Statistical characterization of detail preservation

A novel method of quantifying the level of detail preservation ability of digital filters is proposed. The method assumes only the input distribution of the filter and estimates how much the filter changes the signal. The change is measured by the expectation of the absolute difference between the input and output signal. The method is applicable for many filters and input distributions. As an example case, the formulas for the expectation of the absolute difference for weighted order statistic filters with the uniform and Laplacian (biexponential) input distributions are derived. Finally, the design of weighted order statistic filters using supervised learning is studied. The learning method uses the detail preservation measure as a design criterion to obtain filters with different levels of detail preservation.