Invertible Matrix Fusion Domain: An Efficient Method for Digital Watermark Embedding and Extraction

Digital watermarking technology has become an important means to protect the copyright of digital media. However, existing methods often fail to simultaneously meet the key requirements of high real-time performance, high invisibility, strong robustness, and enhanced security. To overcome this limitation, we propose an efficient digital watermark embedding and extraction method based on an invertible matrix fusion domain, which establishes a balanced trade-off among these competing objectives. This method, for the first time, derives the properties of invertible matrix multiplication in the spatial domain and embeds the watermark by directly calculating the high-energy coefficients and evenly distributing the changes, thereby simplifying the embedding process and improving computational efficiency. To address the error propagation problem in quaternary coding, a minimum error propagation strategy based on quaternary (MEPQ) is proposed to enhance the robustness. In addition, the watermark image is encrypted by using the four-dimensional Lorenz chaotic system, which expands the key space and resists statistical attacks. Experimental results demonstrate the superior performance of the proposed method: it achieves excellent invisibility (PSNR$\gt 40$$dB$, SSIM$\gt 0.98$), strong robustness against various attacks (average NC$\gt 0.98$), high real-time efficiency (embedding time 0.18 seconds, extraction time 0.06 seconds, with$O(n)$complexity), and enhanced security with a large key space ($2^{768}$) to resist statistical attack and brute-force attack. These comprehensive results confirm that our method successfully meets the combined demands of real-time processing, invisibility, robustness, and security.