Recursive Histogram Modification: Establishing Equivalency Between Reversible Data Hiding and Lossless Data Compression

State-of-the-art schemes for reversible data hiding (RDH) usually consist of two steps: first construct a host sequence with a sharp histogram via prediction errors, and then embed messages by modifying the histogram with methods, such as difference expansion and histogram shift. In this paper, we focus on the second stage, and propose a histogram modification method for RDH, which embeds the message by recursively utilizing the decompression and compression processes of an entropy coder. We prove that, for independent identically distributed (i.i.d.) gray-scale host signals, the proposed method asymptotically approaches the rate-distortion bound of RDH as long as perfect compression can be realized, i.e., the entropy coder can approach entropy. Therefore, this method establishes the equivalency between reversible data hiding and lossless data compression. Experiments show that this coding method can be used to improve the performance of previous RDH schemes and the improvements are more significant for larger images.