Color image watermarking scheme based on singular value decomposition of split quaternion matrices

Abstract

As digital media increasingly faces copyright threats, robust protection schemes are crucial. While gray-scale watermarking techniques are well-developed, color watermarking problems require more advanced solutions due to the complex spectral relationships among RGB channels. This paper introduces a novel color watermarking scheme based on the split quaternion matrix model, a 4D algebraic structure that preserves the linear spectral relationships among RGB channels, enhances computational efficiency, and improves color image processing. Watermark embedding employs a double split quaternion singular value decomposition (SVDSQ) process. The host image is divided into patches, and dominant singular values are extracted from each patch using SVDSQ. These values are assembled into a matrix, which undergoes a second SVDSQ to embed the watermark. This dual-layered method enhances the adaptability of the watermark embedding payload. Experimental results show that, under the same experimental conditions, our watermarking scheme demonstrates strong robustness against noise and geometric attacks, while maintaining a high peak signal-to-noise ratio (PSNR $\ge$ 35), compared to recent watermarking schemes. Despite introducing real part redundancy and requiring prior information for the watermark extraction, this approach advances color image processing using split quaternion matrices. Future work will focus on addressing these limitations and exploring new applications.