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Novel schemes for the improvement of lifting wavelet transform-based image watermarking using Schur decomposition

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Abstract

Imperceptibility, robustness, and reliability are essential characteristics of image watermarking. In this paper, two image watermarking schemes, first Lifting wavelet transform (LWT)–Discrete cosine transform (DCT) with zigzag scanning-based embedding in Schur domain and second LWT-Schur decomposition-based embedding scheme in Schur domain itself, are proposed. In this paper, two schemes are proposed in which a pre-processed watermark image is generated using LWT and Schur decomposition, where the principle diagonal coefficients of the upper triangular matrix are embedded into the cover image in LWT-Schur domain. The remaining matrix, after removing diagonal components and other unitary matrix of Schur decomposition of LL sub-band of watermark image are used as keys which provide better security to the watermarking scheme. In the LWT-Schur-based scheme principle diagonal coefficients of upper triangular matrix obtained from the Schur decomposition of the LL sub-band of the cover image are modified with the pre-processed watermark in Schur domain. In the LWT–DCT-based scheme, the low and mid-band frequency coefficients are used to embed the watermark using zigzag scanning to avoid any artifacts like diagonal line problem present in the SVD-based watermarking scheme, especially for larger value of the embedding gain factor. The Schur decomposition has lesser computation complexity as compared to SVD and both the schemes are also free from False positive problem. The LWT–DCT with zigzag scanning-based scheme offers higher robustness against filtering and noise attacks as Normalized correlation coefficient (NCC) value is close to 1.0000. Both the proposed schemes provide better imperceptibility and higher robustness as NCC value of more than 0.9800 against various checkmark attacks. Performance analysis shows that these schemes perform better in terms of Peak signal-to-noise ratio, and NCC under most of the attacks and also have lesser computational time than existing schemes.

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Acknowledgements

The research presented in this manuscript is conducted in the Electronics and communication engineering department MNNIT Allahabad, Prayagraj and free from any sponsored funding.

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Authors and Affiliations

  1. Electronics and Communication Engineering Department, Motilal Nehru National Institute of Technology, Prayagraj, Uttar Pradesh, 211004, India

    Anurag Tiwari & Vinay Kumar Srivastava

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  1. Anurag Tiwari
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  2. Vinay Kumar Srivastava
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AT: algorithm, proposed scheme, manuscript writing. VKS: Supervision, review, editing.

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Correspondence to Anurag Tiwari.

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Tiwari, A., Srivastava, V.K. Novel schemes for the improvement of lifting wavelet transform-based image watermarking using Schur decomposition. J Supercomput 79, 13142–13179 (2023). https://doi.org/10.1007/s11227-023-05167-6

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