Minimax optimization over the class of stack filters

A new optimization theory for stack filters is presented in this paper. This new theory is based on the minimax error criterion rather than the mean absolute error (MAE) criterion used in [8]. In the binary case a methodology will be designed to find the stack filter that minimizes the maximum absolute error between the input and the output signals. The most interesting feature of this optimization procedure is the fact that it can be solved using a linear program (LP) just like in the MAE case [8]. One drawback of this procedure is the problem of randomization due to the lost of structure in the constraint matrix of the LP. Several sub-optimal solutions will be discussed and an algorithm to find an optimal integer solution (still using a LP) under certain conditions will be provided. When generalizing to multiple-level inputs complexity problems will arise and two alternatives will be suggested. One of these approaches assumes a parameterized stochastic model for the noise process and the LP is to pick the stack filter which minimizes the worst effect of the noise on the input signal.