Optimized digital watermarking: Harnessing the synergies of Schur matrix factorization, DCT, and DWT for superior image ownership proofing

The contemporary context of abundant digital dissemination inherently gives rise to the need for media protection and the clear identification of ownership rights. This paper responded to this nagging issue of unauthorized media capture by developing a new digital watermarking approach uniting the Discrete Wavelet Transform DWT, Discrete Cosine Transform DCT, and Schur matrix factorization. The proposed watermark, which was a positive vector uniformly distributed, presented a high degree of robustness to several adversarial operating conditions, including histogram equalization, salt and pepper noise, ripple impact, smoothing attack, and cropping. The obtained results reveal the effectiveness of our approach. The correlation coefficient between watermarked and original images remains exceptionally high at 0.999998, ensuring minimal visual distortion. Mean Squared Error (MSE) graphs for both high-frequency (HH) and low-frequency (LL) domains demonstrate negligible changes after attacks, confirming the watermark's robustness. Notably, the watermark extraction process remains successful even after histogram equalization, as indicated by significantly lower MSE compared to random vectors. Moreover, the average processing times for different attacks are promising; Histogram Equalization and Salt and Pepper attacks each took 0.3 s, Ripple Attack required 0.28 s, Smoothing Attack completed in 0.29 s, and the Cropping Attack took 0.6 s. The robustness of our approach appears against the salt and pepper attack, which historically presented a vulnerability when employing Schur matrix factorization in image watermarking, indicating the novelty of and this contribution to improving media ownership verification. By combining disparate transformation methodologies, this technique offers a promising avenue for reinforcing the integrity and authenticity of digital media, thereby strengthening the foundations of intellectual property rights in the digital domain. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.