Robust Image Estimation in Signal-Dependent Noise.

Conventional image estimates in signal-dependent noise lack robustness for variations in a priori assumptions. In this work, the min-max robustness problem of image estimation in a signal-dependent noise model is explored. The criterion of robustness is the mean square error (MSE). Three cases which correspond to variations in the a priori signal distribution, in the a priori noise distribution and in a parameter of the model are investigated. For variations in the a priori signal (noise) distribution, the signal (noise) distribution is modeled as (epsilon)-contaminated normal. Due to the signal-dependence of noise, the robustness problem is too complicated to be solved analytically. A numerical direct searching algorithm is therefore proposed. In solving this robustness problem, we construct min-max robust estimators based on a number of criteria. For point estimation, these criteria include minimum mean square error (MMSE), minimum mean square error plus mean square bias error (MEB); we also discuss a simple two-step method and an adaptive two -step method. For multiple parameter estimation, we consider only the last two estimation procedures. Also the min -max robust estimator based on minimizing a mean square transformed error is explored. This transformation incorporates knowledge of the nonlinear sensitivity of human eyes to light intensity. Estimation methods based on maximum entropy and on smoothing splines are also briefly discussed. Finally, the restorations of images on a computer are presented to demonstrate the performance of these robust estimators relative to their nonrobust counterparts.