Abstract

We propose an alternate minimization algorithm for estimating the point-spread function (PSF) of a confocal laser scanning microscope and the specimen fluorescence distribution. A three-dimensional separable Gaussian model is used to restrict the PSF solution space and a constraint on the specimen is used so as to favor the stabilization and convergence of the algorithm. The results obtained from the simulation show that the PSF can be estimated to a high degree of accuracy, and those on real data show better deconvolution as compared to a full theoretical PSF model.

© 2009 Optical Society of America

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  1. J.B.Pawley, ed., Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).
  2. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  3. D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191-219 (1984).
    [CrossRef]
  4. R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
    [CrossRef]
  5. B. Zhang, J. Zerubia, and J. C. Olivo-Marin., “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46, 1819-1829 (2007).
    [CrossRef]
  6. J. G. McNally, C. Preza, J.-Á. Conchello, and L. J. Thomas, Jr., “Artifacts in computational optical-sectioning microscopy,” J. Opt. Soc. Am. A 11, 1056-1067 (1994).
    [CrossRef]
  7. J. W. Shaevitz and D. A. Fletcher, “Enhanced three-dimensional deconvolution microscopy using a measured depth-varying point-spread function,” J. Opt. Soc. Am. A 24, 2622-2627 (2007).
    [CrossRef]
  8. P. J. Shaw and D. J. Rawlins, “The point-spread function of a confocal microscope: its measurement and use in deconvolution of 3-D data,” J. Microsc. 163, 151-165 (1991).
  9. P. J. Shaw, “Deconvolution in 3-D optical microscopy,” Histochem. J. 26, 687-694 (1994).
    [CrossRef]
  10. A. Dieterlen, M. Debailleul, A. De Meyer, B. Simon, V. Georges, B. Colicchio, O. Haeberle, and V. Lauer, “Recent advances in 3-D fluorescence microscopy: tomography as a source of information,” Proc. SPIE 7008, 70080S1 (2008).
  11. P. A. Stokseth, “Properties of a defocused optical system,” J. Opt. Soc. Am. A 59, 1314-1321 (1969).
    [CrossRef]
  12. S. F. Gibson and F. Lanni, “Diffraction by a circular aperture as a model for three-dimensional optical microscopy,” J. Opt. Soc. Am. A A6, 1357-1367 (1989).
    [CrossRef]
  13. O. V. Michailovich and D. R. Adam, “Deconvolution of medical images from microscopic to whole body images,” in Blind Image Deconvolution: Theory and Applications, P. Campisi and K. Egiazarian, eds. (CRC, 2007), pp. 169-237.
  14. T. J. Holmes, “Blind deconvolution of quantum-limited incoherent imagery: maximum-likelihood approach,” J. Opt. Soc. Am. A 9, 1052-1061 (1992).
    [CrossRef]
  15. J. Markham and J.-A. Conchello, “Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur,” J. Opt. Soc. Am. A 16, 2377-2391 (1999).
    [CrossRef]
  16. E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J. W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A 24, 1580-1600 (2007).
    [CrossRef]
  17. L. Mandel, “Sub-Poissonian photon statistics in resonance fluorescence,” Opt. Lett. 4, 205-207 (1979).
    [CrossRef]
  18. D. A. Agard, Y. Hiraoka, P. Shaw, and J. W. Sedat, “Fluorescence microscopy in three dimensions,” Methods Cell Biol. 30, 353-377 (1989).
    [CrossRef]
  19. G. B. Avinash, “Data-driven, simultaneous blur and image restoration in 3-D fluorescence microscopy,” J. Microsc. 183, 145-157 (1996).
    [CrossRef]
  20. P. Pankajakshan, L. Blanc-Féraud, Z. Kam, and J. Zerubia, “Point-spread function retrieval in fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2009).
  21. B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett. 28, 801-803 (2003).
    [CrossRef]
  22. C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179-194 (1990).
  23. A. Erhardt, G. Zinser, D. Komitowski, and J. Bille, “Reconstructing 3-D light-microscopic images by digital image processing,” Appl. Opt. 24, 194-200 (1985).
    [CrossRef]
  24. W. A. Carrington, K. E. Fogarty, and F. S. Fay, 3D Fluorescence Imaging of Single Cells Using Image Restoration (Wiley-Liss, 1990), pp. 53-72.
  25. C. Preza, M. I. Miller, L. J. Thomas, Jr., and J. G. McNally, “Regularized linear method for reconstruction of three-dimensional microscopic objects from optical sections,” J. Opt. Soc. Am. A 9, 219-228 (1992).
    [CrossRef]
  26. T. Tommasi, A. Diaspro, and B. Bianco, “3-D reconstruction in optical microscopy by a frequency-domain approach,” Signal Process. 32, 357-366 (1993).
    [CrossRef]
  27. T. J. Holmes, “Maximum-likelihood image restoration adapted for noncoherent optical imaging,” J. Opt. Soc. Am. A 5, 666-673 (1988).
    [CrossRef]
  28. N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260-266(2006).
    [CrossRef]
  29. P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy (CLSM)-proof of concept,” Research Report 6493 (INRIA Sophia-Antipolis, March 2008).
  30. G. M. P. Van Kempen, L. J. Van Vliet, P. J. Verveer, and H. T. M. Van Der Voort, “A quantitative comparison of image restoration methods for confocal microscopy,” J. Microsc. 185, 354-365 (1997).
    [CrossRef]
  31. A. Dieterlen, C. Xu, O. Haeberle, N. Hueber, R. Malfara, B. Colicchio, and S. Jacquey, “Identification and restoration in 3D fluorescence microscopy,” Proc. SPIE 5477, 105-113(2004).
    [CrossRef]
  32. G. Demoment, “Image reconstruction and restoration: overview of common estimation structures and problems,” IEEE Trans. Acoust. Speech Signal Process. 37, 2024-2036 (1989).
    [CrossRef]
  33. A. N. Tikhonov and V. A. Arsenin, Solution of Ill-posed Problems (Winston, 1977).
  34. K. Miller, “Least squares methods for ill-posed problems with a prescribed bound,” SIAM J. Math. Anal. 1, 52-74(1970).
    [CrossRef]
  35. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259-268(1992).
    [CrossRef]
  36. N. Dey, L. Blanc-Féraud, C. Zimmer, P. Roux, Z. Kam, and J. C. Olivo-Marin, “3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization,” Research Report 5272(INRIA, July 2004).
  37. L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745-754(1974).
    [CrossRef]
  38. W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A 62, 55-59 (1972).
    [CrossRef]
  39. A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B. Methodol. 39, 1-38 (1977).
  40. M. Jiang and G. Wang, “Development of blind image deconvolution and its applications,” J. X-Ray Sci. Technol. 11, 13-19(2003).
  41. T. F. Chan and C.-K. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370-375 (1998).
    [CrossRef]
  42. L. Bar, N. A. Sochen, and N. Kiryati, “Variational pairing of image segmentation and blind restoration,” in Proceedings of Eighth European Conference on Computer Vision, T. Pajdla and J. Matas, eds., Vol. 3022 of Lecture Notes in Computer Science (Springer, 2004), pp. 166-177.
  43. A. Santos and I. T. Young, “Model-based resolution: applying the theory in quantitative microscopy,” Appl. Opt. 39, 2948-2958 (2000).
    [CrossRef]
  44. K. E. Atkinson, An Introduction to Numerical Analysis, 2nd ed. (Wiley1989).
  45. A. Jalobeanu, L. Blanc-Féraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum likelihood method,” Pattern Recog. 35, 341-352 (2002).
    [CrossRef]
  46. A. Mohammad-Djafari, “A full Bayesian approach for inverse problems,” in Maximum Entropy and Bayesian Methods, Vol. 79 of Fundamental Theories of Physics, K. Hanson and R. N. Silver, eds. (Kluwer Academic, 1996), pp. 135-143.
  47. P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy,” in Proceedings of IEEE International Conference of Engineering in Medicine and Biology Society (IEEE, 2007), pp. 6531-6534.
  48. M. de Moraes Marim, B. Zhang, J.-C. Olivo-Marin, and C. Zimmer, “Improving single particle localization with an empirically calibrated Gaussian kernel,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 1003-1006.
  49. P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Blind deconvolution for diffraction-limited fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 740-743.

2008

A. Dieterlen, M. Debailleul, A. De Meyer, B. Simon, V. Georges, B. Colicchio, O. Haeberle, and V. Lauer, “Recent advances in 3-D fluorescence microscopy: tomography as a source of information,” Proc. SPIE 7008, 70080S1 (2008).

2007

2006

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260-266(2006).
[CrossRef]

2004

A. Dieterlen, C. Xu, O. Haeberle, N. Hueber, R. Malfara, B. Colicchio, and S. Jacquey, “Identification and restoration in 3D fluorescence microscopy,” Proc. SPIE 5477, 105-113(2004).
[CrossRef]

2003

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase retrieval for high-numerical-aperture optical systems,” Opt. Lett. 28, 801-803 (2003).
[CrossRef]

M. Jiang and G. Wang, “Development of blind image deconvolution and its applications,” J. X-Ray Sci. Technol. 11, 13-19(2003).

2002

A. Jalobeanu, L. Blanc-Féraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum likelihood method,” Pattern Recog. 35, 341-352 (2002).
[CrossRef]

2000

1999

1998

T. F. Chan and C.-K. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370-375 (1998).
[CrossRef]

1997

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

1996

G. B. Avinash, “Data-driven, simultaneous blur and image restoration in 3-D fluorescence microscopy,” J. Microsc. 183, 145-157 (1996).
[CrossRef]

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

1994

1993

T. Tommasi, A. Diaspro, and B. Bianco, “3-D reconstruction in optical microscopy by a frequency-domain approach,” Signal Process. 32, 357-366 (1993).
[CrossRef]

1992

1991

P. J. Shaw and D. J. Rawlins, “The point-spread function of a confocal microscope: its measurement and use in deconvolution of 3-D data,” J. Microsc. 163, 151-165 (1991).

1990

C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179-194 (1990).

1989

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

S. F. Gibson and F. Lanni, “Diffraction by a circular aperture as a model for three-dimensional optical microscopy,” J. Opt. Soc. Am. A A6, 1357-1367 (1989).
[CrossRef]

D. A. Agard, Y. Hiraoka, P. Shaw, and J. W. Sedat, “Fluorescence microscopy in three dimensions,” Methods Cell Biol. 30, 353-377 (1989).
[CrossRef]

1988

1985

1984

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191-219 (1984).
[CrossRef]

1979

1977

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B. Methodol. 39, 1-38 (1977).

1974

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745-754(1974).
[CrossRef]

1972

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A 62, 55-59 (1972).
[CrossRef]

1970

K. Miller, “Least squares methods for ill-posed problems with a prescribed bound,” SIAM J. Math. Anal. 1, 52-74(1970).
[CrossRef]

1969

P. A. Stokseth, “Properties of a defocused optical system,” J. Opt. Soc. Am. A 59, 1314-1321 (1969).
[CrossRef]

Aarsvold, J. N.

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

Adam, D. R.

O. V. Michailovich and D. R. Adam, “Deconvolution of medical images from microscopic to whole body images,” in Blind Image Deconvolution: Theory and Applications, P. Campisi and K. Egiazarian, eds. (CRC, 2007), pp. 169-237.

Agard, D. A.

Arsenin, V. A.

A. N. Tikhonov and V. A. Arsenin, Solution of Ill-posed Problems (Winston, 1977).

Atkinson, K. E.

K. E. Atkinson, An Introduction to Numerical Analysis, 2nd ed. (Wiley1989).

Avinash, G. B.

G. B. Avinash, “Data-driven, simultaneous blur and image restoration in 3-D fluorescence microscopy,” J. Microsc. 183, 145-157 (1996).
[CrossRef]

Bar, L.

L. Bar, N. A. Sochen, and N. Kiryati, “Variational pairing of image segmentation and blind restoration,” in Proceedings of Eighth European Conference on Computer Vision, T. Pajdla and J. Matas, eds., Vol. 3022 of Lecture Notes in Computer Science (Springer, 2004), pp. 166-177.

Bianco, B.

T. Tommasi, A. Diaspro, and B. Bianco, “3-D reconstruction in optical microscopy by a frequency-domain approach,” Signal Process. 32, 357-366 (1993).
[CrossRef]

Bille, J.

Blanc-Féraud, L.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260-266(2006).
[CrossRef]

A. Jalobeanu, L. Blanc-Féraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum likelihood method,” Pattern Recog. 35, 341-352 (2002).
[CrossRef]

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy,” in Proceedings of IEEE International Conference of Engineering in Medicine and Biology Society (IEEE, 2007), pp. 6531-6534.

N. Dey, L. Blanc-Féraud, C. Zimmer, P. Roux, Z. Kam, and J. C. Olivo-Marin, “3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization,” Research Report 5272(INRIA, July 2004).

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy (CLSM)-proof of concept,” Research Report 6493 (INRIA Sophia-Antipolis, March 2008).

P. Pankajakshan, L. Blanc-Féraud, Z. Kam, and J. Zerubia, “Point-spread function retrieval in fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2009).

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Blind deconvolution for diffraction-limited fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 740-743.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Carrington, W. A.

W. A. Carrington, K. E. Fogarty, and F. S. Fay, 3D Fluorescence Imaging of Single Cells Using Image Restoration (Wiley-Liss, 1990), pp. 53-72.

Chan, T. F.

T. F. Chan and C.-K. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370-375 (1998).
[CrossRef]

Chen, C.-T.

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

Chen, J.

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

Cogswell, C. J.

C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179-194 (1990).

Colicchio, B.

A. Dieterlen, M. Debailleul, A. De Meyer, B. Simon, V. Georges, B. Colicchio, O. Haeberle, and V. Lauer, “Recent advances in 3-D fluorescence microscopy: tomography as a source of information,” Proc. SPIE 7008, 70080S1 (2008).

A. Dieterlen, C. Xu, O. Haeberle, N. Hueber, R. Malfara, B. Colicchio, and S. Jacquey, “Identification and restoration in 3D fluorescence microscopy,” Proc. SPIE 5477, 105-113(2004).
[CrossRef]

Conchello, J.-A.

Conchello, J.-Á.

Davies, P.

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

De Meyer, A.

A. Dieterlen, M. Debailleul, A. De Meyer, B. Simon, V. Georges, B. Colicchio, O. Haeberle, and V. Lauer, “Recent advances in 3-D fluorescence microscopy: tomography as a source of information,” Proc. SPIE 7008, 70080S1 (2008).

de Moraes Marim, M.

M. de Moraes Marim, B. Zhang, J.-C. Olivo-Marin, and C. Zimmer, “Improving single particle localization with an empirically calibrated Gaussian kernel,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 1003-1006.

Debailleul, M.

A. Dieterlen, M. Debailleul, A. De Meyer, B. Simon, V. Georges, B. Colicchio, O. Haeberle, and V. Lauer, “Recent advances in 3-D fluorescence microscopy: tomography as a source of information,” Proc. SPIE 7008, 70080S1 (2008).

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, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B. Methodol. 39, 1-38 (1977).

Dey, N.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260-266(2006).
[CrossRef]

N. Dey, L. Blanc-Féraud, C. Zimmer, P. Roux, Z. Kam, and J. C. Olivo-Marin, “3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization,” Research Report 5272(INRIA, July 2004).

Diaspro, A.

T. Tommasi, A. Diaspro, and B. Bianco, “3-D reconstruction in optical microscopy by a frequency-domain approach,” Signal Process. 32, 357-366 (1993).
[CrossRef]

Dieterlen, A.

A. Dieterlen, M. Debailleul, A. De Meyer, B. Simon, V. Georges, B. Colicchio, O. Haeberle, and V. Lauer, “Recent advances in 3-D fluorescence microscopy: tomography as a source of information,” Proc. SPIE 7008, 70080S1 (2008).

A. Dieterlen, C. Xu, O. Haeberle, N. Hueber, R. Malfara, B. Colicchio, and S. Jacquey, “Identification and restoration in 3D fluorescence microscopy,” Proc. SPIE 5477, 105-113(2004).
[CrossRef]

Disz, T.

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

Erhardt, A.

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259-268(1992).
[CrossRef]

Fay, F. S.

W. A. Carrington, K. E. Fogarty, and F. S. Fay, 3D Fluorescence Imaging of Single Cells Using Image Restoration (Wiley-Liss, 1990), pp. 53-72.

Fletcher, D. A.

Fogarty, K. E.

W. A. Carrington, K. E. Fogarty, and F. S. Fay, 3D Fluorescence Imaging of Single Cells Using Image Restoration (Wiley-Liss, 1990), pp. 53-72.

Foster, I.

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

Georges, V.

A. Dieterlen, M. Debailleul, A. De Meyer, B. Simon, V. Georges, B. Colicchio, O. Haeberle, and V. Lauer, “Recent advances in 3-D fluorescence microscopy: tomography as a source of information,” Proc. SPIE 7008, 70080S1 (2008).

Gibson, S. F.

S. F. Gibson and F. Lanni, “Diffraction by a circular aperture as a model for three-dimensional optical microscopy,” J. Opt. Soc. Am. A A6, 1357-1367 (1989).
[CrossRef]

Griem, M.

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

Gustafsson, M. G.

Haase, S.

Haeberle, O.

A. Dieterlen, M. Debailleul, A. De Meyer, B. Simon, V. Georges, B. Colicchio, O. Haeberle, and V. Lauer, “Recent advances in 3-D fluorescence microscopy: tomography as a source of information,” Proc. SPIE 7008, 70080S1 (2008).

A. Dieterlen, C. Xu, O. Haeberle, N. Hueber, R. Malfara, B. Colicchio, and S. Jacquey, “Identification and restoration in 3D fluorescence microscopy,” Proc. SPIE 5477, 105-113(2004).
[CrossRef]

Hanser, B. M.

Hiraoka, Y.

D. A. Agard, Y. Hiraoka, P. Shaw, and J. W. Sedat, “Fluorescence microscopy in three dimensions,” Methods Cell Biol. 30, 353-377 (1989).
[CrossRef]

Holmes, T. J.

Hom, E. F. Y.

Hudson, R.

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

Hueber, N.

A. Dieterlen, C. Xu, O. Haeberle, N. Hueber, R. Malfara, B. Colicchio, and S. Jacquey, “Identification and restoration in 3D fluorescence microscopy,” Proc. SPIE 5477, 105-113(2004).
[CrossRef]

Jacquey, S.

A. Dieterlen, C. Xu, O. Haeberle, N. Hueber, R. Malfara, B. Colicchio, and S. Jacquey, “Identification and restoration in 3D fluorescence microscopy,” Proc. SPIE 5477, 105-113(2004).
[CrossRef]

Jalobeanu, A.

A. Jalobeanu, L. Blanc-Féraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum likelihood method,” Pattern Recog. 35, 341-352 (2002).
[CrossRef]

Jiang, M.

M. Jiang and G. Wang, “Development of blind image deconvolution and its applications,” J. X-Ray Sci. Technol. 11, 13-19(2003).

Kam, Z.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260-266(2006).
[CrossRef]

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy (CLSM)-proof of concept,” Research Report 6493 (INRIA Sophia-Antipolis, March 2008).

N. Dey, L. Blanc-Féraud, C. Zimmer, P. Roux, Z. Kam, and J. C. Olivo-Marin, “3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization,” Research Report 5272(INRIA, July 2004).

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy,” in Proceedings of IEEE International Conference of Engineering in Medicine and Biology Society (IEEE, 2007), pp. 6531-6534.

P. Pankajakshan, L. Blanc-Féraud, Z. Kam, and J. Zerubia, “Point-spread function retrieval in fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2009).

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Blind deconvolution for diffraction-limited fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 740-743.

Kiryati, N.

L. Bar, N. A. Sochen, and N. Kiryati, “Variational pairing of image segmentation and blind restoration,” in Proceedings of Eighth European Conference on Computer Vision, T. Pajdla and J. Matas, eds., Vol. 3022 of Lecture Notes in Computer Science (Springer, 2004), pp. 166-177.

Komitowski, D.

Kwong, M. K.

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

Laird, N. M.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B. Methodol. 39, 1-38 (1977).

Lanni, F.

S. F. Gibson and F. Lanni, “Diffraction by a circular aperture as a model for three-dimensional optical microscopy,” J. Opt. Soc. Am. A A6, 1357-1367 (1989).
[CrossRef]

Lauer, V.

A. Dieterlen, M. Debailleul, A. De Meyer, B. Simon, V. Georges, B. Colicchio, O. Haeberle, and V. Lauer, “Recent advances in 3-D fluorescence microscopy: tomography as a source of information,” Proc. SPIE 7008, 70080S1 (2008).

Lee, T. K.

Lin, B.

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

Lucy, L. B.

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745-754(1974).
[CrossRef]

Malfara, R.

A. Dieterlen, C. Xu, O. Haeberle, N. Hueber, R. Malfara, B. Colicchio, and S. Jacquey, “Identification and restoration in 3D fluorescence microscopy,” Proc. SPIE 5477, 105-113(2004).
[CrossRef]

Mandel, L.

Marchis, F.

Markham, J.

McNally, J. G.

Michailovich, O. V.

O. V. Michailovich and D. R. Adam, “Deconvolution of medical images from microscopic to whole body images,” in Blind Image Deconvolution: Theory and Applications, P. Campisi and K. Egiazarian, eds. (CRC, 2007), pp. 169-237.

Miller, K.

K. Miller, “Least squares methods for ill-posed problems with a prescribed bound,” SIAM J. Math. Anal. 1, 52-74(1970).
[CrossRef]

Miller, M. I.

Mohammad-Djafari, A.

A. Mohammad-Djafari, “A full Bayesian approach for inverse problems,” in Maximum Entropy and Bayesian Methods, Vol. 79 of Fundamental Theories of Physics, K. Hanson and R. N. Silver, eds. (Kluwer Academic, 1996), pp. 135-143.

Olivo-Marin, J. C.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260-266(2006).
[CrossRef]

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy (CLSM)-proof of concept,” Research Report 6493 (INRIA Sophia-Antipolis, March 2008).

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy,” in Proceedings of IEEE International Conference of Engineering in Medicine and Biology Society (IEEE, 2007), pp. 6531-6534.

N. Dey, L. Blanc-Féraud, C. Zimmer, P. Roux, Z. Kam, and J. C. Olivo-Marin, “3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization,” Research Report 5272(INRIA, July 2004).

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Blind deconvolution for diffraction-limited fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 740-743.

Olivo-Marin, J.-C.

M. de Moraes Marim, B. Zhang, J.-C. Olivo-Marin, and C. Zimmer, “Improving single particle localization with an empirically calibrated Gaussian kernel,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 1003-1006.

Olivo-Marin., J. C.

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259-268(1992).
[CrossRef]

Pankajakshan, P.

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy (CLSM)-proof of concept,” Research Report 6493 (INRIA Sophia-Antipolis, March 2008).

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy,” in Proceedings of IEEE International Conference of Engineering in Medicine and Biology Society (IEEE, 2007), pp. 6531-6534.

P. Pankajakshan, L. Blanc-Féraud, Z. Kam, and J. Zerubia, “Point-spread function retrieval in fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2009).

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Blind deconvolution for diffraction-limited fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 740-743.

Preza, C.

Rawlins, D. J.

P. J. Shaw and D. J. Rawlins, “The point-spread function of a confocal microscope: its measurement and use in deconvolution of 3-D data,” J. Microsc. 163, 151-165 (1991).

Richardson, W. H.

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A 62, 55-59 (1972).
[CrossRef]

Roux, P.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260-266(2006).
[CrossRef]

N. Dey, L. Blanc-Féraud, C. Zimmer, P. Roux, Z. Kam, and J. C. Olivo-Marin, “3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization,” Research Report 5272(INRIA, July 2004).

Rubin, D. B.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B. Methodol. 39, 1-38 (1977).

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259-268(1992).
[CrossRef]

Santos, A.

Sedat, J. W.

Shaevitz, J. W.

Shaw, P.

D. A. Agard, Y. Hiraoka, P. Shaw, and J. W. Sedat, “Fluorescence microscopy in three dimensions,” Methods Cell Biol. 30, 353-377 (1989).
[CrossRef]

Shaw, P. J.

P. J. Shaw, “Deconvolution in 3-D optical microscopy,” Histochem. J. 26, 687-694 (1994).
[CrossRef]

P. J. Shaw and D. J. Rawlins, “The point-spread function of a confocal microscope: its measurement and use in deconvolution of 3-D data,” J. Microsc. 163, 151-165 (1991).

Sheppard, C. J. R.

C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179-194 (1990).

Simon, B.

A. Dieterlen, M. Debailleul, A. De Meyer, B. Simon, V. Georges, B. Colicchio, O. Haeberle, and V. Lauer, “Recent advances in 3-D fluorescence microscopy: tomography as a source of information,” Proc. SPIE 7008, 70080S1 (2008).

Sochen, N. A.

L. Bar, N. A. Sochen, and N. Kiryati, “Variational pairing of image segmentation and blind restoration,” in Proceedings of Eighth European Conference on Computer Vision, T. Pajdla and J. Matas, eds., Vol. 3022 of Lecture Notes in Computer Science (Springer, 2004), pp. 166-177.

Stokseth, P. A.

P. A. Stokseth, “Properties of a defocused optical system,” J. Opt. Soc. Am. A 59, 1314-1321 (1969).
[CrossRef]

Thomas, L. J.

Tikhonov, A. N.

A. N. Tikhonov and V. A. Arsenin, Solution of Ill-posed Problems (Winston, 1977).

Tommasi, T.

T. Tommasi, A. Diaspro, and B. Bianco, “3-D reconstruction in optical microscopy by a frequency-domain approach,” Signal Process. 32, 357-366 (1993).
[CrossRef]

Van Der Voort, H. T. M.

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

Van Kempen, G. M. P.

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

Van Vliet, L. J.

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

Verveer, P. J.

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

Wang, G.

M. Jiang and G. Wang, “Development of blind image deconvolution and its applications,” J. X-Ray Sci. Technol. 11, 13-19(2003).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Wong, C.-K.

T. F. Chan and C.-K. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370-375 (1998).
[CrossRef]

Xu, C.

A. Dieterlen, C. Xu, O. Haeberle, N. Hueber, R. Malfara, B. Colicchio, and S. Jacquey, “Identification and restoration in 3D fluorescence microscopy,” Proc. SPIE 5477, 105-113(2004).
[CrossRef]

Young, I. T.

Zerubia, J.

B. Zhang, J. Zerubia, and J. C. Olivo-Marin., “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46, 1819-1829 (2007).
[CrossRef]

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260-266(2006).
[CrossRef]

A. Jalobeanu, L. Blanc-Féraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum likelihood method,” Pattern Recog. 35, 341-352 (2002).
[CrossRef]

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy,” in Proceedings of IEEE International Conference of Engineering in Medicine and Biology Society (IEEE, 2007), pp. 6531-6534.

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy (CLSM)-proof of concept,” Research Report 6493 (INRIA Sophia-Antipolis, March 2008).

P. Pankajakshan, L. Blanc-Féraud, Z. Kam, and J. Zerubia, “Point-spread function retrieval in fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2009).

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Blind deconvolution for diffraction-limited fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 740-743.

Zhang, B.

B. Zhang, J. Zerubia, and J. C. Olivo-Marin., “Gaussian approximations of fluorescence microscope point-spread function models,” Appl. Opt. 46, 1819-1829 (2007).
[CrossRef]

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy (CLSM)-proof of concept,” Research Report 6493 (INRIA Sophia-Antipolis, March 2008).

M. de Moraes Marim, B. Zhang, J.-C. Olivo-Marin, and C. Zimmer, “Improving single particle localization with an empirically calibrated Gaussian kernel,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 1003-1006.

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy,” in Proceedings of IEEE International Conference of Engineering in Medicine and Biology Society (IEEE, 2007), pp. 6531-6534.

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Blind deconvolution for diffraction-limited fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 740-743.

Zimmer, C.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260-266(2006).
[CrossRef]

M. de Moraes Marim, B. Zhang, J.-C. Olivo-Marin, and C. Zimmer, “Improving single particle localization with an empirically calibrated Gaussian kernel,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 1003-1006.

N. Dey, L. Blanc-Féraud, C. Zimmer, P. Roux, Z. Kam, and J. C. Olivo-Marin, “3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization,” Research Report 5272(INRIA, July 2004).

Zinser, G.

Annu. Rev. Biophys. Bioeng.

D. A. Agard, “Optical sectioning microscopy: cellular architecture in three dimensions,” Annu. Rev. Biophys. Bioeng. 13, 191-219 (1984).
[CrossRef]

Appl. Opt.

Astron. J.

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745-754(1974).
[CrossRef]

Histochem. J.

P. J. Shaw, “Deconvolution in 3-D optical microscopy,” Histochem. J. 26, 687-694 (1994).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process.

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. Image Process.

T. F. Chan and C.-K. Wong, “Total variation blind deconvolution,” IEEE Trans. Image Process. 7, 370-375 (1998).
[CrossRef]

J. Microsc.

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

G. B. Avinash, “Data-driven, simultaneous blur and image restoration in 3-D fluorescence microscopy,” J. Microsc. 183, 145-157 (1996).
[CrossRef]

C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179-194 (1990).

P. J. Shaw and D. J. Rawlins, “The point-spread function of a confocal microscope: its measurement and use in deconvolution of 3-D data,” J. Microsc. 163, 151-165 (1991).

J. Opt. Soc. Am. A

P. A. Stokseth, “Properties of a defocused optical system,” J. Opt. Soc. Am. A 59, 1314-1321 (1969).
[CrossRef]

S. F. Gibson and F. Lanni, “Diffraction by a circular aperture as a model for three-dimensional optical microscopy,” J. Opt. Soc. Am. A A6, 1357-1367 (1989).
[CrossRef]

T. J. Holmes, “Blind deconvolution of quantum-limited incoherent imagery: maximum-likelihood approach,” J. Opt. Soc. Am. A 9, 1052-1061 (1992).
[CrossRef]

J. Markham and J.-A. Conchello, “Parametric blind deconvolution: a robust method for the simultaneous estimation of image and blur,” J. Opt. Soc. Am. A 16, 2377-2391 (1999).
[CrossRef]

E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J. W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A 24, 1580-1600 (2007).
[CrossRef]

J. G. McNally, C. Preza, J.-Á. Conchello, and L. J. Thomas, Jr., “Artifacts in computational optical-sectioning microscopy,” J. Opt. Soc. Am. A 11, 1056-1067 (1994).
[CrossRef]

J. W. Shaevitz and D. A. Fletcher, “Enhanced three-dimensional deconvolution microscopy using a measured depth-varying point-spread function,” J. Opt. Soc. Am. A 24, 2622-2627 (2007).
[CrossRef]

C. Preza, M. I. Miller, L. J. Thomas, Jr., and J. G. McNally, “Regularized linear method for reconstruction of three-dimensional microscopic objects from optical sections,” J. Opt. Soc. Am. A 9, 219-228 (1992).
[CrossRef]

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

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. A 62, 55-59 (1972).
[CrossRef]

J. R. Stat. Soc. Ser. B. Methodol.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc. Ser. B. Methodol. 39, 1-38 (1977).

J. X-Ray Sci. Technol.

M. Jiang and G. Wang, “Development of blind image deconvolution and its applications,” J. X-Ray Sci. Technol. 11, 13-19(2003).

Methods Cell Biol.

D. A. Agard, Y. Hiraoka, P. Shaw, and J. W. Sedat, “Fluorescence microscopy in three dimensions,” Methods Cell Biol. 30, 353-377 (1989).
[CrossRef]

Microsc. Res. Tech.

N. Dey, L. Blanc-Féraud, C. Zimmer, Z. Kam, P. Roux, J. C. Olivo-Marin, and J. Zerubia, “Richardson-Lucy algorithm with total variation regularization for 3D confocal microscope deconvolution,” Microsc. Res. Tech. 69, 260-266(2006).
[CrossRef]

Opt. Lett.

Pattern Recog.

A. Jalobeanu, L. Blanc-Féraud, and J. Zerubia, “Hyperparameter estimation for satellite image restoration using a MCMC maximum likelihood method,” Pattern Recog. 35, 341-352 (2002).
[CrossRef]

Phys. D

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259-268(1992).
[CrossRef]

Proc. SPIE

A. Dieterlen, C. Xu, O. Haeberle, N. Hueber, R. Malfara, B. Colicchio, and S. Jacquey, “Identification and restoration in 3D fluorescence microscopy,” Proc. SPIE 5477, 105-113(2004).
[CrossRef]

A. Dieterlen, M. Debailleul, A. De Meyer, B. Simon, V. Georges, B. Colicchio, O. Haeberle, and V. Lauer, “Recent advances in 3-D fluorescence microscopy: tomography as a source of information,” Proc. SPIE 7008, 70080S1 (2008).

R. Hudson, J. N. Aarsvold, C.-T. Chen, J. Chen, P. Davies, T. Disz, I. Foster, M. Griem, M. K. Kwong, and B. Lin, “Optical microscopy system for 3D dynamic imaging,” Proc. SPIE 2655, 187-198 (1996).
[CrossRef]

SIAM J. Math. Anal.

K. Miller, “Least squares methods for ill-posed problems with a prescribed bound,” SIAM J. Math. Anal. 1, 52-74(1970).
[CrossRef]

Signal Process.

T. Tommasi, A. Diaspro, and B. Bianco, “3-D reconstruction in optical microscopy by a frequency-domain approach,” Signal Process. 32, 357-366 (1993).
[CrossRef]

Other

W. A. Carrington, K. E. Fogarty, and F. S. Fay, 3D Fluorescence Imaging of Single Cells Using Image Restoration (Wiley-Liss, 1990), pp. 53-72.

P. Pankajakshan, L. Blanc-Féraud, Z. Kam, and J. Zerubia, “Point-spread function retrieval in fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2009).

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy (CLSM)-proof of concept,” Research Report 6493 (INRIA Sophia-Antipolis, March 2008).

N. Dey, L. Blanc-Féraud, C. Zimmer, P. Roux, Z. Kam, and J. C. Olivo-Marin, “3D microscopy deconvolution using Richardson-Lucy algorithm with total variation regularization,” Research Report 5272(INRIA, July 2004).

A. N. Tikhonov and V. A. Arsenin, Solution of Ill-posed Problems (Winston, 1977).

J.B.Pawley, ed., Handbook of Biological Confocal Microscopy, 3rd ed. (Springer, 2006).

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

O. V. Michailovich and D. R. Adam, “Deconvolution of medical images from microscopic to whole body images,” in Blind Image Deconvolution: Theory and Applications, P. Campisi and K. Egiazarian, eds. (CRC, 2007), pp. 169-237.

A. Mohammad-Djafari, “A full Bayesian approach for inverse problems,” in Maximum Entropy and Bayesian Methods, Vol. 79 of Fundamental Theories of Physics, K. Hanson and R. N. Silver, eds. (Kluwer Academic, 1996), pp. 135-143.

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Parametric blind deconvolution for confocal laser scanning microscopy,” in Proceedings of IEEE International Conference of Engineering in Medicine and Biology Society (IEEE, 2007), pp. 6531-6534.

M. de Moraes Marim, B. Zhang, J.-C. Olivo-Marin, and C. Zimmer, “Improving single particle localization with an empirically calibrated Gaussian kernel,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 1003-1006.

P. Pankajakshan, B. Zhang, L. Blanc-Féraud, Z. Kam, J. C. Olivo-Marin, and J. Zerubia, “Blind deconvolution for diffraction-limited fluorescence microscopy,” in Proceedings of IEEE International Symposium on Biomedical Imaging (IEEE, 2008), pp. 740-743.

L. Bar, N. A. Sochen, and N. Kiryati, “Variational pairing of image segmentation and blind restoration,” in Proceedings of Eighth European Conference on Computer Vision, T. Pajdla and J. Matas, eds., Vol. 3022 of Lecture Notes in Computer Science (Springer, 2004), pp. 166-177.

K. E. Atkinson, An Introduction to Numerical Analysis, 2nd ed. (Wiley1989).

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Figures (8)

Fig. 1
Fig. 1

MRF over a six-member neighborhood η x . By permission of Ariana-INRIA/CNRS.

Fig. 2
Fig. 2

Variation of the energy function J ( o , θ | i ) with respect to (a) lateral ( σ r ) and (b) with axial PSF parameter ( σ z ). For this experiment, the true object o is known and the observation is generated using a known 3D Gaussian model. The axial PSF parameter σ z is varied by a factor ± ϵ to monitor its effect on the estimated parameter σ r and vice versa. σ ( · , true ) is the true parameter value. By permission of Ariana-INRIA/CNRS.

Fig. 3
Fig. 3

3D (a) phantom object (with false coloring), (b) observed image blurred by the PSF model in Eq. (3) and Poisson noise (PSNR, 16.77 dB ; I-divergence, 5.55), (c) restoration after RL–TV deconvolution with the estimated PSF (I-divergence, 1.43), (d) estimated PSF. The intensities of the object, observation, and the restoration are on a linear scale while the PSF is on a logarithmic scale. By permission of Ariana-INRIA/CNRS.

Fig. 4
Fig. 4

Convergence of the cost function and lateral parameter by the GD method (when the original object is known). The Y axis is left-scaled for the cost function J ( θ ^ , o ^ | i ) and right-scaled for the PSF parameter, respectively. By permission of Ariana-INRIA/CNRS.

Fig. 5
Fig. 5

(a) Full model (dashed curve), estimated (solid curve) and the best Gaussian fit (dashed-dotted curve) PSFs are displayed for one direction (off-central plane); the inset shows a section of the plot. (b)  X -Z projection of the residual (RSE < 0.07 % ) between the estimated and the full PSF model is displayed on a log scale. By permission of Ariana-INRIA/CNRS.

Fig. 6
Fig. 6

(a) Rendered subvolume of the original specimen (by permission of Institute of Signaling, Developmental Biology & Cancer UMR6543/CNRS/UNS), and (b) restored image. The intensity is scaled between [0, 130] for display. By permission of Ariana-INRIA/CNRS.

Fig. 7
Fig. 7

Observed root apex of an Arabidopsis thaliana with a volume 146.448 μm × 146.448 μm × 30.222 μm (by permission of INRA). The subvolume chosen for restoration is emphasized.

Fig. 8
Fig. 8

Rendered subvolume of the (a) observed image slices in Fig. 7 (by permission of INRA) and (b) volume rendering of the restored image slices (by permission of Ariana-INRIA/CNRS). ϵ = 0.0001 .

Tables (1)

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Table 1 Algorithm 1: Schema for the Proposed Blind Deconvolution Algorithm

Equations (25)

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γ i ( x ) = P ( γ ( [ h * o ] ( x ) + b ( x ) ) ) , x Ω ,
P ( k x , k y , z ) = { A ( ϕ ) exp ( j k ψ ) , if k x 2 + k y 2 < k sin ϕ max 0 , otherwise ,
h ( x ) = C | h A ( x ; λ e x ) | 2 · x 1 2 + y 1 2 D 2 4 | h A ( x - x 1 , y - y 1 , z ; λ e m ) | 2 d x 1 d y 1 ,
Pr ( i | o , h ) = x Ω [ h * o ] ( x ) i ( x ) e [ h * o ] ( x ) i ( x ) ! ,
Pr ( o , h | i ) = Pr ( i | o , h ) Pr ( o ) Pr ( h ) Pr ( i ) ,
( o ^ , h ^ ) = arg max ( o , h ) { Pr ( o , h | i ) } = arg min ( o , h ) { log [ Pr ( o , h | i ) ] } .
J ( o , h | i ) J obs ( i | o , h ) + ( λ o J reg , o ( o ) + λ h J reg , h ( h ) ) .
o ^ ( n + 1 ) = arg max o { Pr ( i | o , h ^ ( n ) ) Pr ( o ) } , h ^ ( n + 1 ) = arg max h { Pr ( i | o ^ ( n + 1 ) , h ) Pr ( h ) } .
Pr ( o ) = Z λ o 1 e - λ o E ( o ) ,
Pr [ O = o ( x ) ] = Z λ o 1 e λ o x | o ( x ) | ,
| o ( x , y , z ) | ϵ = ( ( o ( x + 1 , y , z ) o ( x , y , z ) ) 2 + ( o ( x , y + 1 , z ) o ( x , y , z ) ) 2 + ( o ( x , y , z + 1 ) o ( x , y , z ) ) 2 + ϵ 2 ) 1 2 ,
J reg , o ( o ( x ) ) = λ o x | o ( x ) | ϵ .
Pr ( o , h ^ | i ) = Z λ o 1 e - λ o x | o ( x ) | · x Ω [ h ^ * o ] ( x ) i ( x ) e [ h ^ * o ] ( x ) i ( x ) ! .
J ( o , h ^ | i ) ( x Ω [ h ^ * o ] ( x ) x Ω i ( x ) log [ h ^ * o ] ( x ) + x Ω log ( i ( x ) ! ) ) + λ o x Ω | o ( x ) | + log [ Z λ o ] .
1 h ^ ( - x ) * ( i ( x ) ( h ^ * o ) ( x ) ) - λ o div ( o ( x ) | o ( x ) | ) = 0 ,
o ^ ( n + 1 ) ( x ) = [ i ( x ) ( o ^ ( n ) * h ^ ) ( x ) * h ^ ( x ) ] · o ^ ( n ) ( x ) 1 λ o div ( o ^ ( n ) ( x ) | o ^ ( n ) ( x ) | ) ,
Pr [ o ( x ) ] : = { Z λ o 1 e - λ o x | o ( x ) | , if o ( x ) 0 0 , ot herwise.
Pr [ o ( x ) ] : = Z n e w , λ o - 1 e λ o x | o ( x ) | · ( 1 ( 1 + exp ( β o ( ϵ o ( x ) ) ) ) ) ,
J ( o , h ^ | i ) ( x Ω [ h ^ * o ] ( x ) x Ω i ( x ) log [ h ^ * o ] ( x ) ) + λ o x Ω | o ( x ) | + log [ Z new , λ o ] log ( 1 ( 1 + exp ( β o ( ϵ o ( x ) ) ) ) ) ,
1 h ^ ( - x ) * ( i ( x ) ( h * o ) ( x ) ) - λ o div ( o ( x ) | o ( x ) | ) - β o exp ( β o ( ϵ o ( x ) ) ) 1 + exp ( β o ( ϵ o ( x ) ) ) = 0 ,
o ^ ( n + 1 ) ( x ) = [ i ( x ) ( o ^ ( n ) * h ^ ) ( x ) * h ^ ( x ) ] · o ^ ( n ) ( x ) 1 λ o div ( o ^ ( n ) ( x ) | o ^ ( n ) ( x ) | ) - β o exp ( β o ( ϵ o ( x ) ) ) 1 + exp ( β o ( ϵ o ( x ) ) ) .
h ( x ) = ( 2 π ) - 3 2 | Σ | - 1 2 exp ( - 1 2 ( x μ ) T Σ 1 ( x μ ) ) ,
J ( o ^ , θ | i ) = x Ω ( i ( x ) log [ h ( θ ) * o ^ ] ( x ) ) + x Ω [ h ( θ ) * o ^ ] ( x ) .
θ l ^ ( n + 1 ) = θ l ^ ( n ) α ( n ) θ l J ( o ^ , θ l ^ ( n ) | i ) ; θ ^ = { σ r ^ , σ z ^ } ,
θ l J ( o ^ , θ l | i ) = x Ω [ θ l h ( θ ) * o ^ ] ( x ) x Ω i ( x ) [ h ( θ ) * o ^ ] ( x ) · [ θ l h ( θ ) * o ^ ] ( x ) , θ l > 0 Θ .

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