Rank-order Filters and Bayes Posterior Decision

This paper gives the optimal stack filtering theory under the mean absolute error (MAE) criterion a completely new meaning in terms of the a posteriori Bayes minimum-cost decision. It is shown that under certain conditions this always leads to a rank-order filter (ROF) as the best filter in the minimum MAE sense. It is further shown that for a mostly practical case, the solution becomes the median filter. The ROFs produced by this approach are subjected to a sensitivity analysis to quantify their dependency upon the cost coefficients. Several design examples will be provided.