Abstract

A general problem with statistically based estimators for images degraded by additive noise is their dependence on average quantities when image intensities vary rapidly and widely. The Wiener estimator, for example, given the stationary power spectrum of the object image and the noise, is known to produce a noisy effect in the flat intensity regions and a blurring or fuzzy effect in the edge regions of the restored image. The power spectra are usually estimated over regions containing both edges and flat regions and therefore are not truly representative of either regional type. In this work, we accept a nonstationary image model and utilize a novel adaptive windowing technique in conjunction with a nonlinear estimator to overcome the cited defects of other estimators. For each picture element, the analysis window for calculating the parameters of mean and variance is adapted according to the current value of an activity index. In this way, the presence of edges or flat regions can be detected for every picture element and duly incorporated into these parameter estimates. Then the object value for that element is estimated by a nonlinear function of those parameter estimates and the image value. This adaptive, nonlinear estimation technique is applied successively to simulated noisy 1-D feature waveforms, noisy images with 1-D windowing, and noisy images with 2-D windowing. In each case, features of the edge and flat regions both are faithfully reconstructed. In fact, the restored images are remarkably sharp and clean. They appear far superior to the comparable Wiener restorations despite the fact that their mean-squared error is about the same or slightly larger.

© 1986 Optical Society of America