Optimal parameter estimation of ε-filter employing distribution distance

As the filter which can effectively remove the small amplitude noises on digital images, the ε - filter has been proposed. In order to effectively use this filter, a smoothing parameter ε - filter should be appropriately estimated before applying it. To address this problem, the authors proposed the parameter estimation method based on Hellinger distance (HD). In the method, HD between a residual signal and assumed noise distribution was evaluated, and a parameter ε of the ε - filter was estimated by finding the value giving minimum distance. However, the enough discussion on use of HD has not been made. s paper, it is attempted to utilize not only the HD, but also various distribution distances in the parameter estimation, and their performances and characteristics are compared and analyzed experimentally. Furthermore, the parameter estimation method is extended to be applicable for the vector ε - filter for the color images. Consequently, through the experiments, it is shown that L1-norm or maximum norm is appropriate as the distribution distance used in the parameter estimation methods from the view points of the simplicity of the calculation and MSE performance in the filtering.