Enhancing watermarking robustness and invisibility with growth optimizer and improved LU decomposition

With the rapid advancement of network technology, the transmission of digital multimedia has accelerated, making copyright protection increasingly critical. To address the challenge of balancing invisibility and robustness in digital watermarking, an enhanced watermarking scheme based on the Growth Optimizer (GO) and improved LU decomposition is proposed in this paper. By utilizing the high-similarity positions of the L-matrix, which align with the maximum value positions of the first column in the original matrix block, the watermark is embedded and extracted directly in the spatial domain, reducing computational complexity. The key contributions of this paper are: (1) The L-matrix block, obtained after using LU decomposition to decompose an image block in the spatial domain, has a higher similarity on the position of the maximum value in the first column of the original pixel block. (2) Innovatively applying the GO to determine the optimal embedding modification and effectively balance invisibility and robustness. (3) Applying the geometric correction to restore the watermarked image affected by geometric attack and to improve resistance. Experimental results show that the proposed method achieves a PSNR above 40 dB and an SSIM above 0.98, ensuring high invisibility while demonstrating superior robustness compared to existing methods. This approach effectively balances invisibility and robustness in digital watermarking.