Optimal watermark detection under quantization in the transform domain

The widespread use of digital multimedia data has increased the need for effective means of copyright protection. Watermarking has attracted much attention, as it allows the embedding of a signature in a digital document in an imperceptible manner. In practice, watermarking is subject to various attacks, intentional or unintentional, which degrade the embedded information, rendering it more difficult to detect. A very common, but not malicious, attack is quantization, which is unavoidable for the compression and transmission of digital data. The effect of quantization attacks on the nearly optimal Cauchy watermark detector is examined in this paper. The quantization effects on this detection scheme are examined theoretically, by treating the watermark as a dither signal. The theory of dithered quantizers is used in order to correctly analyze the effect of quantization attacks on the Cauchy watermark detector. The theoretical results are verified by experiments that demonstrate the quantization effects on the detection and error probabilities of the Cauchy detection scheme.