Statistical-Mechanical Approach for Multiple Watermarks Using Spectrum Spreading

We formulated a Bayes optimum watermarking decoder and derived sub-optimum decoding algorithms for spread spectrum digital image watermarking. The optimum decoder can be obtained by considering the posterior probability under the Gaussian assumption for noise and attacks. The amount of calculation for the decoder is NP-hard. We, therefore, need to derive sub-optimum decoding algorithms in order to decode the watermarks. The proposed decoders are multiple watermark decoders that estimate multiple watermarks at the same time. These methods are based on the multi-stage demodulation method and the partial interference cancellation method, which are two CDMA multiuser demodulation methods. We applied them to the digital watermarking scheme. When the original image is blind, the image itself is regarded as noise. We, therefore, evaluated bit error rates both for cases when the original image is informed and blind. As a result, we found both the multi-stage watermark decoder and the partial interference cancellation decoder were effective for watermarking. The latter performed better than the former.