# On basis images for the digital image representation

## TL;DR

This paper explores basis images in digital and quantum contexts, introducing new orthogonal transforms and a correlation-based data scattering feature, with applications in image coding and watermarking.

## Contribution

It introduces a novel orthogonal transform for multi-dimensional arrays and establishes a quantum analog of basis images, enhancing data scattering analysis.

## Key findings

- New orthogonal transform for multi-dimensional arrays
- Quantum analogues of basis images as quantum operators
- Correlation-based data scattering feature in transforms

## Abstract

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.