Partition Fuzzy Median Filter for Image Restoration

In this paper, a novel adaptive median filter, called the partition fuzzy is proposed. 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 observation vector space and a learning approach are proposed so that the mean square error of the filter output can be minimum. Based on constrained least mean square algorithm, an iterative learning procedure is derived and its convergence property is investigated. As details, extensive experimental results demonstrate that the proposed filter outperforms the other median-based filters in literature.