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Reversible watermarking has been one of the hottest research topics in information hiding domain over the past two decades. Unlike the traditional one (Wang and Zhu, 2015), this technique can extract the hidden data and recover host image to be its original condition losslessly. This reversibility feature is widely used in military, medical and other sensitive fields. Creating a new space by losslessly compressing one bit-plane of image to embed data was first proposed by (Fridrich, Goljan & Du, 2001). Tian (2003) proposed a difference expansion (DE) algorithm by calculating pixel difference to afford more capacity. In addition, prediction-error expansion (PEE) was proposed by Thodi and Rordriguez (2004). The existing reversible watermarking algorithms (Wang, Li, Yang & Guo, 2010; Li, Yang & Zeng, 2011; Chen, Sun, Sun, Zhou & Zhang, 2013; Li, Zhang, Gui & Yang, 2013; Ou, Li, Zhao, Ni & Shi, 2013; Wang & Zhu, 2015)) are mostly based on the aforementioned DE, PEE and histogram shift (HS) techniques. However, they are designed for lossless environment. That is the host image must be transmitted without any attacks such as image compression, geometric attacks, noise etc. Otherwise, the embedded information will no longer be extracted exactly.
Aiming at the problem above, Vleeschouwer et al. (Vleeschouwer, Delaigle & Macq, 2003) proposed a robust reversible method against JPEG compression. By a special circular interpretation of bijective transformation, this method embeds secret data losslessly. At the receiving end, if the host does no experience any attacks, the embedded data can be extracted correctly and the host can be restored to be the same as the initial state. Besides, the hidden data can be still extracted accurately after JPEG compression to some extent. Henceforth, we call such technology as robust lossless data hiding. The drawback of Vleeschouwe et al.’s algorithm is that it may generate salt-pepper noise and spoil the visual quality of host image. In 2008, Ni et al. (Ni, Shi, Ansari, Su, Sun & Lin, 2008) presented a robust lossless algorithm based on statistic histogram modification. The performance of Ni et al.’s method regarding PSNR and robustness is much better than the aforementioned one. Then, a similar scheme was presented by Li (2012). Besides these two schemes carried out in spatial domain, a framework for distortion-free robust image authentication was proposed by Coltuc (2007). This general framework embeds robust data in frequency domain and fragile ones in spatial domain with two stages, which provides inspiration to our work in this paper. Liu et al. (Liu, Ju, Hu, Ma & Zhao, 2015) adopted an intra-prediction model to embed data into integer DCT coefficients in frequency domain. Gao et al. (An, Gao, Li, Tao, Deng & Li, 2012) provided a robust reversible framework based on clustering and wavelet transformation. However, in these above robust lossless schemes, the most focus of robustness is resisting to image compression. Little attention is payed to geometric attacks such as rotation, scale and translation (RST).