Partition fuzzy median filter based on fuzzy rules for image restoration

In this paper, a novel adaptive median-based filter, called the partition fuzzy median (PFM) filter, is proposed for improving the medianbased filter to preserve image details while effectively suppressing impulsive noises. The proposed filter achieves its effect through a summation of the weighted output of the median filter and the related weighted input signal. The weights are set in accordance with the fuzzy rules. In order to design this weight function, a method to partition of the observation vector space and a learning approach are proposed so that the mean square error of the filter output can be minimum. Based on the constrained least mean square algorithm, an iterative learning procedure is derived and its convergence property is investigated. As for the noise suppressing on both fixed- and random-valued impulses without degrading the quality of fine details, extensive experimental results demonstrate that the proposed filter outperforms the other median-based filters in the literature. The new filter also provides excellent robustness with respect to various percentages of impulse noise in our testing examples.