This paper proposes an audio multi-watermarking scheme based on Gram–Schmidt orthogonalization. A random signal generator is applied to the host audio signal to generate the target segment for the local watermarking, thus improving the imperceptibility compared with the conventional global watermarking. The discrete cosine transform low-frequency coefficients of high stability are selected as watermark embedder, to ensure the robustness of this scheme. Consequently, the Gram–Schmidt orthogonalization process is employed to generate a set of orthogonal vectors, into which the spread transform dither modulation is applied to, respectively, embed the multiple watermark messages simultaneously. The orthogonality ensures that multiple watermark messages can be independently extracted without compromising the robustness against attacks. By embedding the multiple watermark messages into the same segment of the host audio signal, the watermark embedding capacity can be greatly enhanced while preserving the imperceptibility and robustness. A variety of experiments are conducted, and the results indicate the good performance of the proposed scheme. The proposed scheme has demonstrated superior performance gains over the state-of-the-art methods.

中文翻译：

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基于 Gram-Schmidt 正交化的音频多重水印方案

本文提出了一种基于 Gram-Schmidt 正交化的音频多水印方案。将随机信号发生器应用于宿主音频信号以生成用于局部水印的目标片段，从而与传统的全局水印相比提高了不可察觉性。选用稳定性高的离散余弦变换低频系数作为水印嵌入器，保证了该方案的鲁棒性。因此，采用 Gram-Schmidt 正交化过程来生成一组正交向量，在其中应用扩展变换抖动调制，分别同时嵌入多个水印消息。正交性确保可以独立提取多个水印消息，而不会影响对攻击的鲁棒性。通过将多个水印消息嵌入到宿主音频信号的同一段中，可以在保持不可感知性和鲁棒性的同时大大增强水印嵌入能力。进行了各种实验，结果表明所提出的方案具有良好的性能。与最先进的方法相比，所提出的方案已经证明了优越的性能提升。