可逆信息隐藏是信息隐藏技术的重要分支，它不仅能从含密载体中提取秘密信息，还能无损地还原原始载体。以图像空域为载体的可逆信息隐藏研究根据图像是否被加密可分为明文域和密文域。早期，该领域研究基本在明文域开展，在保证可逆嵌入的前提下，着重提高嵌入容量与减少嵌入失真。随着人们日益重视隐私保护和数据安全，密文域的信号处理引起广泛关注。密文域可逆信息隐藏结合加密技术和可逆信息隐藏技术，从而达到载体内容保护和秘密信息传递的双重目的。本文梳理现有的相关文献，分别对明文域和密文域的研究进行归纳与分析，按照时间先后顺序帮助理清各类方法的发展脉络及其关联。首先，概括明文域的经典方法，包括差值扩展、直方图平移、预测误差扩展和多直方图修改4种方法及其改进版本。其次，阐述密文域中基于加密后腾出空间、加密前预留空间和通过加密腾出空间3类方法的研究进展。再次，总结指出明文域的研究趋向于减少嵌入失真，而密文域的研究趋向于提高嵌入容量，其在鲁棒性及安全性方面的进展则相对缓慢。最后，结合当前研究面临的实际问题，如载体多元化、有损信道传输和安全性等，进一步展望未来的研究趋势。总之，可逆信息隐藏研究的有效性与实用性仍有待提高，面向不同应用需求时，亟需学者提出新的理论支撑与评价体系。

Reversible data hiding (RDH) is one branch of data hiding technologies, which can extract the secret data from the marked carrier and recover the original carrier losslessly. In terms of the factor of reversible recovery, RDH has been implemented for media annotation and integrity authentication and integrated to other research aspects, such as reversible steganography, robust reversible watermarking, reversible adversarial samples, and reversible image transformation. In accordance with the content (encrypted or not) of image carrier, RDH can be divided into plaintext domain and encrypted domain each. At the beginning, the targeted research area was fundamentally conducted in plaintext domain. On the basis of ensuring reversible embedding, the improvement of embedding capacity and the decrease of embedding distortion have been mainly addressed. Signal processing in the encrypted domain has obtained extensive attention in privacy protection and data security. RDH in encrypted domain integrates encryption and reversible data hiding technology, aiming at realizing carrier content protection and covert communication simultaneously. The current research in plaintext domain and encrypted domain is summarized and analyzed to assist the readers with the knowhow in time sequence. First, the methods of plaintext domain have been summarized like four methods including difference expansion (DE), histogram shifting (HS), prediction error expansion (PEE), and multiple histogram modification (MHM) and their upgraded versions. PEE is developed on the basis of DE, which has higher embedding capacity, while tends to increase embedding distortion at low embedding capacity. Another classical method HS is proposed to reduce the embedding distortion at low embedding capacity. Subsequently, PEE achieves a qualified balance between embedding capacity and embedding distortion via the shifting operation of HS on the histogram. Various prediction error generation methods and two-dimensional histogram modification can improve the performance of PEE. MHM divides the prediction errors of the image into multiple histograms. The performance is improved further via PEE application in each sub-histogram. The current high-fidelity methods of plaintext domain have basically evolved three steps as following:First, neighboring pixels are applied to calculate the prediction error. Next, cluster regions have generated multiple two-dimensional prediction error histograms via similar complexity. At last, mapping rules have been used in reversible modification to the histograms. Hence, accurate pixel value prediction, qualified histogram generation and adaptive mapping rules can be as the research strategies. The other aspect on the research progress of three types of methods in encrypted domain has been demonstrated, which are based on vacating room after encryption (VRAE), reserving room before encryption (RRBE), and vacating room by encryption (VRBE). The VRAE-based methods require the data hider to vacate embeddable room after encryption. The content owner has utilized the standard encryption algorithm to encrypt the original image straightforward, such as stream encryption, block encryption and homomorphic encryption. For the application of spatial correlation of the original image, the RRBE-based methods allow the content owner to perform some pre-processing before encryption. The content owner utilizes the special encryption algorithm to encrypt the original image via the VRBE-based methods. The local spatial correlation can be preserved in the encrypted image. The initial research in encrypted domain is mainly in accordance with the modifications of the least significant bits. These methods could obtain high-quality decrypted image, while they might not be able to restore the original image losslessly, and their embedding capacity is limited. Since the encrypted image itself is a unique noise signal, the modifications of the most significant bits could greatly increase the embedding capacity with ensuring completed reversibility. The research in plaintext domain tends to reduce the embedding distortion, while the research in encrypted domain tends to increase the embedding capacity, and their development in robustness and security is relatively slow. The evaluation of the current methods is mainly based on the rate-distortion performance in reversibility. As the algorithm complexity increases and the solution space expands, the computational cost also increases inevitably. The efficiency evaluation is a comparison of running time as usual. From the perspective of the development of RDH, it is not recommended to always seek breakthroughs in certain indicators. Scientific evaluation of the performance and efficiency can promote the co-development of various methods. In order to meet different application requirements, future research on RDH should not constrain to the balance between reversibility, embedding capacity, and imperceptibility. Computational cost, robustness, and security issues should be evolved.