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We present efficient algorithms for image restoration by using the maximum a posteriori (MAP) method. Assuming Gaussian or Poisson statistics for the noise and either a Gaussian or an entropy prior distribution for the image, corresponding functionals are formulated and minimized to produce MAP estimations. Efficient algorithms are presented for finding the minimum of these functionals in the presence of nonnegativity and support constraints. Performance was tested by using simulated three-dimensional (3-D) imaging with a fluorescence confocal laser scanning microscope. Results are compared with those from two existing algorithms for superresolution in fluorescence imaging. An example is given of the restoration of a 3-D confocal image of a biological specimen.

Efficient superresolution restoration algorithms using maximum a posteriori estimations with application to fluorescence microscopy