Constructing noise-reducing operators from training images

We discuss constructing non-linear noise reduction operators on binary images using a training set of noiseless images. We extract from the training set a probability distribution over local neighborhoods. Our operator changes pixel values when such a change turns a low probability neighborhood into high probability one. 1 1 Motivation We have developed an operator that modiies a pixel based on the probability of the current neighborhood connguration of that pixel. If the probability of a neighborhood connguration is below a given probability, p, and a change will bring the probability above p, then the neighborhood connguration is changed. To implement this operator, we gather information about diierent neighborhood conngurations by sampling neighborhoods from a training set of noiseless images (Milun and Sher, 1991). From this information, we generate a probability distribution of neighborhood conngurations. There are several motivations for using this technique; it is quick, exible and easy to implement.