ORIGINAL PAPER S.T. Wang  F.L. Chung  Y.Y. Li  D.W. Hu X.S. Wu A new gaussian noise filter based on interval type-2 fuzzy logic systems Published online: 12 May 2004 Ó Springer-Verlag 2004 Abstract In this paper, a new selective feedback fuzzy neural network (SFNN) based on interval type-2 fuzzy logic systems is introduced by partitioning input and output spaces and based upon which a new FLS filter is further studied. The experimental results demonstrate that this new FLS filter outperforms other filters (e.g. the mean filter and the Wiener filter) in suppressing Gaussian noise and maintaining the original structure of an image. Keywords Image-processing  Filter  Gaussian noise  Type-2 fuzzy sets  Fuzzy logic systems  Neural networks 1 Introduction Effective removal of noise in degraded images is still a challenging problem in image processing. An efficient tool to suppress Gaussian noise is the mean filter [1], which is a very simple method and has been widely used in image processing. However, the membership grades for all the pixels in the operating window of the mean filter are assumed to be the same so that the fine struc- ture of the image may be destroyed. Many modified mean filters have been proposed to improve the perfor- mance [2, 3]. However, how to effectively determine the exact value of the membership grade for each pixel has not yet been solved. In [4], it has been shown by the theoretical analysis and demonstrated by the comprehensive experimental results that the type-2 fuzzy logic system (FLS) has obvious superiority in suppressing Gaussian noise in signal processing applications. In this paper, we focus on utilizing the type-2 fuzzy logic system (FLS) to cope with the problem of removing Gaussian noise in degraded images. Based on the interval type-2 FLS, a new selec- tive feedback fuzzy neural network (SFNN) is con- structed to express a given two-dimensional (2-D) digital image. The SFNN is a universal approximator and it works well as a filter to improve the performance of the mean filter and the Wiener filter in the suppression of Gaussian noise and maintaining the fine structure of the image. The new FLS filter, which is presented based on the new SFNN, not only has the same advantage as many other modified filtering approaches, such as the capability to provide superior performance to the simple mean filter and to describe images by the flexible soft techniques, but also integrates the new SFNN with im- age-processing techniques. In Sect. 2, we give a brief overview of the recently developed theory of type-2 FLS. In Sect. 3, the new SFNN structure is presented and it is shown that the SFNN is a universal approximator. In Sect. 4, we present the new FLS filter based on the new SFNN and several image examples are used to demonstrate that the new FLS filter has obvious advantage over the mean filter and the Wiener filter in removing Gaussian noise in images. The final section concludes this paper. 2 Type-2 fuzzy logic systems: a brief overview The type-2 fuzzy set was introduced by Zadeh [5] as an extension of the ordinary fuzzy set (typically called type- 1 fuzzy set). A type-2 fuzzy set is characterized by a fuzzy membership function, i.e., the membership value (or membership grade) for each element of this set is a fuzzy set in [0, 1]. This contrasts with the type-1 set where the element’s membership grade is a crisp number Soft Comput (2005) 9: 398–406 DOI 10.1007/s00500-004-0362-y S.T. Wang (&)  F.L. Chung Department of Computing, Hong Kong Polytechnic University, Hong Kong E-mail: wxwangst@yahoo.com.cn S.T. Wang  Y.Y. Li  X.S. Wu School of Information Engineering, Southern Yangtze University, Wuxi, China D.W. Hu School of Automation, National Defense University of Science and Technology, ChangSha, China