Median filter based on fuzzy rules and its application to image restoration

A novel median-type filter controlled by fuzzy rules is proposed in order to remove impulsive noises on signals such as images. Median filter is well known for removing impulsive noises but this filter distorts the fine structure of signals as well. The filter proposed here is obtained as a weighted sum of the input signal and the output of the median filter, and the weight is set based on fuzzy rules concerning the states of the input signal sequence. Moreover, this weight is obtained optimally by a learning method, so that the mean square error of the filter output for some training signal data can be the minimum. Some results of image processing show the high performance of this filter. Moreover, the influence of the training signal on the filter performance is shown.