L. A. Denisov

V. N. Gorbachev, L. A. Denisov, E. M. Kaynarova et al.

Digital array orthogonal transformations that can be presented as a decomposition over basis items or basis images are considered. The orthogonal transform provides digital data scattering, a process of pixel energy redistributing, that is illustrated with the help of basis images. Data scattering plays important role for applications as image coding and watermarking. We established a simple quantum analogues of basis images. They are representations of quantum operators that describe transition of single particle between its states. Considering basis images as items of a matrix, we introduced a block matrix that is suitable for orthogonal transforms of multi-dimensional arrays such as block vector, components of which are matrices. We present an orthogonal transform that produces correlation between arrays. Due to correlation new feature of data scattering was found. A presented detection algorithm is an example of how it can be used in frequency domain watermarking.

V. N. Gorbachev, L. A. Denisov, E. M. Kaynarova et al.

Digital images can be copied without authorization and have to be protected. Two schemes for watermarking images in PDF document were considered. Both schemes include a converter to extract images from PDF pages and return the protected images back. Frequency and spatial domain embedding were used for hiding a message presented by a binary pattern. We considered visible and invisible watermarking and found that spatial domain LSB technique can be more preferable than frequency embedding using DWT.

V. N. Gorbachev, L. A. Denisov, E. M. Kainarova

For watermarking of the digital grayscale image its Gray planes have been used. With the help of the introduced representation over Gray planes the LSB embedding method and detection have been discussed. It found that data, a binary image, hidden in the Gray planes is more robust to JPEG lossy compression than in the bit planes.