Histogram-based fuzzy filter for image restoration

In this paper, we present a novel approach to the restoration of noise-corrupted image, which is particularly effective at removing highly impulsive noise while preserving image details. This is accomplished through a fuzzy smoothing filter constructed from a set of fuzzy membership functions for which the initial parameters are derived in accordance with input histogram. A principle of conservation in histogram potential is incorporated with input statistics to adjust the initial parameters so as to minimize the discrepancy between a reference intensity and the output of defuzzification process. Similar to median filters (MF), the proposed filter has the benefits that it is simple and it assumes no a priori knowledge of specific input image, yet it shows superior performance over conventional filters (including MF) for the full range of impulsive noise probability. Unlike in many neuro-fuzzy or fuzzy-neuro filters where random strategy is employed to choose initial membership functions for subsequent lengthy training, the proposed filter can achieve satisfactory performance without any training.