Superresolution and convergence properties of the expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent images.
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.
Conchello
J A
JA
Institute for Biomedical Computing, Washington University, St. Louis, Missouri 63110, USA. josec@ibc.wustl.edu
D000465:Algorithms; D003198:Computer Simulation; D007091:Image Processing, Computer-Assisted; D016013:Likelihood Functions; D008856:Microscopy, Fluorescence; D008962:Models, Theoretical; D055095:Optics and Photonics