STATISTICAL ANALYSIS OF THE IMPACT OF LOSSY COMPRESSION ALGORITHMS ON THE STRUCTURE OF DIGITAL IMAGES

Abstract

This paper investigates the impact of lossy compression algorithms on the statistical structure of digital images. Compression is a necessary step in data storage and transmission, but it changes the original characteristics of the signal, which can complicate further analysis in computer vision, remote sensing, and medical diagnostics. Traditional quality metrics (MSE, PSNR, SSIM) do not fully reflect these statistical changes, so the analysis of histograms and moments of distortion distribution is relevant. The aim of this study is to quantitatively assess the impact of JPEG, JPEG2000, WebP, and AVIF codecs on the stochastic properties of images. For this purpose, two types of data were used: a synthetic test image with a well-defined structure and a real image with natural textural inhomogeneities. Both images were compressed at different quality parameters (Q = 30, 50, 70, 90). Subsequent analysis included constructing histograms of the difference images and calculating the mean, standard deviation, skewness, and kurtosis, as well as checking the spatial consistency of the distortions. The obtained results showed that for the codecs under study, a decrease in the quality parameter Q leads to an increase in variance and kurtosis, while the values of the mean and asymmetry remain close to zero. For the synthesized image, JPEG2000 produces the largest variation in stochastic characteristics, while WebP and AVIF produce the smallest, with AVIF generating very narrow distributions with high kurtosis. At the same time, for the real compressed image, there is an overall decrease in the standard deviation and kurtosis values compared to the synthetic case, and the heavy-tailed distributions typical of AVIF and WebP on the test data are less pronounced. This can be explained by the presence of natural textures, over which compression errors are more evenly distributed. The study of spatial dependencies confirmed the local nature of the distortions, without significant correlation between the rows of the difference images. The analysis results show that different formats affect the statistical properties of images in different ways. The use of both synthetic and real images made it possible to demonstrate the differences between limiting scenarios and practical conditions of using the codecs under study. The results can be used to improve methods for evaluating compression quality and to develop efficient procedures for automated processing and statistical classification of images.