Data-dependent weighted median filtering based on fuzzy rules

When a signal containing rapid changes, such as an image signal, is degraded by additive noise, a weighted median filter, which is a generalization of the median filter, is useful in its restoration. The weight of the weighted median filter is designed by using training signals, and is designed to be optimal for all training signals. The designed filter, however, cannot be optimal for local training signals. From that viewpoint, this paper presents a data-dependent weighted median filter in which the weight is made variable according to local information from the signal to be processed. A data-dependent weighted filter is of course desirable for highly accurate restoration of signals with mixed properties, as in image signals. In order to realize a, high performance data-dependent filter, it is crucial to know accurately the local properties of the signal and to reflect them in the weights determined. In this study three kinds of local information are used to represent the local properties of a signal, and a method for the derivation of weights using fuzzy inference is established. A data-dependent weighted median filter is constructed employing the proposed method. Its performance and effectiveness are examined in several application examples. (C) 1998 Scripta Technica.