Weighted fuzzy mean filters for heavy-tailed noise removal

A new fuzzy filter, called weighted fuzzy mean (WFM) filter is proposed and analyzed in this paper. The WFM filter is powerful for removing heavy additive impulse noises from images. By the filtering of each WFM filter, the filtered output signal is the mean value of the corrupted signals in a sample matrix, and these signals are weighted respectively by a membership grade of an associated fuzzy number stored in a knowledge base. The knowledge base contains a set of fuzzy numbers decided by experts or derived from the histogram of referred image. When the probability of occurrence of mixed impulse noises is over 0.3, the WFM filter can recover the noise-corrupted image quite well in contrast with the conventional filters, for examples, the median filters, nonlinear mean filters, RCRS, WOS, CWM, and stack filters, based on the mean absolute error (MAE) and mean square error (MSE) criteria. Besides, on the subjective evaluation of filtered images, the WFM filter results in a higher quality of global restoration.