An optimal nonlinear extension of linear filters based on distributed arithmetic

Distributed arithmetic (DA) based implementation of linear filters relies on the linear nature of this operation and has been suggested as a multiplication free solution. In this work we introduce a nonlinear extension of linear filters optimizing under MSE criterion the memory function (MF, multivariate Boolean function with not only binary output) which is in the core of DA based implementation. Such an extension will improve the filtering of noise which can contain non Gaussian components without increasing the complexity of implementation. Experiments on real images have shown the superiority of the proposed filter over the optimal linear filters. Different versions of these filters are also considered for the removal of impulsive noise, processing with the large input data windows and fast processing.