Eliminating orthonormal constraints of SVD to guarantee full retrievability of blind watermarking

Blind watermarking schemes based on Singular Value Decomposition (SVD), which decomposes a matrix into a product of two orthogonal matrices and a diagonal matrix in between them, typically manipulate orthonormal matrices to hide identity information. However, these manipulations can compromise orthonormality and result in incorrect and unstable watermark extraction, even in the absence of any attack. In this paper, we develop this idea by using an enhanced version of SVD called E-SVD, which releases all constraints on orthonormal matrices without information loss. By embedding watermarks freely while maintaining orthonormality, E-SVD theoretically guarantees the full retrievability of the watermark in the absence of an attack. We also derive the analytical relationship between the only parameter and imperceptibility, which facilitates the optimal trade-off between imperceptibility and robustness in the watermarking. To improve performance, a nonparametric extraction scheme is further leveraged. Experimental results demonstrate that our proposed scheme outperforms existing baselines and remains robust against various attacks, making it widely applicable in multiple scenarios. To the best of our knowledge, this is the first time that a theoretical guarantee for the full retrievability of SVD-based blind watermarking has been provided, which removes all restrictions imposed by orthonormality and paves the way for future innovations in blind watermarking.