On the optimal modification of images projections onto basic vectors within the information hidden embedding

This work is devoted to the problem of developing methods for hidden control over the use and distribution of digital images based on the modification of the decomposition coefficients (projections) of images in various systems of basic vectors, determined with the use of two-dimensional transform. In this work, it was proposed to apply the evaluation of the distortion values of the projection on the subband matrices eigenvectors of given transform for estimating of the image-containers distortion within an information hidden embedding on the basis of the two-dimensional cosine transform subband analysis. The problem of searching for the optimal modified values of the projections is formulated and analytically solved from the position of minimizing the image-container distortion, which is set as the square of the Euclidean norm of the difference between the original and modified images. Computational experiments were performed to illustrate the advantages of the developed method of projection values optimal modification. It is shown that the application of the developed method allows to obtain smaller distortions of the analyzed image-containers in comparison with the known methods of hidden data embedding into images.