Proposal of median‐type fuzzy filter and its optimum design

This paper proposes a median-type fuzzy filter, aiming at the signal estimation in the case where the impulse and white Gaussian noise are superposed on the signal with sudden changes, such as the image signal. The filter is realized by generalizing the fuzzy filter previously proposed by the authors. In the previously proposed fuzzy filter, the signal point to be estimated is taken as the reference point and the signal is estimated by determining the input signals relatively close to the reference point, using the fuzzy clustering; whereas the filter proposed in this paper uses the median value of the input signal sequence as the reference point and the signal is estimated by determining the input signals close to that reference point using the fuzzy clustering. The signal is estimated by determining the center of gravity of the cluster of the points close to the median. Furthermore, in the proposed filter, the optimum design is realized by learning with respect to appropriate training signals. It is in general not possible to decide definitely whether or not the input signal is close to the median, and thus the fuzzy clustering is effective since it takes into consideration the ambiguity of the signal. By introducing the fuzzy clustering, it is shown in particular that an effective signal estimation is realized for the signal with subtle changes.