A class of noniterative estimators for nonlinear image restoration

Noniterative estimators for the nonlinear image restoration problem are investigated. A general, nonlinear image formation model is considered in conjunction with a minimum-mean-square-error (MMSE) restoration approach. In the special case of a logarithmic nonlinearity, the optimal estimator is analytically derived within the class of algorithms that involve the inverse of the system´s nonlinearity, followed by a linear transformation. This class of estimators is initiated by the nonlinear pseudo-inverse solution. The introduction of a combined-objective-function approach compensates for the stationarity assumption, incorporating both spatial and spectral information in the nonlinear MMSE algorithm. This approach results in an adaptive algorithm, which adjusts its performance with respect to the detailed structure of the image. The nonlinear restoration algorithms introduced are demonstrated through examples