Measure of filtering quality assessment of image noise using nonparametric statistic

The paper proposes a new numerical measure for filtering quality assessment of additive white Gaussian noise in digital images based on the analysis of closeness of the difference image to white noise. Such analysis is often conducted visually that leads to undesirable subjectivism. The numerical analysis of difference image using the properties of nonparametric BDS statistic was performed in this paper aimed at reducing the impact of subjectivism on the filtering quality assessment. The specified statistic is applied for the analysis of time sequence in testing the hypothesis on independence and identical distribution of its values. It can serve as a measure of quality of different filtering methods of noisy images. This statistic complements the toolkit of known practical measures of image quality, such as PSNR, MSE and SSIM. It is well known that a good quality of image filtering, from the viewpoint of these measures, not always corresponds to the better quality of filtering from the viewpoint of its visual perception. It has been shown that the measure using the values of BDS statistic demonstrates a high sensitivity to the structuring (dependence) of elements of difference image determined by the chosen filtering method. Using the simulation of image filtering algorithms implementing the methods of local and non-local filtering, a comparative analysis of their quality was conducted based on using BDS statistic