Adaptive Stack Filtering with Application to Image Processin

With the aid of threshold decomposition, it is shown that optimal stack filters under the mean absolute error (MAE) criterion are equal to optimal (or Bayesian) classifiers subject to stacking constraints under the mean classification error (MCE) criterion. Nonadaptive and adaptive constrained least mean absolute (LMA) algorithms are developed for the esti- mation of stack filters through the linearization of the unit step function in the objective function. The convergence of the al- gorithms is proven under certain conditions. Although the methods do not generally give optimal stack filters under the MAE criterion, these algorithms have several distinct merits compared to other stack filter optimization methods: 1) the op- timization problem has a unique solution that approximates the optimal stack filters in the least mean square sense; 2) the meth- ods can be implemented in the binary and real domains; and 3) for stack filters defined by linearly separable positive Boolean functions (PBF's) or weighted order statistic (WOS) filters, the number of the parameters to be estimated is reduced to the window width of the filter. A comparison between images re- stored by the new algorithms and the stack filtering algorithm optimal under the MAE criterion confirms the effectiveness of the proposed algorithms.