BREAKDOWN POINTS, BREAKDOWN PROBABILITIES, MIDPOINT SENSITIVITY CURVES, AND OPTIMIZATION OF STACK FILTERS

Three new concepts - breakdown points, breakdown probabilities, and mi dpoint sensitivity curves - for stack filter analysis are introduced a nd analyzed in this paper. Breakdown points and probabilities can be u sed as measures of the robustness of stack filters. Midpoint sensitivi ty curves in turn give information on how sensitive the output of a st ack filter is to the changes of a single value in the input window. Th e second major contribution of this paper is the extension of the curr ent optimality theory of stack filters. This theory combines noise att enuation and different constraints on the filter's behavior. New const raints are introduced in this paper. A new optimization approach based on breakdown probability as a noise attenuation measure is also deriv ed. In certain special cases it is shown that the optimal stack filter that achieves the best noise attenuation subject to given constraints can be obtained in closed form. An algorithm for finding this form is given in this paper, and its modification for finding a stack filter having (approximately) a required rank selection vector is presented.