Fast impulsive noise removal

A generic n-dimensional filter with the primary purpose of eliminating impulsive-like noise is presented. This recursive nonlinear filter is composed of two conditional rules, which are applied independently, in any order, one after the other. It identifies noisy items by inspection of their surrounding neighborhood, and afterwards it replaces their values with the most "conservative" ones out of their neighbors' values. In this way, no new values are introduced and the histogram distribution range is conserved. This n-dimensional filter can be decomposed recursively to a lower dimensional space, each time generating two sets of n(n-1)-dimensional filters. This study, which focuses on the case of two-dimensional signals (gray scale images), explores one possible implementation of this new filter and orients the evaluation of its performance toward the median filter, as this filter is the basis of many more sophisticated filters for impulsive noise reduction. Tests were carried out using both real and artificial images. We found this new filter to be much faster than the median filter while performing comparably in terms of both image information conservation and noise reduction, which suggests that it could replace the median filter for the preliminary processing included in state-of-the-art noise removal filters. This new filter should either eliminate or attenuate most noisy pixels in synthetic and natural images not excessively contaminated. It has a slight smoothing effect on nonnoisy image regions. In addition, it is scalable, easily implemented, and adaptable to specific applications.