General Expansion-Shifting Model for Reversible Data Hiding: Theoretical Investigation and Practical Algorithm Design

As a specific data hiding technique, reversible data hiding (RDH) has recently received extensive attention. By this technique, both the embedded data and the original cover image can be exactly extracted from the marked image. In our previous work, a general expansion-shifting model for RDH is proposed by introducing the so-called reversible embedding function (REF). With REF, RDH can be designed and the corresponding rate-distortion formulations can be established, providing an approach to optimize the reversible embedding performance. In this paper, by extending our previous work, optimal REF for one-dimensional histogram is investigated, and all optimal REF are derived in this case when the maximum modification to the cover pixel is limited as a small value. Moreover, based on the derived optimal REF for one-dimensional histogram and multiple histograms modification, a practical RDH scheme is presented and it is experimental verified better than some state-of-the-art algorithms in terms of capacity-distortion performance.