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The development of a geometric invariant audio watermarking scheme without degrading acoustical quality is challenging work. This paper proposes a multi-bit spread-spectrum audio watermarking scheme based on a geometric invariant log coordinate mapping (LCM) feature. The LCM feature is very robust to audio geometric distortions. The watermark is embedded in the LCM feature, but it is actually embedded in the Fourier coefficients which are mapped to the feature via LCM, so the embedding is actually performed in the DFT domain without interpolation, thus eliminating completely the severe distortion resulted from the non-uniform interpolation mapping. The watermarked audio achieves high auditory quality in both objective and subjective quality assessments. A mixed correlation between the LCM feature and a key-generated PN tracking sequence is proposed to align the log-coordinate mapping, thus synchronizing the watermark efficiently with only one FFT and one IFFT. Both the theoretical analysis and experimental results show that the proposed audio watermarking scheme is not only resilient against common signal processing operations, including low-pass filtering, MP3 recompression, echo addition, volume change, normalization, test functions in the Stirmark benchmark, and DA/AD conversion, but also has conquered the challenging audio geometric distortion and achieves the best robustness against simultaneous geometric distortions, such as pitch invariant time-scale modification (TSM) by ±20%, tempo invariant pitch shifting by 20%, resample TSM with scaling factors between 75% and 140%, and random cropping by 95%. This is mainly contributed by the proposed geometric invariant LCM feature. To our best knowledge, audio watermarking based on LCM has not been reported before.
Kang et al. (Tue,) studied this question.