<title>Adaptive multistage weighted order-statistic filters for image restoration</title>

Abstract

In this paper multistage weighted order statistic (MWOS) filters are introduced. With the aid of threshold decomposition, it is shown that any MWOS filter in real domain corresponds to a multistage threshold logic gate, or a multilayer perceptron in binary domain, which can be viewed as another representation of a stack filter. The MWOS filter requires much fewer parameters to represent a stack filter than the truth table of the positive Boolean function. An adaptive filtering algorithm, named as constrained backpropagation (CBP) algorithm, is developed for finding the optimal MWOS filters under the mean absolute error (MAE) criterion. The CBP algorithm is the same as the backpropagation algorithm used in multilayer perceptrons except the positivity of the parameters of MWOS filters, equal to the stacking property of stack filters, is imposed. Simulation results on image restoration are provided to compare the performance of the adaptive MWOS filters and the adaptive stack filters.