A neuro-fuzzy network based impulse noise filtering for gray scale images Yueyang Li n , Jun Sun n , Haichi Luo Key Laboratory of Advanced Process Control for Light Industry, Jiangnan University, Wuxi, China article info Article history: Received 22 April 2013 Received in revised form 4 August 2013 Accepted 5 August 2013 Communicated by V. Palade Available online 19 October 2013 Keywords: Neuro-fuzzy system Image processing Filtering Impulse noise abstract A neuro-fuzzy network based impulse noise filtering for gray scale images is presented. The proposed filter is constructed by combining two neuro-fuzzy filters with a postprocessor, which generates the final output. Each neuro-fuzzy filter is a first order Sugeno type fuzzy inference system with 4-inputs and 1- output. The proposed impulse noise filter consists of two modes of operation, namely, training and testing (filtering). As demonstrated by the experimental results, the proposed filter not only has the ability of noise attenuation but also possesses desirable capability of detail preservation. It significantly outperforms other conventional filters. & 2013 Elsevier B.V. All rights reserved. 1. Introduction Images are often corrupted by noise during the acquisition or transmission process. Thus noise cancellation/filtering is an impor- tant task in image processing, especially when the final product is used for edge detection, image segmentation, and data compres- sion [1,2]. Image signals are composed of flat regional parts and abrupt changing areas, such as edges, which carry important information in visual perception. In the case of corruption by impulse noise, nonlinear techniques seem to perform better than linear ones, which tend to blur the edges and degrade the lines, edges, and other fine image details. As such, a great majority of filtering methods for the removal of impulse noise from images are based on median filtering techniques. The standard median filter (SMF) [3] is a simple nonlinear operation that outputs a median value of the pixels in a predefined filtering window to replace the center pixel of the window. The weighted median filter (WMF) [4] and the center weighted median filter (CWMF) [5] are extensions of the median filter, which give more weight to the appropriate pixels within the filtering window. Since these filters are spatially invariant operators, they inevitably distort the uncorrupted pixels in image while restoring the corrupted pixels. In the case of impulse noise removal, the aim of optimal filtering is to design noise reduction algorithm that would affect only corrupted image pixels, whereas the undistorted image pixels should be invariant under the filtering operation. Therefore, many algorithms have been proposed to combine the median filter with a decision mechanism which attempts to determine whether the center pixel of a detecting window is corrupted or not. The edge- detecting median filter (EDMF) [6] has been proposed to combine the median filter with an impulse detector which is based on the minimum absolute value of four convolutions obtained using one- dimensional Laplacian operators. A median based switching scheme, called multi-state median filter (MSMF) [7] was developed to adaptively switch among a group of center weighted median filters that have different weights by using a simple thresholding logic. The signal-dependent rand-ordered mean filter (SDROMF) [8] was conditioned on a state variable defined as the output of a classifier operating on the differences between the input pixel and the remaining rand-ordered pixels in a sliding window. The progressive switching median filter (PSMF) [9] is a modified switch- ing median filter, in which both the impulse detection and the noise filtering procedures are progressively applied through sev- eral iterations. The performances of these filtering methods depend on one or more tuning parameters. However, in the filtering experiments, it is hard to choose the optimal values for these parameters, which are heuristically determined. In addition to the conventional filters discussed above, a number of filtering methods based on neural networks and fuzzy systems have been proposed. Recently, there has been a growing research interest in the applications of neuro-fuzzy systems which combining neural networks and fuzzy systems [10–15]. Fuzzy systems are fundamentally well suited to model the uncertainty Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/neucom Neurocomputing 0925-2312/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.neucom.2013.08.015 n Corresponding authors. E-mail address: jsyueyangli@gmail.com (Y. Li). Neurocomputing 127 (2014) 190–199