An adaptive fuzzy filter for image denoising

This study considers the problem of fuzzy modeling of the images in pixel domain. A zero-order Takagi–Sugeno type fuzzy model provides fuzzy smoothing to the image intensities for removing the additive noise from an image. An adaptive fuzzy filtering algorithm is suggested for estimating the parameters of the fuzzy model with noisy image data. The mathematical analysis of the proposed filtering algorithm has been provided in both deterministic and stochastic framework. The deterministic robustness of the filtering algorithm was shown by deriving an upper bound on the magnitude of estimation errors. The fuzzy filtering algorithm doesn’t demand Gaussian assumption of the noise and is also optimal in the “ sense ” of variation Bayes towards Student-t distributed noises.