Extended permutation filters and their application to edge enhancement

Extended permutation (EP) filters are defined and analyzed in this paper. In particular, we focus on extended permutation rank selection (EPRS) filters. These filters are constrained to output an order statistic from an extended observation vector. This extended vector includes N observation samples and K statistics that are functions of the observation samples. By selecting an appropriate extended observation space, we show that the EPRS filters can be designed to have excellent edge enhancement characteristics. Moreover, the EPRS filters can perform edge enhancement in the presence of noise making them a powerful filter class