RANK ORDER OPERATORS AND THE MEAN ABSOLUTE ERROR CRITERION

The author shows that among all randomizing stack filters whose output decisions are based on the sum of the bits in the window on each level of the threshold decomposition architecture, rank-order operators are optimal under an error criterion which is the sum of the absolute error incurred on each level of the threshold decomposition architecture. He also shows that if the filtering class being optimized obeys a deterministic stacking property, then the traditional multilevel mean absolute error criterion reduces to the sum of the absolute error incurred to each level. This leads to an efficient algorithm for choosing the rank-order filter which minimizes the multilevel mean absolute error criterion.