Improve The Recursive Construction for Decompression and Message Extraction by using Joint Encoding and Decoding

In reversible data hiding (shortly RDH), the original cover can be lossless restored after the embedded information is extracted. A famous author Kalker and Willems established a rate–distortion model for RDH, in which they proved out the rate–distortion bound and proposed a recursive code construction. In previous concept, improved the recursive construction to approach the rate distortion bound. But In this approach, I will use a decompression algorithm as the coding scheme for embedding data. And prove that the generalized codes can reach the rate distortion bound as long as the compression algorithm reaches entropy. By proposed binary codes, I improve three RDH schemes that use binary feature sequence as covers, i.e., an RS scheme for spatial images, one scheme for JPEG images, and a pattern substitution for binary images. By modifying the histogram shift (HS) manner, I also apply this coding method to one scheme that uses HS, showing that the proposed codes can be also exploited to improve integer-operation-based schemes.