Transportation spherical watermarking

During the past twenty years, there has been a great interest in the study of spread spectrum (SS) watermarking. However, it is still a challenging task to design a secure and robust SS watermarking method. In this paper, we first define a family of secure SS watermarking methods, named as spherical watermarking (SW). The watermarked correlation of SW is defined to be uniformly distributed on a spherical surface, and this makes SW be key-secure against the watermarked-only attack. Then, we propose an implementation of SW, called transportation SW (TSW), which is designed to decrease embedding distortion in a recursive manner using the transportation theory, meanwhile keeping the security of SW. Moreover, we present a theoretical analysis of the embedding distortion and robustness of the proposed method. Finally, extensive experiments are conducted on simulated signals and real images. The experimental results show that TSW is more robust than existing secure SS watermarking methods.