On the robustness and imperceptibility of digital fingerprints

For the majority of digital watermarking applications, two of the most desirable properties are robustness and imperceptibility. This paper presents a theoretical analysis of watermarking, in which an attacker estimates the watermark with the Wiener filter. A watermark´s robustness and imperceptibility can then be expressed in terms of its L ₂-efficiency-the amount of watermark energy that an attacker can remove. It is demonstrated that a power-spectrum condition (PSC) must be satisfied for maximum L₂-efficiency: the watermark´s power spectrum should be a scaled version of the original document´s power spectrum. Among watermarks that are independent of the original document, a PSC-compliant watermark is maximally L₂-efficient. Analysis of 1-D and 2-D signal models and experiments with real images further encourage the use of PSC-compliant watermarks