
[Crossref]

Press, W. H.

W. H. Press, Numerical recipes : the art of scientific computing, 3rd ed. (Cambridge University, 2007).

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]

Roda-Navarro, P.

Roudot, P.

P. Roudot, C. Kervrann, F. Waharte, and J. Boulanger, “Lifetime map reconstruction in frequency-domain fluorescence lifetime imaging microscopy,” in proceedings of IEEE International Conference on Image Processing, (IEEE, 2012), pp. 2537–2540.

P. Roudot, C. Kervrann, J. Boulanger, and F. Waharte, “Noise modeling for intensified camera in fluorescence imaging: Application to image denoising,” in proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2013), pp. 600–603.

Salmon, J.

J. Salmon, C.-A. Deledalle, R. Willett, and Z. Harmany, “Poisson noise reduction with non-local PCA,” in proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2012), pp. 1109–1112.

Schnabel, R.

R. Byrd, R. Schnabel, and G. Shultz, “Approximate solution of the trust region problem by minimization over two-dimensional subspaces,” Math. Program. 40, 247–263 (1988).
[Crossref]

Seok, J.

Shah, D.

U. Niesen, D. Shah, and G. W. Wornell, “Adaptive alternating minimization algorithms,” IEEE Trans. Inf. Theory 55, 1423–1429 (2009).
[Crossref]

Shultz, G.

R. Byrd, R. Schnabel, and G. Shultz, “Approximate solution of the trust region problem by minimization over two-dimensional subspaces,” Math. Program. 40, 247–263 (1988).
[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]

Sorensen, D.

J. Moré and D. Sorensen, “Computing a trust region step,” SIAM J. Sci. Comput. 4, 553–572 (1983).
[Crossref]

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]

Studer, V.

V. Studer, J. Bobin, M. Chahid, H. S. Mousavi, E. Candes, and M. Dahan, “Compressive fluorescence microscopy for biological and hyperspectral imaging,” Proceedings of the National Academy of Sciences 109, E1679–E1687 (2012).
[Crossref]

Talbot, C.

S. C. Warren, A. Margineanu, D. Alibhai, D. J. Kelly, C. Talbot, Y. Alexandrov, I. Munro, M. Katan, C. Dunsby, and P. M. W. French, “Rapid global fitting of large fluorescence lifetime imaging microscopy datasets,” PLoS ONE 8, e70687 (2013).
[Crossref] [PubMed]

Talbot, H.

A. Jezierska, C. Chaux, J.-C. Pesquet, H. Talbot, and G. Engler, “An EM approach for time-variant poisson-gaussian model parameter estimation,” IEEE Trans. Signal Process. 62, 17–30 (2014).
[Crossref]

Verveer, P. J.

H. E. Grecco, P. Roda-Navarro, and P. J. Verveer, “Global analysis of time correlated single photon counting FRER-FLIM data,” Opt. Express 17, 6493–6508 (2009).
[Crossref] [PubMed]

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]

Waharte, F.

P. Roudot, C. Kervrann, J. Boulanger, and F. Waharte, “Noise modeling for intensified camera in fluorescence imaging: Application to image denoising,” in proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2013), pp. 600–603.

P. Roudot, C. Kervrann, F. Waharte, and J. Boulanger, “Lifetime map reconstruction in frequency-domain fluorescence lifetime imaging microscopy,” in proceedings of IEEE International Conference on Image Processing, (IEEE, 2012), pp. 2537–2540.

Wang, Y.

Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci.248–272 (2008).
[Crossref]

Warren, S. C.

S. C. Warren, A. Margineanu, D. Alibhai, D. J. Kelly, C. Talbot, Y. Alexandrov, I. Munro, M. Katan, C. Dunsby, and P. M. W. French, “Rapid global fitting of large fluorescence lifetime imaging microscopy datasets,” PLoS ONE 8, e70687 (2013).
[Crossref] [PubMed]

Willett, R.

J. Salmon, C.-A. Deledalle, R. Willett, and Z. Harmany, “Poisson noise reduction with non-local PCA,” in proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2012), pp. 1109–1112.

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Y. Wang, J. Yang, W. Yin, and Y. Zhang, “A new alternating minimization algorithm for total variation image reconstruction,” SIAM J. Imaging Sci.248–272 (2008).
[Crossref]

J. Salmon, C.-A. Deledalle, R. Willett, and Z. Harmany, “Poisson noise reduction with non-local PCA,” in proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2012), pp. 1109–1112.

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Figures (4)

Fig. 1
Fig. 1 Intensity parameter images from different optimization methods: (a) true intensity parameter image; (b) estimated intensity parameter image using pixel-wise independent optimization without global analysis; (c) estimated intensity parameter image using the trust region reflective simultaneous optimization method; (d) estimated intensity parameter image using the proposed method
Fig. 2
Fig. 2 Likelihood value and estimated parameters as functions of CPU time for different optimization methods: (a) likelihood; (b) τ1; (c) τ2; (d) A1 of (8, 16) location; (e) A2 of (8, 16) location;
Fig. 3
Fig. 3 True amplitude images in simulation 2: (a) amplitude 1; (b) amplitude 2; (c) amplitude 3;
Fig. 4
Fig. 4 Estimated decay parameters as functions of CPU time for different optimization methods: (a) τ1; (b) τ2; (c) amplitude 1 using the global analysis; (d) amplitude 2 using the global analysis; (e) amplitude 1 using the pixel-wise independent estimation; (f) amplitude 2 using the pixel-wise independent estimation;

Equations (20)

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y i ( t k ) ~ Poisson { λ i ( t k ; τ , A i ) } , k = 0 , 1 , , K 1 .
λ i ( t k ; τ , A i ) = j = 0 J 1 a i j g ( t k ; τ j ) ,
g ( t ; τ j ) = e t τ j * h ( t ) .
L ( τ , A ; y ) = k = 0 K 1 i = 0 I 1 λ i ( t k ; τ , A i ) + y i ( t k ) log λ i ( t k ; τ , A i ) log y i ( t k ) ! ,
( τ ^ , A ^ ) = argmin τ , A > 0 L ( τ , A ; y ) .
τ n + 1 = argmin τ > 0 L ( τ ; A n , y ) ,
A n + 1 = argmin A > 0 L ( A ; τ n + 1 , y ) .
τ n + 1 = τ n + H 1 ( τ n ; A , y ) L ( τ n ; A n , y ) ,
h p q = k = 0 K 1 i = 0 I 1 ( y i ( t k ) ( j a i j g ( t k ; τ j n ) ) 2 ) ( a i j t k τ p 2 g ( t k ; τ p n ) ) ( a i j t k τ q 2 g ( t k ; τ q n ) ) .
Q ( θ ; θ m ) Φ ( θ ) ,
Q ( θ m ; θ m ) = Φ ( θ m ) .
L ( A ; τ n + 1 , y ) = k = 0 K 1 i = 0 I 1 { j = 0 J 1 a i j g ( t k ; τ j n + 1 ) y i ( t k ) log ( j = 0 J 1 a i j g ( t k ; τ j n + 1 ) ) } .
j a i j g ( t k ; τ j n + 1 ) = j ( a i j ( n , m ) g ( t k ; τ j n + 1 ) j a i j ( n , m ) g ( t k ; τ j n + 1 ) ) ( a i j a i j ( n , m ) j a i j ( n , m ) g ( t k ; τ j n + 1 ) ) ,
log ( j ( a i j ( n , m ) g ( t k ; τ j n + 1 ) j a i j ( n , m ) g ( t k ; τ j n + 1 ) ) ( a i j a i j ( n , m ) j a i j ( n , m ) g ( t k ; τ j n + 1 ) ) ) j ( a i j ( n , m ) g ( t k ; τ j n + 1 ) j a i j ( n , m ) g ( t k ; τ j n + 1 ) ) log ( a i j a i j ( n , m ) j a i j ( n , m ) g ( t k ; τ j n + 1 ) ) .
Q ( A ; A ( n , m ) ) = i , j , k a i j g ( t k ; τ j n + 1 ) ( y i ( t k ) a i j ( n , m ) g ( t k ; τ j n + 1 ) j a i j ( n , m ) g ( t k ; τ j n + 1 ) ) log ( a i j a i j ( n , m ) j a i j ( n , m ) g ( t k ; τ j n + 1 ) ) .
Q ( A ; A ( n , m ) ) a i j = k g ( t k ; τ j n + 1 ) k y i ( t k ) ( a i j ( n , m ) g ( t k ; τ j n + 1 ) j a i j ( n , m ) g ( t k ; τ j n + 1 ) ) 1 a i j .
a i j ( n , m + 1 ) = a i j ( n , m ) k g ( t k ; τ j n + 1 ) k ( y i ( t k ) g ( t k ; τ j n + 1 ) j a i j n g ( t k ; τ j n + 1 ) ) .
a i j n + 1 = a i j ( n , M ) .
λ i ( t k ; τ 1 , τ 2 , c i 1 , A ) = A * { c i 1 g ( t k ; τ 1 ) + ( 1 c i 1 ) g ( t k ; τ 2 ) } ,
λ i ( t k ; τ 1 , τ 2 , A 1 , A 2 , A 3 ) = A 1 i g ( t k ; τ 1 ) + A 2 i g ( t k ; τ 2 ) + A 3 i g ( t k ; τ 2 ) ,

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