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
(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
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)