Optical Spatial Filtering with the Least Mean-Square-Error Filter*

Experimental studies dealing with the restoration of photographic images by optical spatial-filtering techniques are reported. The spatial filters are of a class incorporating predictions of optimum-filtering theory in the presence of random additive noise. This theory was derived using the criterion of least-mean-square error. Measured-modulation-transfer-function curves of both filtered and unfiltered scenes are presented, as well as restorations of continuous tone and binary (Sayce) images distorted by linear motion during exposure. Results show that this type of filtering is superior to that of the infinite signal-to-noise-ratio spatial filter.