Fuzzy stack filters: definition and design methods

Rank-order based filters have received considerable attention due to their inherent outlier rejection and detail preservation properties. One of the most important rank-order based filters is the stack filter. There are two different approaches to the design of stack filters. One might be called the structural approach, while the other might be called the estimation approach. On the other hand, we have proposed a fuzzy stack filter in order to extend the class of stack filters. Fuzzy stack filters are very important for signal processing, because these filters include FIR filters and weighted median filters. In this paper, we introduce the fuzzy stack filter and show design methods for the two different approaches (i.e. the structural approach and the estimation approach). Experimental results show that the fuzzy stack filter outperforms the (crisp) stack filter.