Efficient design of minmax ODIF robust stack filters

The design of an optimal stack filter may be reduced to a linear programming problem, where the criterion is the mean absolute error between a clean signal and noisy version of it. We introduce robustness considerations in the optimization problem. Our approach is to minimize the maximum value of the output distributional influence function (ODIF) associated with the signal and the additive noise. This leads to a new linear programming problem, solved with interior-point methods. We also present a heuristic that allows a significant reduction of the problem size, without sacrificing the quality of the resulting filter.