Recursive Histogram Modification: Establishing Equivalency Between Reversible Data Hiding and Lossless Data Compression
Recursive Histogram Modification: Establishing Equivalency Between Reversible Data Hiding and Lossless Data Compression
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DOI：
10.1109/tip.2013.2257814
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发表时间：
2013-04
影响因子：
10.6
通讯作者：
Weiming Zhang;Xiaocheng Hu;Xiaolong Li;Nenghai Yu
中科院分区：
文献类型：
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作者：
Weiming Zhang;Xiaocheng Hu;Xiaolong Li;Nenghai Yu
可逆数据隐藏（RDH）的最先进的方案通常由两个步骤组成：首先通过预测错误构建具有锋利直方图的主机序列，然后通过使用方法来修改直方图（例如差异扩展和差异扩展）来嵌入消息直方图移动。在本文中，我们专注于第二阶段，并为RDH提出了一种直方图修改方法，该方法通过递归利用熵编码器的解压缩和压缩过程来嵌入消息。我们证明，对于独立分布的（i.i.d.）灰度主机信号，只要可以实现完美的压缩，即辅助压缩，即熵编码器即可接近熵，则提出的方法渐近地接近RDH的速率延伸。因此，此方法建立了可逆数据隐藏与无损数据压缩之间的等效性。实验表明，这种编码方法可用于改善先前的RDH方案的性能，并且对于较大图像而言，改进更为重要。
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.