Generalized stack filters and minimum mean absolute error estimation

A class of sliding window operators called generalized stack filters is developed. This class of filters, which includes all rank order filters, stack filters, and digital morphological filters, is the set of all filters possessing the threshold decomposition architecture and a consistency property called the stacking property. A linear program is provided which determines a generalized stack filter which minimizes the mean absolute error (MAE) between the output of the filter and a desired input signal, given noisy observations of that signal. These results show that choosing the generalized stack filter that minimizes the MAE is equivalent to massively parallel threshold-crossing decision-making when these decisions are consistent with each other.<>