Gram–Schmidt Orthogonalization-Based Audio Multiple Watermarking Scheme

Xiaochen Yuan, Mianjie Li

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)3958-3977
Number of pages20
JournalCircuits, Systems, and Signal Processing
Issue number8
Publication statusPublished - 1 Aug 2020
Externally publishedYes


  • Discrete cosine transform (DCT)
  • Gram–Schmidt orthogonalization
  • Local multiple watermarking
  • Spread transform dither modulation (STDM)


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