###### Abstract  
Over the past few years, a considerable number of researchers have shown great interest in reversible data hiding for encrypted images (RDHEI). One popular category among various RDHEI methods is the reserving room before encryption (RRBE) approach, which leverages data redundancy in the original image before encryption to create space for data hiding and to achieve high embedding rates (ERs). This paper introduces an RRBE-based RDHEI method that employs pixel prediction, quadtree decomposition, and bit plane reordering to provide high embedding capacity and error-free reversibility. Initially, the content owner predicts the error image using a prediction method, followed by mapping it to a new error image with positive pixel values and a compressed binary label map is generated for overhead pixels. Subsequently, quadtree decomposition is applied to each bit plane of the mapped prediction error image to identify homogeneous blocks, which are then reordered to create room for data embedding. After generating the encrypted image with the encryption key, the data hider employs the data hiding key to embed the data based on the auxiliary information added to each embeddable bit plane's beginning. Finally, the receiver is able to retrieve the secret message without any error, decrypt the image, and restore it without any loss or distortion. The experimental results demonstrate that the proposed RDHEI method achieves significantly higher ERs than previous competitors, with an average ER exceeding 3.6 bpp on the BOSSbase and BOWS-2 datasets. pixel prediction; quadtree decomposition; bit planes reordering; image encryption; data hiding; data extraction; image recovery +
Footnote †: journal: Medical Image Computing  
The initial VRAE method was suggested by [PERSON] et al. [2]. It is a joint method where each 4 \(\times\) 4 block of pixels in the original image is encrypted using the Advanced Encryption Standard (AES). After encryption, one bit of the confidential data is embedded into each encrypted block using bit substitution. The outcome is known as the marked encrypted image, and the confidential data can be extracted by acquiring the bits in the substituted positions. During decryption, the local standard deviation analysis is executed to regain the original image. The payload of this approach is 0.0625 bpp, which is very small. [PERSON] [3] suggested encrypting the image by applying the bit-XOR operator between the original bits and the pseudo-random bits produced from a standard stream cipher. Following that, a data-hider can modify the encrypted image marginally to embed extra data without knowing the original image content. In the data embedding process, the encrypted image is firstly segmented into different non-overlapping blocks. Next, each block's pixels are pseudo-randomly divided into two sets based on a data-hiding key. Afterward, three least significant bits (LSBs) of each encrypted pixel from the first or the second sets are flipped according to the values of the embedded bits. The average ER is 0.033 bpp. [PERSON] [4] introduced the first separable approach, in which the encrypted image's LSBs are compressed using a data-hiding key to create a sparse space to accommodate the additional data. The embedded data can be retrieved at the receiver side using the data-hiding key. As the data embedding only affects the LSB, decrypting the encrypted image with the encryption key can yield an image similar to the original. The use of both encryption and data-hiding keys enable the receiver to have a successful extraction of the embedded data and a perfect recovery of the original image by exploiting the spatial correlation present in the natural images. While [PERSON] [2] was the pioneer in proposing a VRAE-based RDHEI method, [PERSON] et al. [5] introduced an innovative and practical approach based on the RRBE framework. They proposed the following three steps: image partition, self-reversible embedding, and image encryption.