  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.
