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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 5 — May. 1, 2001
  • pp: 1062–1071

Fast maximum-likelihood image-restoration algorithms for three- dimensional fluorescence microscopy

Joanne Markham and José-Angel Conchello  »View Author Affiliations

JOSA A, Vol. 18, Issue 5, pp. 1062-1071 (2001)

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We have evaluated three constrained, iterative restoration algorithms to find a fast, reliable algorithm for maximum-likelihood estimation of fluorescence microscopic images. Two algorithms used a Gaussian approximation to Poisson statistics, with variances computed assuming Poisson noise for the images. The third method used Csiszár’s information-divergence (I-divergence) discrepancy measure. Each method included a nonnegativity constraint and a penalty term for regularization; optimization was performed with a conjugate gradient method. Performance of the methods was analyzed with simulated as well as biological images and the results compared with those obtained with the expectation-maximization–maximum-likelihood (EM-ML) algorithm. The I-divergence-based algorithm converged fastest and produced images similar to those restored by EM-ML as measured by several metrics. For a noiseless simulated specimen, the number of iterations required for the EM-ML method to reach a given log-likelihood value was approximately the square of the number required for the I-divergence-based method to reach the same value.

© 2001 Optical Society of America

OCIS Codes
(100.1830) Image processing : Deconvolution
(100.3020) Image processing : Image reconstruction-restoration
(100.3190) Image processing : Inverse problems
(100.6640) Image processing : Superresolution
(100.6890) Image processing : Three-dimensional image processing
(180.6900) Microscopy : Three-dimensional microscopy

Original Manuscript: July 5, 2000
Revised Manuscript: November 3, 2000
Manuscript Accepted: November 6, 2000
Published: May 1, 2001

Joanne Markham and José-Angel Conchello, "Fast maximum-likelihood image-restoration algorithms for three- dimensional fluorescence microscopy," J. Opt. Soc. Am. A 18, 1062-1071 (2001)

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  1. B. R. Frieden, “Optical transfer of the three-dimensional object,” J. Opt. Soc. Am. 57, 56–66 (1967). [CrossRef]
  2. J. A. Conchello, E. W. Hansen, “Enhanced 3-D reconstruction from confocal scanning microscope images. I. Deterministic and maximum likelihood reconstructions,” Appl. Opt. 29, 3795–3804 (1990). [CrossRef] [PubMed]
  3. P. J. Shaw, “Comparison of wide-field/deconvolution and confocal microscopy for 3D imaging,” in Handbook of Biological Confocal Microscopy, 2nd ed., J. B. Pawley, ed. (Plenum, New York, 1995), pp. 373–387.
  4. H. T. M. van der Voort, K. C. Strasters, “Restoration of confocal images for quantitative image analysis,” J. Microsc. 178, 165–181 (1995). [CrossRef]
  5. 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]
  6. H. Kano, H. T. M. van der Voort, M. Schrader, G. M. P. van Kempen, S. W. Hell, “Avalanche photodiode detection with object scanning and image restoration provides 2–4 fold resolution increase in two-photon fluorescence microscopy,” Bioimaging 4, 187–197 (1996). [CrossRef]
  7. C. Preza, M. I. Miller, J.-A. Conchello, “Image reconstruction for 3-D light microscopy with a regularized linear method incorporating a smoothness prior,” in Biomedical Image Processing and Biomedical Visualization, R. S. Acharya, D. B. Goldgof, eds., Proc. SPIE1905, 129–139 (1993). [CrossRef]
  8. D. A. Agard, “Optical sectioning microscopy,” Annu. Rev. Biophys. Bioeng. 13, 191–219 (1984). [CrossRef]
  9. D. A. Agard, Y. Hiraoka, P. Shaw, J. W. Sedat, “Fluorescence microscopy in three-dimensions,” Methods Cell Biol. 30, 353–377 (1989). [CrossRef]
  10. W. A. Carrington, R. M. Lynch, E. D. W. 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]
  11. A. Erhardt, G. Zinser, D. Komitowski, J. Bille, “Reconstructing 3-D light-microscopic images by digital image processing,” Appl. Opt. 24, 194–200 (1985). [CrossRef] [PubMed]
  12. S. S. Stefanou, E. W. Hansen, “Restoration of edges under Poisson noise using convex constraints with application to 3D optical microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing IV, C. J. Cogswell, J.-A. Conchello, T. Wilson, eds., Proc. SPIE2984, 232–242 (1997).
  13. T. J. Holmes, “Expectation-maximization restoration of band limited, truncated point-process intensities with application in microscopy,” J. Opt. Soc. Am. A 6, 1006–1014 (1989). [CrossRef]
  14. T. J. Holmes, “Maximum-likelihood image restoration adapted for noncoherent optical imaging,” J. Opt. Soc. Am. A 5, 666–673 (1988). [CrossRef]
  15. S. Joshi, M. I. Miller, “Maximum a posteriori estimation with Good’s roughness for optical sectioning microscopy,” J. Opt. Soc. Am. A 10, 1078–1085 (1993). [CrossRef] [PubMed]
  16. C. Preza, M. I. Miller, L. J. Thomas, 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] [PubMed]
  17. P. J. Verveer, T. M. Jovin, “Efficient superresolution restoration algorithms using maximum a posteriori estimations with application to fluorescence microscopy,” J. Opt. Soc. Am. A 14, 1696–1706 (1997). [CrossRef]
  18. 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]
  19. W. A. Carrington, “Image restoration in 3D microscopy with limited data,” in Bioimaging and Two-Dimensional Spectroscopy, L. Smith, ed., Proc. SPIE1205, 72–83 (1990). [CrossRef]
  20. W. A. Carrington, F. E. Fogarty, F. S. Fay, “3D fluorescence imaging of single cells using image restoration,” in Noninvasive Techniques in Cell Biology, J. K. Fosket, S. Grinstein, eds. (Wiley–Liss, New York, 1990), pp. 53–72.
  21. J. A. Conchello, J. G. McNally, “Fast regularization technique for expectation maximization algorithm for optical sectioning microscopy,” in Three-Dimensional Microscopy: Image Acquisition and Processing III, C. J. Cogswell, G. S. Kino, T. Wilson, eds., Proc. SPIE2655, 199–208 (1996).
  22. A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Statist. Soc. B 39, 1–38 (1977).
  23. J. A. Conchello, “Super-resolution and point spread function sensitivity analysis of the expectation-maximization algorithm for computational optical sectioning microscopy,” in Image Reconstruction and Restoration, T. J. Schulz, D. L. Snyder, eds., Proc. SPIE2302, 369–378 (1994). [CrossRef]
  24. J. A. Conchello, “Superresolution 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]
  25. J. A. Conchello, J. J. Kim, E. W. Hansen, “Enhanced 3-D reconstruction from confocal scanning microscope images. II. Depth discrimination vs. signal-to-noise ratio in partially confocal images,” Appl. Opt. 33, 3740–3750 (1994). [CrossRef] [PubMed]
  26. L. Kaufman, “Implementing and accelerating the EM algorithm for positron emission tomography,” IEEE Trans. Med. Imaging MI-6, 37–51 (1987). [CrossRef]
  27. T. J. Holmes, Y. H. Liu, “Acceleration of maximum-likelihood image restoration for fluorescence microscopy and other noncoherent imagery,” J. Opt. Soc. Am. A 8, 893–907 (1991). [CrossRef]
  28. D. S. C. Biggs, M. Andrews, “Acceleration of iterative image restoration algorithms,” Appl. Opt. 36, 1766–1775 (1997). [CrossRef] [PubMed]
  29. I. Csiszár, “Why least squares and maximum entropy:—An axiomatic approach to inference for linear inverse problems,” Ann. Stat. 19, 2032–2066 (1991). [CrossRef]
  30. D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,” IEEE Trans. Signal Process. 40, 1143–1150 (1992). [CrossRef]
  31. A. N. Tikhonov, V. Y. Arsenin, Solutions to Ill-Posed Problems (Wiley, New York, 1977), p. 70.
  32. J. P. Butler, J. A. Reeds, S. V. Dawson, “Estimating solutions of first kind integral equations with nonnegative constraints and optimal smoothing,” SIAM J. Numer. Anal. 18, 381–397 (1981). [CrossRef]
  33. The XCOSM deconvolution package is available from URL http://www.ibc.wustl.edu/bcl/xcosm/xcosm.html .
  34. R. Fletcher, C. M. Reeves, “Function minimization by conjugate gradients,” Comput. J. 7, 149–154 (1964). [CrossRef]
  35. G. A. F. Seber, C. J. Wild, Nonlinear Regression (Wiley, New York, 1989), p. 610.
  36. M. Al-Baali, R. Fletcher, “On the order of convergence of preconditioned nonlinear conjugate gradient methods,” SIAM J. Sci. Comput. 17, 658–665 (1996). [CrossRef]
  37. N. H. Clinthorne, T.-S. Pan, P.-C. Chiao, W. L. Rogers, “Preconditioning methods for improved convergence rates in iterative reconstructions,” IEEE Trans. Med. Imaging 12, 78–83 (1993). [CrossRef] [PubMed]
  38. J. M. Ortega, W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic, New York, 1970), p. 259.
  39. F. S. Gibson, F. Lanni, “Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy,” J. Opt. Soc. Am. A 8, 1601–1613 (1991). [CrossRef]
  40. J. G. McNally, C. Preza, J. A. Conchello, L. J. Thomas, “Artifacts in computational optical-sectioning microscopy,” J. Opt. Soc. Am. A 11, 1056–1067 (1994). [CrossRef]
  41. J. Markham, J. A. Conchello, “Tradeoffs in regularized maximum-likelihood image restoration,” in Three-Dimensional Microscopy: Image Acquisition and Processing IV, C. Cogswell, J. A. Conchello, T. Wilson, eds., Proc. SPIE2984, 136–145 (1997).
  42. E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1974), p. 354.
  43. G. M. P. van Kempen, L. J. van Vliet, “Background estimation in nonlinear image restoration,” J. Opt. Soc. Am. A 17, 425–433 (2000). [CrossRef]
  44. I. J. Good, R. A. Gaskins, “Nonparametric roughness penalties for probability densities,” Biometrika 58, 255–277 (1971). [CrossRef]

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