Design of optimal stack filters with structural constraints under the Mae criterion

The use of the concepts of preservation, removal, and modification of specific signal structures is extended to the set of filters known as stack filters. Since their definition is motivated by the two properties of the median filter, namely, the threshold decomposition an the stacking property, it should be possible be characterize stack filters by the signal structures they preserve or delete. It is shown that it is possible to design a stack filter which minimizes the mean absolute error subject to constraints on, or goals for, its behavior with regard to any list of signal structures specified by the designer. Thus, this approach unites the structural and estimation approaches to the design of stack filters under a single analytical methodology.<>