Abstract

Linear and nonlinear image restoration methods have been studied in depth but have always been treated separately. In this paper several well-known linear and nonlinear restoration methods are written as recursive algorithms, and some new recursive algorithms are developed. The nonlinear restoration algorithms are based on the assumption that the noise is either a Poisson or a Gaussian process. The linear algorithms are shown to be related to the nonlinear methods through the partial derivative, with respect to the object, of a Poisson or a Gaussian likelihood function. A table of results is given, along with applications to real imagery.

© 1986 Optical Society of America

Maximum-entropy image restoration: Lagrange and recursive techniques

Edward S. Meinel
J. Opt. Soc. Am. A 5(1) 25-29 (1988)

Origins of linear and nonlinear recursive restoration algorithms: errata

Edward S. Meinel
J. Opt. Soc. Am. A 3(12) 2121-2121 (1986)

Fast maximum-likelihood image-restoration algorithms for three- dimensional fluorescence microscopy

Joanne Markham and José-Angel Conchello
J. Opt. Soc. Am. A 18(5) 1062-1071 (2001)

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

Peter J. Verveer and Thomas M. Jovin
J. Opt. Soc. Am. A 14(8) 1696-1706 (1997)

Image restoration with the Viterbi algorithm

Casey Miller, Bobby R. Hunt, Michael W. Marcellin, and Mark A. Neifeld
J. Opt. Soc. Am. A 17(2) 265-275 (2000)