A unified design method for rank order, stack, and generalized stack filters based on classical Bayes decision

The authors present a unified method for designing optimal rank order filters (ROFs), stack filters, and generalized stack filters (GSFs) under the mean absolute error (MAE) criterion. The method is based on classical Bayes minimum-cost decision. Both the a priori and the a posteriori approaches are considered. It is shown that designing the minimum MAE stack filters and GSFs is equivalent to the a priori Bayes decision. The authors develop a suboptimal routine which requires no linear program (LP) for finding reasonably good filters. They determine sufficient conditions under which the suboptimal routine produces optimal solutions. The procedure is developed separately for ROFs, stack filters, and GSFs. Some design examples are presented, and the application of stack filters and GSFs to image recovery from impulsive noise is considered. It is shown how the complexity of finding optimal stack filters and GSFs can be reduced