A method of choosing optimal threshold of ε-filter in image restoration

To restore image contaminated by impulse noise, median filter and its variations have been extensively used to remove the impulse noise. Standard median filter is able to remove a large amount of impulse noise but at the same time it makes some false-alarms. One type of modified median filter is the ε-filter which processes each pixel of the output of standard median filter in a binary manner, keeping the output of median filter unchanged or replacing it with the original pixel value. The binary decision making is controlled by comparing the absolute difference between the median filter output and the original image to a preset threshold. In most cases, the ε-filter produces better results than the standard median filter in terms of mean squared error. The problem of applying the ε-filter in image restoration is to choose a proper threshold. A threshold too low or high will generate sub-optimal results. In this paper, we present a method of choosing an approximately optimal threshold in the sense of minimizing the mean squared error of the ε-filter. We use examples to demonstrate the performance of our method.