A new block selection strategy from LU decomposition domain for robust image watermarking

The piracy of digital products has become an urgent problem to be solved. Robust watermarking is a promising technique for copyright protection. To go against rapidly increasing attacks, many techniques have been proposed in the transform domain for ensuring the quality of water marked image, the robustness of extracted watermark, and execution time. Among these techniques, the LU decomposition is considered an out- standing transformation in terms of computation. However, some pixel matrices cannot be decomposed as the product of a lower triangular matrix and an upper triangular matrix, and embedding them into two elements reduces the quality of the watermark image. Therefore, this paper proposes a novel image watermarking scheme based on a LU block selection strategy and an improved embedding algorithm. First, a pixel block is only applied LU decomposition and embedded a watermark bit when all determinants of sub-matrices are non-zero. Second, an effective embedding formula is proposed where the watermark is embedded into one element of suitable blocks. This solution helps to limit the modification of pixel values and enhance the quality of the watermarked image. Third, to decrease the extraction time, a novel formula is built for calculating embedded elements instead of LU decomposition. The experimental results show that our proposed method has the better visual quality of watermarked images and can effectively extract the watermark under some attacks, such as blurring, sharpening, and salt & pepper noise. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.