Division of Mathematics and Computer Applications Dept., University of Technology-Iraq, Alsina’a street, 10066 Baghdad, Iraq.


The close connection between mathematics, especially linear algebra, and computer science has greatly impacted the development of several fields, and the most important is image processing. Algebraic methods aroused interest in building digital image watermarking techniques and are used to find the features of the image to hide the watermark. This paper aims to use the algebraic Hessemberge decomposition method (HDM) for the first time as a transformation to extract the features of the image without using any popular transformation for building zero watermarking. To achieve the aim, two techniques are used, HDM with and without discrete cosine transform (DCT); both depend on the advantage of the algebraic HDM to convert the image to another domain in the YCbCr space. After applying eleven common attacks to images in both techniques, the results showed that the NC values ​​under the influence of many attacks were higher in the second technique than the NC values ​​in the first technique. In contrast, the NC values ​​for salt and pepper attack in the first technique are higher than the NC values ​​in the second technique.

Graphical Abstract


  • Build the zero watermarking techniques used the algebraic Hessenberg decomposition method to extract features from the host images for the first time.
  • The employing of the HDM is successful, not only algebraically, but the strength and importance of the obtained outcomes are equivalent to the best outcomes obtained from employing any common transform that extracts the features of the image optimally. · Based on the outcomes of the NC values obtained from the two methods mentioned in this paper, it is found that the NC values improved with the employ of DCT.
  • The suggested technique gave good robustness contra various kinds of popular attacks.


Main Subjects

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