A NEW CLASS OF NONLINEAR FILTERS - NEURAL FILTERS

In this paper we define a new class of nonlinear filters called neural filters based on the threshold decomposition and neural networks. It is shown that the neural filters include all filters defined either by continuous functions, such as linear FIR filters, or by Boolean functions, such as generalized stack filters. Adaptive least mean absolute error (LMA) and adaptive least mean square error (LMS) algorithms are derived for determining optimal neural filters. As special cases, adaptive generalized stack and adaptive generalized weighted order statistic filtering algorithms under both error criteria are derived. Experimental results in 1-D and 2-D signal processing are presented to compare the performance of the adaptive neural filters and other widely used filters.