This paper describes an innovative watermarking method that combines discrete wavelet transform (DWT), Hessenberg decomposition (HD), and singular value decomposition (SVD). To do this, the main image and the watermark are divided into three channels (red, green and blue – RGB). Then, each part of the main image individually undergoes the steps of DWT, HD and SVD, while the watermark components are processed by SVD. Insertion of the watermark is carried out by adjusting the singular values of the watermark and the main image, using a watermark scaling factor ($\alpha$). The optimal choice of $\alpha$ poses a challenge, so the transit search algorithm is employed to find a trade-off between visibility and robustness. To evaluate this method, comparisons are made with other studies using various optimization algorithms such as particle swarm optimization, artificial bee colony and fly optimization algorithm. The results of the experiments confirm the effectiveness of this technique.
- Wang H., Yuan Z., Chen S., Su Q. Embedding color watermark image to color host image based on 2D-DCT. Optik. 274, 170585 (2023).
- Zhang Y., Gong Y., Wang J., Sun J., Wan W. Towards perceptual image watermarking with robust texture measurement. Expert Systems with Applications. 219, 119649 (2023).
- Singh R., Saraswat M., Ashok A., Mittal H., Tripathi A., Pandey A. C., Pal R. From classical to soft computing based watermarking techniques: A comprehensive review. Future Generation Computer Systems. 141, 738–754 (2023).
- Wang C., Li S., Liu Y., Meng L., Zhang K., Wan W. Cross-scale feature fusion-based JND estimation for robust image watermarking in quaternion DWT domain. Optik. 272, 170371 (2023).
- Sharma S., Sharma H., Sharma J. B., Poonia R. C. A secure and robust color image watermarking using nature-inspired intelligence. Neural Computing and Applications. 35, 4919–4937 (2023).
- Şenel F. A., Gökçe F., Yüksel A. S., Yiğit T. A novel hybrid PSO–GWO algorithm for optimization problems. Engineering with Computers. 35 (4), 1359–1373 (2019).
- Liu J., Huang J., Luo Y., Cao L., Yang S., Wei D., Zhou R. An Optimized Image Watermarking Method Based on HD and SVD in DWT Domain. IEEE Access. 7, 80849–80860 (2019).
- Mirrashid M., Naderpour H. Transit search: An optimization algorithm based on exoplanet exploration. Results in Control and Optimization. 7, 100127 (2022).
- Yashchuk Y. O., Tajs-Zielinska K. Solving topology optimization problems using cellular automata and mortar finite element method. Mathematical Modeling and Computing. 7 (2), 239–247 (2020).
- Seti Ju. O., Tkach M. V., Vereshko E. Ju., Voitsekhivska O. M. Modeling of optimized cascade of quantum cascade detector operating in far infrared range. Mathematical Modeling and Computing. 7 (1), 186–195 (2020).
- Pashchuk Y. M., Salnyk Y. P., Pashkovskyi V. V., Zaiets Y. H., Miskiv V.-M. V., Shkiliuk O. P. Method for structural optimization of avionics of unmanned aerial vehicle. Mathematical Modeling and Computing. 7 (2), 373–388 (2020).
- Tahiri M. A., Karmouni H., Sayyouri M., Qjidaa H. 2D and 3D image localization, compression and reconstruction using new hybrid moments. Multidimensional Systems and Signal Processing. 33, 769–806 (2022).
- El ogri O., Karmouni H., Sayyouri M., Qjidaa H. A novel image encryption method based on fractional discrete Meixner moments. Optics and Lasers in Engineering. 137, 106346 (2021).