A new threshold decomposition architecture is introduced to implement stack filters. The architecture is also generalized to a new class of nonlinear filters known as threshold decomposition (TD) filters which are shown to be equivalent to the class of L1-filters under certain conditions. Another new class of filters known as linear and order statistic (LOS) filters result from the intersection of the class of TD and L1-filters. Performance comparisons among several filters are then presented. It was found that TD is compatible with L1, LOS, and linear filters in suppressing Gaussian noise, and is superior in suppressing salt-and-pepper noise. LOS filters, however, provide a better compromise in performance and complexity.

Stack filters are a class of sliding-window nonlinear digital filters that possess the weak superposition property (threshold decomposition) and the ordering property known as the stacking property. They have been demonstrated to be robust in suppressing noise. Two methods are introduced to adaptively configure a stack filter. One is by employing the least mean square (LMS) algorithm and the other is based on perceptron learning. Experimental results are presented to demonstrate the effectiveness of the methods for noise suppression.>

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 which minimizes the MAE is equivalent to massively parallel threshold-crossing decision making when these decisions are consistent with each other.>