Applying generalized weighted mean aggregation to impulsive noise removal of images

In this paper, we apply generalized weighted mean to construct interval-valued fuzzy relations for grayscale image impulse noise detection and correction. First, we employ two weighting parameters and perform the weighted mean aggregation for the central pixel and its eight neighbor pixels in a 3×3 sliding window across the image. Then, to counter the over-weighting of a big difference term, we apply a saturation threshold transfer function to these eight pixel difference values. Finally, the image noise map is obtained through a threshold operation on the cumulative differences. To decrease the noise detection error, weighting parameters of the mean can be learned by the gradient method caste in discrete formulation. Moreover, to get higher PSNR in the corrected image, we have experienced from the training that we will select weight of 20 for noise rate smaller than 20% and 50 for noise rate greater than 20%, on erroneous noisy than that on the erroneous non-noise pixel. By the experiment, we have shown that the integration of interval-valued fuzzy relations with the weighted mean aggregation algorithm can effectively detect the image noise pixels and then correct them thereafter.