Reversible watermarking based on multi-dimensional prediction-error expansion

The reversible watermarking algorithm has been extensively studied in the field of information security in recent years, and prediction-error expansion (PEE) is a widely used technology for reversible watermarking embedding. Ou et al. (IEEE Trans Image Process 22(12):5010–5021, 2013) proposed a two-dimensional histogram shifting method to extend the conventional method, which yields better performance. This paper further expands the two-dimensional histogram shifting method, proposes a reversible watermarking algorithm based on multi-dimensional PEE and reduces the distortion by abandoning the embedding mappings with high distortion. The experimental result shows that the multi-dimensional PEE method can achieve relatively higher Peak Signal to Noise Ratio (PSNR) at the same embedding rate. In addition, it also proves that, the multi-dimensional PEE algorithm only needs to consider the simplest case of the embedding distortion threshold, and it is more suitable for images with simple and smooth texture.