Abstract

Current image estimators have the property that the estimation error or noise has positive correlation with the true object. In principle, therefore, the estimation noise can be further processed to extract more information about the object. The estimators therefore fall short of the goal of extracting as much information as possible about the object. To remove this deficiency, a new estimator is proposed which attempts simultaneously to maximize the correlation between the estimate and the object (or minimize the correlation between the error and object) and minimize the mean-square error. It turns out that this is an optimization problem with competing objectives. The solution is a compromise between the usual minimum mean-square error (Wiener) estimator (which produces an error uncorrelated with the image) and an inverse filter. The resulting new estimator (which is called MEMO for minimum-error minimum-correlation) is applied to images degraded by linear space-invariant blur and additive noise. Simulations are undertaken with different images having different extents of blur and degrees of noise degradation, where object estimates are obtained through the new MEMO estimator and, for comparison, the Wiener estimator. The MEMC estimator produced sharper and clearer restorations, especially at the lower signal-to-noise ratios.

© 1985 Optical Society of America