Hierarchical reversible data hiding based on statistical information: Preventing embedding unbalance

For reversible data hiding, the histogram-based difference expansion (DE) is one family of the generic methods where secret bits are embedded into an image by DE on prediction error. However, the ratio of the count of bit 0 to that of bit 1, embedded into the pixels with the same prediction error, will vary with the image and the secret bits, which leads to the embedding unbalance and image distortion. Therefore, a novel hierarchical embedding scheme is proposed to remove the unbalance level by level. We only implement it in two levels considering the complexity of constructing reversible transform for the hierarchical embedding. In the first level, the histogram is divided into different groups according to prediction error, and then two group exchange operations are designed to remove the embedding unbalance depending on the statistical information of this level. For further removing the unbalance, two adjacent groups are combined to a composite group in the second level, and another two composite group exchange operations are constructed to eliminate the unbalance by using the statistical information of the second level. Simulations demonstrate that the proposed hierarchical algorithm can achieve better performance in comparison with other existing histogram-based DE methods.

► The embedding unbalance is firstly pointed out in the histogram-based DE methods.
► A hierarchical embedding method is proposed to eliminate the unbalance.
► Two pairs of invertible integer transforms are designed to remove the unbalance.
► Two pairs of optimal integer transforms are integrated into the proposed method.
► Numerical simulation showed that effectiveness of the proposed method.