Synthesis of optimal detail-restoring stack filters for image processing

A two-step method is presented to synthesize optimal stack filters under the mean absolute error (MAE) criterion. First, the probabilities needed in the optimal filter design are estimated based on images. Second, the linear program (LP) required for finding the best filter is avoided by a `reasonably good´ suboptimal routine which only involves data comparisons. A sufficient condition under which the suboptimal routine results in optimal solutions is given and shown to hold in most practical cases. The proposed method is then applied to synthesize a family of optimal stack filters for the task of restoring an image in impulsive noise. Testing results show that the synthesized filters lead to a greatly improved image-detail restoration compared to standard median filters, although median filters remove noise better