MATHEMATICAL METHOD FOR IDENTIFYING AI-GENERATED IMAGES BASED ON SVD AND LINEAR REGRESSION

Abstract

The rapid advancement of artificial intelligence technologies, particularly generative models such as Stable Diffusion, has led to an increase in AI-generated images, creating significant challenges for countering disinformation andensuring the integrity of digital content in social media, journalism, and legal contexts. The proposed mathematical method addresses this issue by providing an automated and effective approach to identifying synthetic patterns in images, offering practical value for ethical AI oversight and forensic applications. This research is particularly timely given the growing need for robust tools to detect image manipulations, such as deepfakes and copy-move forgeries, in an era of rapidly evolving AI capabilities.The purpose of this study is to develop and test a mathematical method for detecting the authenticity of digital images, utilizing singular value decomposition (SVD) and linear regression, with the tangent of the slope (slope) as the key criterionfor distinguishing real images from those generated by artificial intelligence (AI). The proposed approach aims to identifydifferences in the energy distribution of images, enabling the detection of synthetic patterns characteristic of AI-generated content, and to evaluate the method’s effectiveness through practical examples.The methodology involves transforming a digital image into a pixel matrix, applying singular value decomposition to obtain singular values, performing their logarithmic approximation, and constructing linear regression. The tangent of theslope is calculated as the regression coefficient, reflecting the rate of energy decay. To enhance accuracy, a block-based methodis employed, dividing the image into 16x16 pixel submatrices, with the resulting slope values compared against an empiricalthreshold (e.g., <-0,8 for authentic images). Experiments were conducted on a dataset comprising real photographs and imagesgenerated by models such as Stable Diffusion, followed by statistical evaluation of the results.The scientific novelty lies in the integration of SVD with linear regression to model the decay of logarithms of singular values, emphasizing the slope as a differential feature. Unlike traditional methods relying on frequency analysis or keypoints, thisapproach enables automated classification without the need for manual parameter tuning. It effectively detects manipulations,including copy-move forgery and deepfakes, addressing the rapid advancement of AI technologies.Conclusions. The findings of the study confirm the high effectiveness of the method for distinguishing between real andAI-generated images, where the average slope value for authentic images is -1,4026, and for synthetic images, it is -0.5829.The method demonstrates an accuracy of 87,76% on a test set of 98 images, along with a Recall of 93,55% and Specificity of 85,07%, though limitations were identified in analyzing images with uniform textures and the presence of 7 false positives. The results underscore the practical significance of the approach for protecting against disinformation, supporting jurisprudence,and ethical AI control, with prospects for further improvement through integration with techniques such as SIFT (Scale- Invariant Feature Transform) or CNN (Convolutional Neural Network).