OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 10 — Oct. 1, 1998
  • pp: 2609–2619

Superresolution and convergence properties of the expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent images

José-Angel Conchello  »View Author Affiliations


JOSA A, Vol. 15, Issue 10, pp. 2609-2619 (1998)
http://dx.doi.org/10.1364/JOSAA.15.002609


View Full Text Article

Acrobat PDF (455 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Computational optical-sectioning microscopy with a nonconfocal microscope is fundamentally limited because the optical transfer function, the Fourier transform of the point-spread function, is exactly zero over a conic region of the spatial-frequency domain. Because of this missing cone of optical information, images are potentially artifactual. To overcome this limitation, superresolution, in the sense of band extrapolation, is necessary. I present a frequency-domain analysis of the expectation-maximization algorithm for maximum-likelihood image estimation that shows how the algorithm achieves this band extrapolation. This analysis gives the theoretical absolute bandwidth of the restored image; however, this absolute value may not be realistic in many cases. Then a second analysis is presented that assumes a Gaussian point-spread function and a specimen function and shows more realistic behavior of the algorithm and demonstrates some of its properties. Experimental results on the superresolving capability of the algorithm are also presented.

© 1998 Optical Society of America

OCIS Codes
(100.1830) Image processing : Deconvolution
(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

Citation
José-Angel 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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-10-2609


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. D. L. Snyder, T. J. Schultz, and J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,” IEEE Trans. Sig. Proc. 40, 1143–1150 (1992).
  2. J. Biemond, R. L. Lagendijk, and R. M. Meresereau, “Iterative methods for image deblurring,” Proc. IEEE 78, 856–883 (1990).
  3. J. G. McNally, C. Preza, J. A. Conchello, and L. J. Thomas, Jr., “Artifacts in computational optical-sectioning microscopy,” J. Opt. Soc. Am. A 11, 1056–1067 (1994).
  4. M. Bertero, P. Boccacci, G. J. Brakenhoff, F. Malfanti, and H. T. M. van der Voort, “Three-dimensional image restoration and super-resolution in fluorescence confocal microscopy,” J. Microsc. 157, 3–20 (1990).
  5. B. Bertero, D. De Mol, and E. R. Pike, “Analytic inversion formula for confocal scanning microscopy,” J. Opt. Soc. Am. A 4, 1748–1750 (1987).
  6. H. C. Andrews and C. L. Patterson, “Singular value decompositions and digital image processing,” IEEE Trans. Acoust., Speech, Signal Process. ASSP-24, 26–53 (1976).
  7. 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).
  8. C. Preza, M. I. Miller, L. J. Thomas, Jr., and J. G. McNally, “Regularized method for reconstruction of three-dimensional microscopic objects from optical sections,” J. Opt. Soc. Am. A 9, 219–228 (1992).
  9. E. Scalas and G. A. Viano, “Resolving power and information theory in signal recovery,” J. Opt. Soc. Am. A 10, 991–996 (1993).
  10. P. J. Verveer and T. M. Jovin, “Efficient superresolutionrestoration algorithms using maximum a posteriori estimations with applications to fluorescence microscopy,” J. Opt. Soc. Am. A 14, 1696–1706 (1997).
  11. T. J. Holmes, “Maximum-likelihood image restoration adapted for noncoherent optical imaging,” J. Opt. Soc. Am. A 5, 666–673 (1988).
  12. 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).
  13. P. J. Sementilli, B. R. Hunt, and M. S. Nadar, “Analysis of the limit to superresolution in incoherent imaging,” J. Opt. Soc. Am. A 10, 2265–2276 (1993).
  14. J. A. Conchello, “Three-dimensional reconstruction of noisy images from partially confocal scanning microscope,” Ph.D. dissertation (Dartmouth College, Hanover, N.H., 1990).
  15. 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 and D. L. Snyder, eds., Proc. SPIE 2302, 369–378 (1994).
  16. D. O. Walsh and P. A. Nielsen-Delaney, “Direct method for superresolution,” J. Opt. Soc. Am. A 11, 572–579 (1994).
  17. W. A. Carrington, R. M. Lynch, E. D. W. Moore, G. Isenberg, K. Fogarty, and F. S. Fay, “Superresolution three-dimensional images of fluorescence in cells with minimal light exposure,” Science 268, 1483–1487 (1995).
  18. B. R. Frieden, “How well can a lens system transmit entropy?” J. Opt. Soc. Am. 58, 1105–1112 (1968).
  19. G. Toraldo di Francia, “Degrees of freedom of an image,” J. Opt. Soc. Am. 59, 799–804 (1969).
  20. J. A. Conchello and E. W. Hansen, “Enhanced 3-D reconstruction from confocal scanning microscope images. 1: Deterministic and maximum likelihood reconstructions,” Appl. Opt. 29, 3795–3804 (1990).
  21. B. R. Frieden, “Optical transfer of the three-dimensional object,” J. Opt. Soc. Am. 57, 56–66 (1967).
  22. C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik (Stuttgart) 72, 131–133 (1986).
  23. P. A. Stokseth, “Properties of a defocused optical system,” J. Opt. Soc. Am. 59, 1314–1321 (1969).
  24. N. Streibl, “Depth transfer by an imaging system,” Opt. Acta 31, 1233–1241 (1984).
  25. N. Streibl, “Fundamental restrictions for 3-D light distributions,” Optik (Stuttgart) 66, 341–354 (1984).
  26. N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. A 2, 121–127 (1985).
  27. C. J. R. Sheppard and X. Q. Mao, “Three-dimensional imaging in a microscope,” J. Opt. Soc. Am. A 6, 1260–1269 (1989).
  28. C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging II,” Optik (Stuttgart) 74, 128–129 (1986).
  29. R. V. Churchill and J. W. Brown, Complex Variables and Applications 4e (McGraw-Hill, New York, 1984), Sect. 103.
  30. J. A. Conchello, J. J. Kim, and E. W. Hansen, “Enhanced three-dimensional reconstruction from confocal scanning microscope images. 2: depth discrimination versus signal-to-noise ratio in partially confocal images,” Appl. Opt. 33, 3740–3750 (1994).
  31. R. N. Bracewell, The Fourier Transform and Its Applications 2e (McGraw-Hill, New York, 1978), pp. 148–156.
  32. R. N. Bracewell, The Fourier Transform and Its Applications 2e (McGraw-Hill, New York, 1978), pp. 160–163.
  33. R. N. Bracewell, The Fourier Transform and Its Applications 2e (McGraw-Hill, New York, 1978), p. 157.
  34. T. J. Holmes and 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).
  35. F. S. Gibson and 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).
  36. R. S. Aikens, D. A. Agard, and J. W. Sedat, “Solid-state imagers for microscopy,” in Methods in Cell Biology, Y.-L. Wang and D. L. Taylor, eds. (Academic, New York, 1989), Vol. 29, pp. 291–313.
  37. D. L. Snyder, A. M. Hammoud, and R. L. White, “Image recovery from data acquired with a charge-coupled-device camera,” J. Opt. Soc. Am. A 10, 1014–1023 (1993).
  38. S. Joshi and M. I. Miller, “Maximum a posteriori estimation with Good’s roughness for optical sectioning microscopy,” J. Opt. Soc. Am. A 10, 1078–1085 (1993).
  39. D. L. Snyder, M. I. Miller, L. J. Thomas, Jr., and D. G. Politte, “Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography,” IEEE Trans. Med. Imag. MI-6, 228–238 (1987).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited