Median type filters and perceptrons

Threshold composition shows that any multilayer perceptron with positive weights in the binary domain corresponds to a multistage weighted order statistic (MWOS) filter in the real domain. Two adaptive MWOS filtering algorithms, the constrained least mean absolute back-propagation (CLMA-BP) algorithm and the constrained least mean square back-propagation (CLMS-BP) algorithm, are derived for finding the optimal MWOS filters under the mean absolute error (MAE) and the mean square error (MSE) criteria, respectively. Experimental results for image restoration are provided to compare the performance of the adaptive MWOS filters and the adaptive stack filters. It is concluded that, as a concise representation of stack filters, MWOS filters can save heavy computations and significant memory requirements both during the filter training process and in the actual filtering process compared to stack filters