Fuzzy Sets and Systems 147 (2004) 75–97 www.elsevier.com/locate/fss Partition fuzzy median lter based on fuzzy rules for image restoration  Tzu-Chao Lin, Pao-Ta Yu ∗ Department of Computer Science and Information Engineering, National Chung Cheng University, Chia-Yi 62107, Taiwan, ROC Received 17 April 2002; received in revised form 23 December 2002; accepted 13 May 2003 Abstract In this paper, a novel adaptive median-based lter, called the partition fuzzy median (PFM) lter, is proposed for improving the median-based lter to preserve image details while eectively suppressing impulsive noises. The proposed lter achieves its eect through a summation of the weighted output of the median lter 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 lter 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 xed- and random-valued impulses without degrading the quality of ne details, extensive experimental results demonstrate that the proposed lter outperforms the other median-based lters in the literature. The new lter also provides excellent robustness with respect to various percentages of impulse noise in our testing examples. c  2003 Elsevier B.V. All rights reserved. Keywords: Impulse noise; Median lter; Fuzzy rule; Least mean square 1. Introduction Due to faulty communications or noisy channels, digital images are often corrupted by impulsive noises while the images are transmitted over channels. To remove the impulsive noises and enhance image restoration quality, many nonlinear lters proposed in the literature have more satisfactory results in contrast to linear lters [4]. The median lter is a well-known nonlinear lter, which  This work was partially supported by National Science Council of the Republic of China under Grant NSC 90-2213-E-194-043 and NSC 91-2520-S-194-006. * Corresponding author. Tel.: +886-52720411; fax: +886-52720859. E-mail address: csipty@cs.ccu.edu.tw (P.-T. Yu). 0165-0114/$ - see front matter c  2003 Elsevier B.V. All rights reserved. doi:10.1016/S0165-0114(03)00209-4