Recursive optimization of spherical watermarking using transportation theory

In this paper, we first define a class of secure spread spectrum (SS) watermarking, called spherical watermarking (SW), of which the distribution of the watermarked correlations has a uniform distribution over a spherical surface. Then, we propose an implementation of SW, namely transportation SW (TSW), which recursively minimizes embedding distortion using transportation theory. A theoretical analysis is also presented on the performance of the proposed TSW scheme in terms of the watermark to content power ratio (WCR), and is validated by our simulations. Simulation results show that TSW performs better in terms of WCR and robustness than existing secure SS watermarking schemes.