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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


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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

History
Original Manuscript: November 17, 1997
Revised Manuscript: March 23, 1998
Manuscript Accepted: May 26, 1998
Published: October 1, 1998

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

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