Rate and Distortion Optimization for Reversible Data Hiding Using Multiple Histogram Shifting

Histogram shifting (HS) embedding as a typical reversible data hiding scheme is widely investigated due to its high quality of stego-image. For HS-based embedding, the selected side information, i.e., peak and zero bins, usually greatly affects the rate and distortion performance of the stego-image. Due to the massive solution space and burden in distortion computation, conventional HS-based schemes utilize some empirical criterion to determine those side information, which generally could not lead to a globally optimal solution for reversible embedding. In this paper, based on the developed rate and distortion model, the problem of HS-based multiple embedding is formulated as the one of rate and distortion optimization. Two key propositions are then derived to facilitate the fast computation of distortion due to multiple shifting and narrow down the solution space, respectively. Finally, an evolutionary optimization algorithm, i.e., genetic algorithm is employed to search the nearly optimal zero and peak bins. For a given data payload, the proposed scheme could not only adaptively determine the proper number of peak and zero bin pairs but also their corresponding values for HS-based multiple reversible embedding. Compared with previous approaches, experimental results demonstrate the superiority of the proposed scheme in the terms of embedding capacity and stego-image quality.