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Optimal-order fractional fourier transform with graph modeling for audio zero-watermarking
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DOI：10.1007/s11760-026-05274-w.png)
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Abstract
En 中文
In the digital age, digital watermarking is widely used for copyright protection. This work proposes an audio zero-watermarking scheme that operates in a fractional domain and explicitly examines the processing sequence between time-frequency transform and graph modeling. The framework first applies a fractional Fourier transform (FrFT) with an optimally selected order to map audio frames into a fractional time-frequency domain, then constructs a data-adaptive graph on the resulting coefficients, and finally uses singular value decomposition (SVD) to summarize the fractional-domain graph representation into a compact fingerprint that is bound to the watermark without modifying the host audio. Within a unified zero-watermarking protocol, we further compare transform-then-graph and graph-then-transform designs to examine how constructing the kNN graph in the time domain versus the transform domain affects synchronization robustness. Experiments show that, in the fractional domain, the transform-then-graph configuration achieves lower BER and higher NC than its counterpart in most cases, with especially clear gains under time-scale modification and cropping. These results indicate that building data-adaptive graphs in a suitably chosen fractional domain provides a robust yet transparent foundation for audio zero-watermarking.
Keywords:
Graph Signal Processing
Fractional Fourier Transform
Optimal Order
Zero-Watermarking
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