Abstract

One of the essential ways in which nonlinear image restoration algorithms differ from linear, convolution-type image restoration filters is their capability to restrict the restoration result to nonnegative intensities. The iterative constrained Tikhonov–Miller (ICTM) algorithm, for example, incorporates the nonnegativity constraint by clipping all negative values to zero after each iteration. This constraint will be effective only when the restored intensities have near-zero values. Therefore the background estimation will have an influence on the effectiveness of the nonnegativity constraint of these algorithms. We investigated quantitatively the dependency of the performance of the ICTM, Carrington, and Richardson–Lucy algorithms on the estimation of the background and compared it with the performance of the linear Tikhonov–Miller restoration filter. We found that the performance depends critically on the background estimation: An underestimation of the background will make the nonnegativity constraint ineffective, which results in a performance that does not differ much from the Tikhonov–Miller filter performance. A (small) overestimation, however, degrades the performance dramatically, since it results in a clipping of object intensities. We propose a novel general method to estimate the background based on the dependency of nonlinear restoration algorithms on the background, and we demonstrate its applicability on real confocal images.

© 2000 Optical Society of America

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  1. R. L. Lagendijk, J. Biemond, Iterative Identification and Restoration of Images, Vol. IP (Kluwer Academic, Dordrecht, The Netherlands, 1991).
  2. H. T. M. van der Voort, K. C. Strasters, “Restoration of confocal images for quantitative image analysis,” J. Microsc. 178, 165–181 (1995).
    [CrossRef]
  3. W. A. Carrington, “Image restoration in 3D microscopy with limited data,” in Bioimaging and Two-Dimensional Spectroscopy, L. C. Smith, ed., Proc. SPIE1205, 72–83 (1990).
    [CrossRef]
  4. W. A. Carrington, R. M. Lynch, E. M. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
    [CrossRef] [PubMed]
  5. T. J. Holmes, “Maximum-likelihood image restoration adapted for noncoherent optical imaging,” J. Opt. Soc. Am. A 5, 666–673 (1988).
    [CrossRef]
  6. G. M. P. van Kempen, “Image restoration in fluorescence microscopy,” Ph.D. Thesis (Delft University of Technology, Delft, The Netherlands, 1999).
  7. A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. B Sect. 39, 1–37 (1977).
  8. Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 80, 8–35 (1985).
    [CrossRef]
  9. L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113–121 (1982).
    [CrossRef]
  10. D. L. Snyder, A. M. Hammoud, R. L. White, “Image recovery from data acquired with a charge-coupled-device camera,” J. Opt. Soc. Am. A 10, 1014–1023 (1993).
    [CrossRef] [PubMed]
  11. G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, H. T. M. van der Voort, “A quantitative comparison of image restoration methods for confocal microscopy,” J. Microsc. 185, 354–365 (1997).
    [CrossRef]
  12. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 55–59 (1972).
    [CrossRef]
  13. R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 14, 709–720 (1979).
  14. A. K. Jain, Fundamentals of Digital Image Processing, Vol. IP (Prentice Hall, Englewood Cliffs, N.J., 1989).
  15. J.-A. Conchello, “Superesolution and convergence properties of the expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent images,” J. Opt. Soc. Am. A 15, 2609–2619 (1998).
    [CrossRef]
  16. J.-A. Conchello, J. G. McNally, “Fast regularization technique for expectation maximization algorithm for optical sectioning microscopy,” presented at the conference on Three-Dimensional Microscopy: Image Acquisition and Processing III, San Jose, Calif., February 1–3, 1996.
  17. H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).
  18. M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (IOP, London, 1998).
  19. L. J. van Vliet, D. Sudar, I. T. Young, “Digital fluorescence imaging using cooled charge-coupled device array cameras,” in Cell Biology: A Laboratory Handbook, 2nd ed., J. E. Celis, ed. (Academic, London, 1998), Vol. 3, pp. 109–120.
  20. J. Art, “Photon detectors for confocal microscopy,” in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed. (Plenum, New York, 1995), pp. 183–196.
  21. A. N. Tikhonov, V. Y. Arsenin, Solutions of Ill-Posed Problems (Wiley, New York, 1977).
  22. T. Wilson, J. B. Tan, “Three dimensional image reconstruction in conventional and confocal microscopy,” Bioimaging 1, 176–184 (1993).
    [CrossRef]
  23. G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, “Application of image restoration methods for confocal fluorescence microscopy,” presented at the conference on Three-Dimensional Microscopy: Image Acquisition and Processing IV, San Jose, Calif., February 12–13, 1997.
  24. P. J. Verveer, M. J. Gemkow, T. M. Jovin, “A comparison of image restoration approaches applied to three-dimensional confocal and wide-field fluorescence microscopy,” J. Microsc. 193, 50–61 (1999).
    [CrossRef]
  25. P. J. Verveer, T. M. Jovin, “Acceleration of the ICTM image restoration algorithm,” J. Microsc. 188, 191–195 (1997).
    [CrossRef]
  26. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed., Vol. CS (Cambridge U. Press, Cambridge, UK, 1992).
  27. W. A. Carrington, K. E. Fogarty, “3-D molecular distribution in living cells by deconvolution of optical sections using light microscopy,” presented at the 13th Annual Northeast Bioengineering Conference, Philadelphia, Pa., March 12–13, 1987.
  28. D. L. Snyder, M. I. Miller, Random Point Processes in Time and Space, Vol. SP (Springer Verlag, Berlin, 1991).
  29. K. M. Perry, S. J. Reeves, “Generalized cross-validation as a stopping rule for the Richardson–Lucy algorithm,” presented at the conference on Restoration of HST Images and Spectra II, Baltimore, Md., November 18–19, 1993.
  30. P. W. Verbeek, H. A. Vrooman, L. J. van Vliet, “Low-level image processing by max-min filters,” Signal Process. 15, 249–258 (1988).
    [CrossRef]
  31. I. T. Young, “Automated Leukocyte Recognition,” in Automated Cell Identification and Cell Sorting, G. L. Wied, G. F. Bahr, eds. (Academic, New York, 1970), pp. 187–194.
  32. I. Heertje, E. C. Roijers, H. A. C. M. Hendrickx, “Liquid crystalline phases in the structuring of food products,” Lebensm.-Wiss. Technol. 31, 387–396 (1998).
    [CrossRef]
  33. G. M. P. van Kempen, N. van den Brink, L. J. van Vliet, M. van Ginkel, P. W. Verbeek, H. Blonk, “The application of a local dimensionality estimator to the analysis of 3-D microscopic network structures,” presented at the 11th Scandinavian Conference on Image Analysis, Kangerlussuaq, Greenland, June 7–11, 1999.
  34. P. J. Verveer, “Computational and optical methods for improving resolution and signal quality in fluorescence microscopy,” Ph.D. thesis (Delft University of Technology, Delft, The Netherlands, 1998).
  35. G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems,” IEEE Trans. Acoust., Speech, Signal Process. 37, 2024–2036 (1989).
    [CrossRef]

1999 (1)

P. J. Verveer, M. J. Gemkow, T. M. Jovin, “A comparison of image restoration approaches applied to three-dimensional confocal and wide-field fluorescence microscopy,” J. Microsc. 193, 50–61 (1999).
[CrossRef]

1998 (2)

I. Heertje, E. C. Roijers, H. A. C. M. Hendrickx, “Liquid crystalline phases in the structuring of food products,” Lebensm.-Wiss. Technol. 31, 387–396 (1998).
[CrossRef]

J.-A. Conchello, “Superesolution and convergence properties of the expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent images,” J. Opt. Soc. Am. A 15, 2609–2619 (1998).
[CrossRef]

1997 (2)

P. J. Verveer, T. M. Jovin, “Acceleration of the ICTM image restoration algorithm,” J. Microsc. 188, 191–195 (1997).
[CrossRef]

G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, H. T. M. van der Voort, “A quantitative comparison of image restoration methods for confocal microscopy,” J. Microsc. 185, 354–365 (1997).
[CrossRef]

1995 (2)

H. T. M. van der Voort, K. C. Strasters, “Restoration of confocal images for quantitative image analysis,” J. Microsc. 178, 165–181 (1995).
[CrossRef]

W. A. Carrington, R. M. Lynch, E. M. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

1993 (2)

T. Wilson, J. B. Tan, “Three dimensional image reconstruction in conventional and confocal microscopy,” Bioimaging 1, 176–184 (1993).
[CrossRef]

D. L. Snyder, A. M. Hammoud, R. L. White, “Image recovery from data acquired with a charge-coupled-device camera,” J. Opt. Soc. Am. A 10, 1014–1023 (1993).
[CrossRef] [PubMed]

1989 (1)

G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems,” IEEE Trans. Acoust., Speech, Signal Process. 37, 2024–2036 (1989).
[CrossRef]

1988 (2)

T. J. Holmes, “Maximum-likelihood image restoration adapted for noncoherent optical imaging,” J. Opt. Soc. Am. A 5, 666–673 (1988).
[CrossRef]

P. W. Verbeek, H. A. Vrooman, L. J. van Vliet, “Low-level image processing by max-min filters,” Signal Process. 15, 249–258 (1988).
[CrossRef]

1985 (1)

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 80, 8–35 (1985).
[CrossRef]

1982 (1)

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113–121 (1982).
[CrossRef]

1979 (1)

R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 14, 709–720 (1979).

1977 (1)

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. B Sect. 39, 1–37 (1977).

1972 (1)

Andrews, H. C.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Arsenin, V. Y.

A. N. Tikhonov, V. Y. Arsenin, Solutions of Ill-Posed Problems (Wiley, New York, 1977).

Art, J.

J. Art, “Photon detectors for confocal microscopy,” in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed. (Plenum, New York, 1995), pp. 183–196.

Bertero, M.

M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (IOP, London, 1998).

Biemond, J.

R. L. Lagendijk, J. Biemond, Iterative Identification and Restoration of Images, Vol. IP (Kluwer Academic, Dordrecht, The Netherlands, 1991).

Blonk, H.

G. M. P. van Kempen, N. van den Brink, L. J. van Vliet, M. van Ginkel, P. W. Verbeek, H. Blonk, “The application of a local dimensionality estimator to the analysis of 3-D microscopic network structures,” presented at the 11th Scandinavian Conference on Image Analysis, Kangerlussuaq, Greenland, June 7–11, 1999.

Boccacci, P.

M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (IOP, London, 1998).

Carrington, W. A.

W. A. Carrington, R. M. Lynch, E. M. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

W. A. Carrington, “Image restoration in 3D microscopy with limited data,” in Bioimaging and Two-Dimensional Spectroscopy, L. C. Smith, ed., Proc. SPIE1205, 72–83 (1990).
[CrossRef]

W. A. Carrington, K. E. Fogarty, “3-D molecular distribution in living cells by deconvolution of optical sections using light microscopy,” presented at the 13th Annual Northeast Bioengineering Conference, Philadelphia, Pa., March 12–13, 1987.

Conchello, J.-A.

J.-A. Conchello, “Superesolution and convergence properties of the expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent images,” J. Opt. Soc. Am. A 15, 2609–2619 (1998).
[CrossRef]

J.-A. Conchello, J. G. McNally, “Fast regularization technique for expectation maximization algorithm for optical sectioning microscopy,” presented at the conference on Three-Dimensional Microscopy: Image Acquisition and Processing III, San Jose, Calif., February 1–3, 1996.

Demoment, G.

G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems,” IEEE Trans. Acoust., Speech, Signal Process. 37, 2024–2036 (1989).
[CrossRef]

Dempster, A. P.

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. B Sect. 39, 1–37 (1977).

Fay, F. S.

W. A. Carrington, R. M. Lynch, E. M. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed., Vol. CS (Cambridge U. Press, Cambridge, UK, 1992).

Fogarty, K. E.

W. A. Carrington, R. M. Lynch, E. M. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

W. A. Carrington, K. E. Fogarty, “3-D molecular distribution in living cells by deconvolution of optical sections using light microscopy,” presented at the 13th Annual Northeast Bioengineering Conference, Philadelphia, Pa., March 12–13, 1987.

Gemkow, M. J.

P. J. Verveer, M. J. Gemkow, T. M. Jovin, “A comparison of image restoration approaches applied to three-dimensional confocal and wide-field fluorescence microscopy,” J. Microsc. 193, 50–61 (1999).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 14, 709–720 (1979).

Hammoud, A. M.

Heertje, I.

I. Heertje, E. C. Roijers, H. A. C. M. Hendrickx, “Liquid crystalline phases in the structuring of food products,” Lebensm.-Wiss. Technol. 31, 387–396 (1998).
[CrossRef]

Hendrickx, H. A. C. M.

I. Heertje, E. C. Roijers, H. A. C. M. Hendrickx, “Liquid crystalline phases in the structuring of food products,” Lebensm.-Wiss. Technol. 31, 387–396 (1998).
[CrossRef]

Holmes, T. J.

Hunt, B. R.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Isenberg, G.

W. A. Carrington, R. M. Lynch, E. M. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing, Vol. IP (Prentice Hall, Englewood Cliffs, N.J., 1989).

Jovin, T. M.

P. J. Verveer, M. J. Gemkow, T. M. Jovin, “A comparison of image restoration approaches applied to three-dimensional confocal and wide-field fluorescence microscopy,” J. Microsc. 193, 50–61 (1999).
[CrossRef]

P. J. Verveer, T. M. Jovin, “Acceleration of the ICTM image restoration algorithm,” J. Microsc. 188, 191–195 (1997).
[CrossRef]

Kaufman, L.

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 80, 8–35 (1985).
[CrossRef]

Lagendijk, R. L.

R. L. Lagendijk, J. Biemond, Iterative Identification and Restoration of Images, Vol. IP (Kluwer Academic, Dordrecht, The Netherlands, 1991).

Laird, N. M.

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. B Sect. 39, 1–37 (1977).

Lynch, R. M.

W. A. Carrington, R. M. Lynch, E. M. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

McNally, J. G.

J.-A. Conchello, J. G. McNally, “Fast regularization technique for expectation maximization algorithm for optical sectioning microscopy,” presented at the conference on Three-Dimensional Microscopy: Image Acquisition and Processing III, San Jose, Calif., February 1–3, 1996.

Miller, M. I.

D. L. Snyder, M. I. Miller, Random Point Processes in Time and Space, Vol. SP (Springer Verlag, Berlin, 1991).

Moore, E. M.

W. A. Carrington, R. M. Lynch, E. M. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

Perry, K. M.

K. M. Perry, S. J. Reeves, “Generalized cross-validation as a stopping rule for the Richardson–Lucy algorithm,” presented at the conference on Restoration of HST Images and Spectra II, Baltimore, Md., November 18–19, 1993.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed., Vol. CS (Cambridge U. Press, Cambridge, UK, 1992).

Reeves, S. J.

K. M. Perry, S. J. Reeves, “Generalized cross-validation as a stopping rule for the Richardson–Lucy algorithm,” presented at the conference on Restoration of HST Images and Spectra II, Baltimore, Md., November 18–19, 1993.

Richardson, W. H.

Roijers, E. C.

I. Heertje, E. C. Roijers, H. A. C. M. Hendrickx, “Liquid crystalline phases in the structuring of food products,” Lebensm.-Wiss. Technol. 31, 387–396 (1998).
[CrossRef]

Rubin, D. B.

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. B Sect. 39, 1–37 (1977).

Shepp, L. A.

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 80, 8–35 (1985).
[CrossRef]

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113–121 (1982).
[CrossRef]

Snyder, D. L.

Strasters, K. C.

H. T. M. van der Voort, K. C. Strasters, “Restoration of confocal images for quantitative image analysis,” J. Microsc. 178, 165–181 (1995).
[CrossRef]

Sudar, D.

L. J. van Vliet, D. Sudar, I. T. Young, “Digital fluorescence imaging using cooled charge-coupled device array cameras,” in Cell Biology: A Laboratory Handbook, 2nd ed., J. E. Celis, ed. (Academic, London, 1998), Vol. 3, pp. 109–120.

Tan, J. B.

T. Wilson, J. B. Tan, “Three dimensional image reconstruction in conventional and confocal microscopy,” Bioimaging 1, 176–184 (1993).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed., Vol. CS (Cambridge U. Press, Cambridge, UK, 1992).

Tikhonov, A. N.

A. N. Tikhonov, V. Y. Arsenin, Solutions of Ill-Posed Problems (Wiley, New York, 1977).

van den Brink, N.

G. M. P. van Kempen, N. van den Brink, L. J. van Vliet, M. van Ginkel, P. W. Verbeek, H. Blonk, “The application of a local dimensionality estimator to the analysis of 3-D microscopic network structures,” presented at the 11th Scandinavian Conference on Image Analysis, Kangerlussuaq, Greenland, June 7–11, 1999.

van der Voort, H. T. M.

G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, H. T. M. van der Voort, “A quantitative comparison of image restoration methods for confocal microscopy,” J. Microsc. 185, 354–365 (1997).
[CrossRef]

H. T. M. van der Voort, K. C. Strasters, “Restoration of confocal images for quantitative image analysis,” J. Microsc. 178, 165–181 (1995).
[CrossRef]

van Ginkel, M.

G. M. P. van Kempen, N. van den Brink, L. J. van Vliet, M. van Ginkel, P. W. Verbeek, H. Blonk, “The application of a local dimensionality estimator to the analysis of 3-D microscopic network structures,” presented at the 11th Scandinavian Conference on Image Analysis, Kangerlussuaq, Greenland, June 7–11, 1999.

van Kempen, G. M. P.

G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, H. T. M. van der Voort, “A quantitative comparison of image restoration methods for confocal microscopy,” J. Microsc. 185, 354–365 (1997).
[CrossRef]

G. M. P. van Kempen, “Image restoration in fluorescence microscopy,” Ph.D. Thesis (Delft University of Technology, Delft, The Netherlands, 1999).

G. M. P. van Kempen, N. van den Brink, L. J. van Vliet, M. van Ginkel, P. W. Verbeek, H. Blonk, “The application of a local dimensionality estimator to the analysis of 3-D microscopic network structures,” presented at the 11th Scandinavian Conference on Image Analysis, Kangerlussuaq, Greenland, June 7–11, 1999.

G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, “Application of image restoration methods for confocal fluorescence microscopy,” presented at the conference on Three-Dimensional Microscopy: Image Acquisition and Processing IV, San Jose, Calif., February 12–13, 1997.

van Vliet, L. J.

G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, H. T. M. van der Voort, “A quantitative comparison of image restoration methods for confocal microscopy,” J. Microsc. 185, 354–365 (1997).
[CrossRef]

P. W. Verbeek, H. A. Vrooman, L. J. van Vliet, “Low-level image processing by max-min filters,” Signal Process. 15, 249–258 (1988).
[CrossRef]

G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, “Application of image restoration methods for confocal fluorescence microscopy,” presented at the conference on Three-Dimensional Microscopy: Image Acquisition and Processing IV, San Jose, Calif., February 12–13, 1997.

L. J. van Vliet, D. Sudar, I. T. Young, “Digital fluorescence imaging using cooled charge-coupled device array cameras,” in Cell Biology: A Laboratory Handbook, 2nd ed., J. E. Celis, ed. (Academic, London, 1998), Vol. 3, pp. 109–120.

G. M. P. van Kempen, N. van den Brink, L. J. van Vliet, M. van Ginkel, P. W. Verbeek, H. Blonk, “The application of a local dimensionality estimator to the analysis of 3-D microscopic network structures,” presented at the 11th Scandinavian Conference on Image Analysis, Kangerlussuaq, Greenland, June 7–11, 1999.

Vardi, Y.

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 80, 8–35 (1985).
[CrossRef]

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113–121 (1982).
[CrossRef]

Verbeek, P. W.

P. W. Verbeek, H. A. Vrooman, L. J. van Vliet, “Low-level image processing by max-min filters,” Signal Process. 15, 249–258 (1988).
[CrossRef]

G. M. P. van Kempen, N. van den Brink, L. J. van Vliet, M. van Ginkel, P. W. Verbeek, H. Blonk, “The application of a local dimensionality estimator to the analysis of 3-D microscopic network structures,” presented at the 11th Scandinavian Conference on Image Analysis, Kangerlussuaq, Greenland, June 7–11, 1999.

Verveer, P. J.

P. J. Verveer, M. J. Gemkow, T. M. Jovin, “A comparison of image restoration approaches applied to three-dimensional confocal and wide-field fluorescence microscopy,” J. Microsc. 193, 50–61 (1999).
[CrossRef]

G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, H. T. M. van der Voort, “A quantitative comparison of image restoration methods for confocal microscopy,” J. Microsc. 185, 354–365 (1997).
[CrossRef]

P. J. Verveer, T. M. Jovin, “Acceleration of the ICTM image restoration algorithm,” J. Microsc. 188, 191–195 (1997).
[CrossRef]

P. J. Verveer, “Computational and optical methods for improving resolution and signal quality in fluorescence microscopy,” Ph.D. thesis (Delft University of Technology, Delft, The Netherlands, 1998).

G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, “Application of image restoration methods for confocal fluorescence microscopy,” presented at the conference on Three-Dimensional Microscopy: Image Acquisition and Processing IV, San Jose, Calif., February 12–13, 1997.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed., Vol. CS (Cambridge U. Press, Cambridge, UK, 1992).

Vrooman, H. A.

P. W. Verbeek, H. A. Vrooman, L. J. van Vliet, “Low-level image processing by max-min filters,” Signal Process. 15, 249–258 (1988).
[CrossRef]

White, R. L.

Wilson, T.

T. Wilson, J. B. Tan, “Three dimensional image reconstruction in conventional and confocal microscopy,” Bioimaging 1, 176–184 (1993).
[CrossRef]

Young, I. T.

I. T. Young, “Automated Leukocyte Recognition,” in Automated Cell Identification and Cell Sorting, G. L. Wied, G. F. Bahr, eds. (Academic, New York, 1970), pp. 187–194.

L. J. van Vliet, D. Sudar, I. T. Young, “Digital fluorescence imaging using cooled charge-coupled device array cameras,” in Cell Biology: A Laboratory Handbook, 2nd ed., J. E. Celis, ed. (Academic, London, 1998), Vol. 3, pp. 109–120.

Bioimaging (1)

T. Wilson, J. B. Tan, “Three dimensional image reconstruction in conventional and confocal microscopy,” Bioimaging 1, 176–184 (1993).
[CrossRef]

IEEE Trans. Acoust., Speech, Signal Process. (1)

G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems,” IEEE Trans. Acoust., Speech, Signal Process. 37, 2024–2036 (1989).
[CrossRef]

IEEE Trans. Med. Imaging (1)

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113–121 (1982).
[CrossRef]

J. Am. Stat. Assoc. (1)

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,” J. Am. Stat. Assoc. 80, 8–35 (1985).
[CrossRef]

J. Microsc. (4)

G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, H. T. M. van der Voort, “A quantitative comparison of image restoration methods for confocal microscopy,” J. Microsc. 185, 354–365 (1997).
[CrossRef]

H. T. M. van der Voort, K. C. Strasters, “Restoration of confocal images for quantitative image analysis,” J. Microsc. 178, 165–181 (1995).
[CrossRef]

P. J. Verveer, M. J. Gemkow, T. M. Jovin, “A comparison of image restoration approaches applied to three-dimensional confocal and wide-field fluorescence microscopy,” J. Microsc. 193, 50–61 (1999).
[CrossRef]

P. J. Verveer, T. M. Jovin, “Acceleration of the ICTM image restoration algorithm,” J. Microsc. 188, 191–195 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. R. Stat. Soc. B Sect. (1)

A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. B Sect. 39, 1–37 (1977).

Lebensm.-Wiss. Technol. (1)

I. Heertje, E. C. Roijers, H. A. C. M. Hendrickx, “Liquid crystalline phases in the structuring of food products,” Lebensm.-Wiss. Technol. 31, 387–396 (1998).
[CrossRef]

Opt. Acta (1)

R. W. Gerchberg, “Super-resolution through error energy reduction,” Opt. Acta 14, 709–720 (1979).

Science (1)

W. A. Carrington, R. M. Lynch, E. M. Moore, G. Isenberg, K. E. Fogarty, F. S. Fay, “Superresolution three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
[CrossRef] [PubMed]

Signal Process. (1)

P. W. Verbeek, H. A. Vrooman, L. J. van Vliet, “Low-level image processing by max-min filters,” Signal Process. 15, 249–258 (1988).
[CrossRef]

Other (18)

I. T. Young, “Automated Leukocyte Recognition,” in Automated Cell Identification and Cell Sorting, G. L. Wied, G. F. Bahr, eds. (Academic, New York, 1970), pp. 187–194.

G. M. P. van Kempen, L. J. van Vliet, P. J. Verveer, “Application of image restoration methods for confocal fluorescence microscopy,” presented at the conference on Three-Dimensional Microscopy: Image Acquisition and Processing IV, San Jose, Calif., February 12–13, 1997.

G. M. P. van Kempen, N. van den Brink, L. J. van Vliet, M. van Ginkel, P. W. Verbeek, H. Blonk, “The application of a local dimensionality estimator to the analysis of 3-D microscopic network structures,” presented at the 11th Scandinavian Conference on Image Analysis, Kangerlussuaq, Greenland, June 7–11, 1999.

P. J. Verveer, “Computational and optical methods for improving resolution and signal quality in fluorescence microscopy,” Ph.D. thesis (Delft University of Technology, Delft, The Netherlands, 1998).

R. L. Lagendijk, J. Biemond, Iterative Identification and Restoration of Images, Vol. IP (Kluwer Academic, Dordrecht, The Netherlands, 1991).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed., Vol. CS (Cambridge U. Press, Cambridge, UK, 1992).

W. A. Carrington, K. E. Fogarty, “3-D molecular distribution in living cells by deconvolution of optical sections using light microscopy,” presented at the 13th Annual Northeast Bioengineering Conference, Philadelphia, Pa., March 12–13, 1987.

D. L. Snyder, M. I. Miller, Random Point Processes in Time and Space, Vol. SP (Springer Verlag, Berlin, 1991).

K. M. Perry, S. J. Reeves, “Generalized cross-validation as a stopping rule for the Richardson–Lucy algorithm,” presented at the conference on Restoration of HST Images and Spectra II, Baltimore, Md., November 18–19, 1993.

J.-A. Conchello, J. G. McNally, “Fast regularization technique for expectation maximization algorithm for optical sectioning microscopy,” presented at the conference on Three-Dimensional Microscopy: Image Acquisition and Processing III, San Jose, Calif., February 1–3, 1996.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (IOP, London, 1998).

L. J. van Vliet, D. Sudar, I. T. Young, “Digital fluorescence imaging using cooled charge-coupled device array cameras,” in Cell Biology: A Laboratory Handbook, 2nd ed., J. E. Celis, ed. (Academic, London, 1998), Vol. 3, pp. 109–120.

J. Art, “Photon detectors for confocal microscopy,” in Handbook of Biological Confocal Microscopy, J. B. Pawley, ed. (Plenum, New York, 1995), pp. 183–196.

A. N. Tikhonov, V. Y. Arsenin, Solutions of Ill-Posed Problems (Wiley, New York, 1977).

G. M. P. van Kempen, “Image restoration in fluorescence microscopy,” Ph.D. Thesis (Delft University of Technology, Delft, The Netherlands, 1999).

W. A. Carrington, “Image restoration in 3D microscopy with limited data,” in Bioimaging and Two-Dimensional Spectroscopy, L. C. Smith, ed., Proc. SPIE1205, 72–83 (1990).
[CrossRef]

A. K. Jain, Fundamentals of Digital Image Processing, Vol. IP (Prentice Hall, Englewood Cliffs, N.J., 1989).

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Figures (14)

Fig. 1
Fig. 1

Generation of object, boundary, and background region gray-weighted masks with use of the gradient magnitude of the image.

Fig. 2
Fig. 2

Mean-square-error performance of the ICTM, Tikhonov–Miller, Richardson–Lucy, RL–Conchello, clipped Tikhonov–Miller (TM), Carrington, and unclipped ICTM algorithms together with the performance of the unrestored data as a function of the estimated background value.

Fig. 3
Fig. 3

Enlargement of Fig. 2 around the true background.

Fig. 4
Fig. 4

Mean-square-error performance of the ICTM, Tikhonov–Miller, Richardson–Lucy, RL–Conchello, and clipped TM algorithms measured inside the bandwidth of the OTF.

Fig. 5
Fig. 5

Mean-square-error performance of the ICTM, Tikhonov–Miller, Richardson–Lucy, RL–Conchello, and clipped TM algorithms measured outside the bandwidth of the OTF.

Fig. 6
Fig. 6

Mean-square-error performance of the ICTM, Tikhonov–Miller, Richardson–Lucy, RL–Conchello, and clipped TM algorithms measured inside the object.

Fig. 7
Fig. 7

Mean-square-error performance of the ICTM, Tikhonov–Miller, Richardson–Lucy, RL–Conchello, and clipped TM algorithms measured around the edges of the object.

Fig. 8
Fig. 8

Mean-square-error performance of the ICTM, Tikhonov–Miller, Richardson–Lucy, RL–Conchello, and clipped TM algorithms measured in the background.

Fig. 9
Fig. 9

Mean square error in the center ωxωy slice of the ICTM (top), RL–Conchello (middle), and clipped TM (bottom) algorithms for an estimated background of 12.0 (left), 16.0 (center), and 20.0 (right). The gray scaling is constant over all nine images.

Fig. 10
Fig. 10

Histogram of a simulated confocal image as used in the experiment described in Section 3.

Fig. 11
Fig. 11

Mean square error between the acquired image and the blurred restoration result as a function of the background.

Fig. 12
Fig. 12

XY slice of a 3-D confocal image of a monoglyceride stained with Nile Red.

Fig. 13
Fig. 13

Histogram of the 3-D confocal images shown in Fig. 12.

Fig. 14
Fig. 14

Plot of the proposed discrepancy function for background estimation as a function of the background for the clipped TM, ICTM, and RL–Conchello algorithms.

Equations (17)

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

m(x, y, z)=N[h(x, y, z)f(x, y, z)+b(x, y, z)].
g(x, y, z)=m(x, y, z)-b(x, y, z)=h(x, y, z)f(x, y, z)+n(x, y, z).
g[x, y, z]=i=1Mxj=1Myk=1Mzh(x-i, y-j, z-k)×f(i, j, k)+n(x, y, z),
g=Hf+n,
fˆ=Wg
Φ(fˆ)=Hfˆ-g2+λCfˆ2,
WTM=(HTH+λCTC)-1HT.
fˆΦi=0andfˆi>0orfˆΦi0andfˆi=0,
Ψ(c)=12P(HTc)2-cTg+12λc2.
P(Fi|fi)=fiFi exp(-fi)Fi!.
E[m]=Hf+b,
L(f)=-Hf+mT ln(Hf+b),
fˆk+1=fˆkHTmHfˆk+b.
Q(f|fˆk)=-f+E[F|m, fˆk]T ln f-αf2.
E[F|m, fˆk]fˆregularizedk+1-2αfˆregularizedk+1-1=0.
fˆregularizedk+1=-1+(1+2λfˆk+1)1/2λ,
[g-(Hfˆ+b)]2,

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