Abstract 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.

中文翻译：

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基于非参数统计的图像噪声滤波质量评估方法

摘要 本文在分析差分图像与白噪声的接近度的基础上，提出了一种新的数字图像加性高斯白噪声滤波质量评估的数值度量方法。这种分析通常以视觉方式进行，这会导致不良的主观主义。本文利用非参数BDS统计量的性质对差分图像进行数值分析，旨在减少主观主义对过滤质量评估的影响。指定的统计量用于时间序列分析，以检验其值的独立性和相同分布的假设。它可以作为噪声图像不同过滤方法的质量度量。该统计数据补充了已知的实用图像质量测量工具包，例如 PSNR、MSE 和 SSIM。众所周知，从这些措施的角度来看，良好的图像滤波质量并不总是对应于从视觉感知的角度来看的更好的滤波质量。已经表明，使用 BDS 统计值的测量表明对由所选过滤方法确定的差异图像元素的结构化（相关性）具有高度敏感性。通过对实现局部和非局部滤波方法的图像滤波算法进行仿真，基于BDS统计对其质量进行了比较分析。已经表明，使用 BDS 统计值的测量表明对由所选过滤方法确定的差异图像元素的结构化（相关性）具有高度敏感性。通过对实现局部和非局部滤波方法的图像滤波算法的仿真，基于BDS统计对其质量进行了比较分析。已经表明，使用 BDS 统计值的测量表明对由所选过滤方法确定的差异图像元素的结构化（相关性）具有高度敏感性。通过对实现局部和非局部滤波方法的图像滤波算法进行仿真，基于BDS统计对其质量进行了比较分析。