Adaptive neuro-fuzzy inference systems based approach to nonlinear noise cancellation for images

The adaptive neuro-fuzzy inference system (ANFIS) is an effective tool that can be applied to induct rules from observations, e.g. pattern recognition. In this paper, we extend the nonlinear noise cancellation method using ANFIS from 1-D signals to 2-D counterpart images. First, the image restoration contaminated with Gaussian noise is investigated in nonlinear passage dynamics of order 2. We inspect eight types of membership functions (MF): bell MF, triangle MF, Gaussian MF, two sided Gaussian MF, pi-shaped MF, product of two sigmoidal MFs, difference of two sigmoidal MFs, and trapezoidal MF. In addition, the other parameters, such as the training epochs, the number of MFs for each input, the optimization method, the type of output MFs, and the over-fitting problem, are investigated. For comparison with the noise cancellation using ANFIS, we simulate 22 conventional filtering techniques: spatial filters, optimal Wiener filter, frequency domain filters, wavelet, wavelet packet, 2-D adaptive filters, etc. The quality in terms of mean square error (MSE) of image restoration using the proposed noise cancellation using ANFIS (Pi-shaped MF) is at least 75 times better for Gaussian noise than that derived using any of these conventional filtering techniques.