Training recursive structures for weighted order statistic filtering

The weighted order statistics (WOS) filter is an extension of the median filter where the inputs are weighted. As in linear filtering, optimal filtering theory has been developed for non-recursive WOS-filters. This theory is analogous to optimal FIR filtering. In this paper we develop optimal filtering theory for recursive WOS filters. A recursive WOS filter contains previously calculated outputs within the sample window and is analogous to the IIR filter. We show by simulation that, like the IIR filter, the advantage of the optimal recursive WOS filter is that it requires fewer sample points within the sample window compared to the optimal non-recursive WOS filter. Furthermore, the recursive WOS filter does not have the stability problems of the IIR filter. The optimal recursive WOS filter requires fewer sample points than the corresponding non-recursive WOS filter. A smaller sample window leads to a reduction in the complexity of the WOS implementation